1

Here are two statements from my Mathematica program.

Print[ExpandAll[Chop[Integrate[Resi*Cos[7*1*\[Theta]]*Sin[(1*Pi*x)/L], {\[Theta],    
     0,2*Pi},{x,0, L}], 10^-6]]];

This line gives me the output

1043.84 A[1,7][t]-115072. A[1,0][t] A[1,7][t]+112.933 A[1,0][t]^2 A[1,7][t]+12415.3 A[1,7][t]^3-1327.67 A[1,7][t] A[1,14][t]+387.315 A[1,0][t] A[1,7][t] A[1,14][t]+50249.8 A[1,7][t] A[1,14][t]^2+12415.3 A[1,7][t] B[1,7][t]^2-1327.67 B[1,7][t] B[1,14][t]+387.315 A[1,0][t] B[1,7][t] B[1,14][t]+50249.8 A[1,7][t] B[1,14][t]^2+0.000108481 (A[1,7]^\[Prime]\[Prime])[t]

whereas when I reverse the order of integration

Print[ExpandAll[Chop[Integrate[Resi*Cos[7*1*\[Theta]]*Sin[(1*Pi*x)/L], {x, 0, L}, {\[Theta], 0, 2*Pi}], 10^-6]]];

I get the following output

 2087.69 A[1,7][t]-230144. A[1,0][t] A[1,7][t]+225.866 A[1,0][t]^2 A[1,7][t]+24830.6 A[1,7][t]^3-2655.34 A[1,7][t] A[1,14][t]+774.631 A[1,0][t] A[1,7][t] A[1,14][t]+100500. A[1,7][t] A[1,14][t]^2+24830.6 A[1,7][t] B[1,7][t]^2-2655.34 B[1,7][t] B[1,14][t]+774.631 A[1,0][t] B[1,7][t] B[1,14][t]+100500. A[1,7][t] B[1,14][t]^2+0.000216962 (A[1,7]^\[Prime]\[Prime])[t]

The order of integration should not matter. Then why are the outputs different? Note that the wrong output that is the first one is just the half of the second(correct) output. I ask this because the order that is giving me the correct answer is taking a lot of time. I have many such integrals in my program.

The expression for Resi is a huge term but let me give you a small part of it 

  1754.2 Sin[(\[Pi] x)/200] A[1, 0][t] + 
  6.64531 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] + 
  3.01996 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] A[1, 0][t] A[1, 7][t] - 
  861.531 Cos[7 \[Theta]] Sin[(\[Pi] x)/200]^2 A[1, 0][t] A[1, 7][t] + 
  0.533983 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t]^2 A[1, 7][
  t] - 0.369945 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
  200] A[1, 0][t]^2 A[1, 7][t] - 107.444 A[1, 7][t]^2 + 
  107.444 Cos[(\[Pi] x)/100] A[1, 7][t]^2 - 
  3.95111 Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/200]^2 A[1, 7][t]^2 + 
  3.95111 Cos[(\[Pi] x)/200]^2 Sin[7 \[Theta]]^2 A[1, 7][t]^2 + 
  0.533983 Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 7][
  t]^2 - 1.84972 Cos[(\[Pi] x)/100] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
  200] A[1, 0][t] A[1, 7][t]^2 + 
  0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 7][
  t]^2 - 1.47978 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[
  7 \[Theta]]^2 A[1, 0][t] A[1, 7][t]^2 + 
  52.6477 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t]^3 - 
  52.6477 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
  200] A[1, 7][t]^3 + 
  0.133496 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
    t]^3 + 39.1352 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t] + 
  0.987777 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] A[1, 0][t] A[1, 14][
   t] - 3438.75 Cos[14 \[Theta]] Sin[(\[Pi] x)/200]^2 A[1, 0][
   t] A[1, 14][t] + 
   0.533983 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t]^2 A[1, 14][
    t] - 0.484011 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/
   200] A[1, 0][t]^2 A[1, 14][t] + 
    13.5898 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] A[1, 7][t] A[1, 14][t] + 
    0.0257425 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] A[1, 7][t] A[1, 14][
   t] - 10.542 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/
      200]^2 A[1, 7][t] A[1, 14][t] + 
   8.43363 Cos[(\[Pi] x)/200]^2 Sin[7 \[Theta]] Sin[
   14 \[Theta]] A[1, 7][t] A[1, 14][t] + 
   0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 7][
   t] A[1, 14][t] - 
   1.66475 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
    200] A[1, 0][t] A[1, 7][t] A[1, 14][t] + 
     1.06797 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][
   t] A[1, 7][t] A[1, 14][t] - 
   7.25708 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Cos[
   14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 7][t] A[1, 14][
   t] + 0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][
   t] A[1, 7][t] A[1, 14][t] - 
   0.0283811 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/
   200] A[1, 0][t] A[1, 7][t] A[1, 14][t] - 
   3.92758 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[7 \[Theta]] Sin[
   14 \[Theta]] A[1, 0][t] A[1, 7][t] A[1, 14][t] + 
   0.266991 Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 7][t]^2 A[1, 14][
   t] - 8.32376 Cos[(\[Pi] x)/100] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
     200] A[1, 7][t]^2 A[1, 14][t] + 
     210.591 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t]^2 A[1, 14][
    t] - 210.591 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/
   200] A[1, 7][t]^2 A[1, 14][t] + 
  0.133496 Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 7][t]^2 A[1, 14][
  t] + 0.266991 Cos[7 \[Theta]] Cos[21 \[Theta]] Sin[(\[Pi] x)/
  200] A[1, 7][t]^2 A[1, 14][t] - 
    0.040995 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Cos[
     21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t]^2 A[1, 14][t] - 
       6.65901 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[
   7 \[Theta]]^2 A[1, 7][t]^2 A[1, 14][t] - 
   0.0378415 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[7 \[Theta]] Sin[
   21 \[Theta]] A[1, 7][t]^2 A[1, 14][t] - 429.778 A[1, 14][t]^2 + 
   429.778 Cos[(\[Pi] x)/100] A[1, 14][t]^2 - 
   1.06283 Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/200]^2 A[1, 14][t]^2 + 
   1.06283 Cos[(\[Pi] x)/200]^2 Sin[14 \[Theta]]^2 A[1, 14][t]^2 + 
 0.533983 Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 14][
 t]^2 - 2.42005 Cos[(\[Pi] x)/100] Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/
  200] A[1, 0][t] A[1, 14][t]^2 + 
  0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] A[1, 14][
  t]^2 - 
  1.93604 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[
  14 \[Theta]]^2 A[1, 0][t] A[1, 14][t]^2 + 
  210.591 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] A[1, 14][
  t]^2 - 210.591 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
      200] A[1, 7][t] A[1, 14][t]^2 + 
    0.266991 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
     t] A[1, 14][t]^2 - 
 28.3008 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Cos[
 14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] A[1, 14][t]^2 + 
 0.266991 Cos[14 \[Theta]] Cos[21 \[Theta]] Sin[(\[Pi] x)/
 200] A[1, 7][t] A[1, 14][t]^2 - 
 0.0788365 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Cos[
 21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] A[1, 14][t]^2 + 
 0.133496 Cos[7 \[Theta]] Cos[28 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
 t] A[1, 14][t]^2 - 
 13.318 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[7 \[Theta]] Sin[
 14 \[Theta]] A[1, 7][t] A[1, 14][t]^2 - 
 0.075683 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[14 \[Theta]] Sin[
 21 \[Theta]] A[1, 7][t] A[1, 14][t]^2 + 
 842.364 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t]^3 - 
 842.364 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/
  200] A[1, 14][t]^3 + 
  0.133496 Cos[14 \[Theta]] Cos[28 \[Theta]] Sin[(\[Pi] x)/
 200] A[1, 14][t]^3 + 
 6.64531 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][t] + 
     3.01996 Cos[(\[Pi] x)/100] Sin[7 \[Theta]] A[1, 0][t] B[1, 7][t] - 
  861.531 Sin[(\[Pi] x)/200]^2 Sin[7 \[Theta]] A[1, 0][t] B[1, 7][t] + 
 0.533983 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 0][t]^2 B[1, 7][
   t] - 0.369945 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 0][t]^2 B[1, 7][t] - 
 7.90221 Cos[(\[Pi] x)/200]^2 Cos[7 \[Theta]] Sin[7 \[Theta]] A[1, 7][
 t] B[1, 7][t] - 
 7.90221 Cos[7 \[Theta]] Sin[(\[Pi] x)/200]^2 Sin[7 \[Theta]] A[1, 7][
 t] B[1, 7][t] + 
 1.06797 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 0][
 t] A[1, 7][t] B[1, 7][t] - 
 3.69945 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 7][t] + 
 2.95956 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
 7 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 7][t] + 
 0.266991 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 0][t] A[1, 7][
 t] B[1, 7][t] + 
 52.6477 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][t]^2 B[1, 7][t] - 
 52.6477 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 7][t]^2 B[1, 7][t] + 
 0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][
 t]^2 B[1, 7][t] + 
 0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 7][
 t]^2 B[1, 7][t] - 
 13.5898 Cos[(\[Pi] x)/100] Sin[7 \[Theta]] A[1, 14][t] B[1, 7][t] - 
 10.542 Cos[14 \[Theta]] Sin[(\[Pi] x)/200]^2 Sin[
 7 \[Theta]] A[1, 14][t] B[1, 7][t] - 
 8.43363 Cos[(\[Pi] x)/200]^2 Cos[7 \[Theta]] Sin[
 14 \[Theta]] A[1, 14][t] B[1, 7][t] + 
 0.0257425 Cos[(\[Pi] x)/100] Sin[21 \[Theta]] A[1, 14][t] B[1, 7][
 t] - 0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 0][
 t] A[1, 14][t] B[1, 7][t] + 
 1.66475 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 7][t] + 
 1.06797 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 0][
   t] A[1, 14][t] B[1, 7][t] - 
 7.25708 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 7][t] + 
 3.92758 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
 14 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 7][t] + 
 0.266991 Sin[(\[Pi] x)/200] Sin[21 \[Theta]] A[1, 0][t] A[1, 14][
  t] B[1, 7][t] - 
  0.0283811 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
  21 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 7][t] + 
  0. Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][
 t] A[1, 14][t] B[1, 7][t] + 
 0. Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][
 t] A[1, 14][t] B[1, 7][t] - 
 0.040995 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0. Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
 7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0.0378415 Cos[(\[Pi] x)/200] Cos[21 \[Theta]] Sin[(\[Pi] x)/100] Sin[
  7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
  14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[21 \[Theta]] A[1, 7][
  t] A[1, 14][t] B[1, 7][t] - 
 0.040995 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
  21 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 0.0378415 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
  21 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 7][t] + 
 210.591 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 14][t]^2 B[1, 7][
 t] - 210.591 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
 7 \[Theta]] A[1, 14][t]^2 B[1, 7][t] - 
  0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
  7 \[Theta]] A[1, 14][t]^2 B[1, 7][t] + 
  28.3008 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
    7 \[Theta]] A[1, 14][t]^2 B[1, 7][t] + 
  0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] Sin[
   7 \[Theta]] A[1, 14][t]^2 B[1, 7][t] - 
   13.318 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
  14 \[Theta]] A[1, 14][t]^2 B[1, 7][t] + 
  0.075683 Cos[(\[Pi] x)/200] Cos[21 \[Theta]] Sin[(\[Pi] x)/100] Sin[
   14 \[Theta]] A[1, 14][t]^2 B[1, 7][t] + 
   0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
   21 \[Theta]] A[1, 14][t]^2 B[1, 7][t] - 
   0.0788365 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
   21 \[Theta]] A[1, 14][t]^2 B[1, 7][t] - 107.444 B[1, 7][t]^2 + 
   107.444 Cos[(\[Pi] x)/100] B[1, 7][t]^2 + 
   3.95111 Cos[(\[Pi] x)/200]^2 Cos[7 \[Theta]]^2 B[1, 7][t]^2 - 
  3.95111 Sin[(\[Pi] x)/200]^2 Sin[7 \[Theta]]^2 B[1, 7][t]^2 - 
   0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] B[1, 7][
   t]^2 - 1.47978 Cos[(\[Pi] x)/200] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
   100] A[1, 0][t] B[1, 7][t]^2 + 
   0.533983 Sin[(\[Pi] x)/200] Sin[7 \[Theta]]^2 A[1, 0][t] B[1, 7][
    t]^2 - 1.84972 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]]^2 A[1, 0][t] B[1, 7][t]^2 + 
     52.6477 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] B[1, 7][t]^2 - 
   52.6477 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
    200] A[1, 7][t] B[1, 7][t]^2 - 
    0.133496 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
      t] B[1, 7][t]^2 + 
    0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[14 \[Theta]] A[1, 7][
     t] B[1, 7][t]^2 + 
   210.591 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t] B[1, 7][
   t]^2 - 210.591 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/
     200] A[1, 14][t] B[1, 7][t]^2 - 
    0.133496 Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 14][t] B[1, 7][
     t]^2 + 6.65901 Cos[(\[Pi] x)/200] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
      100] A[1, 14][t] B[1, 7][t]^2 - 
      0.0378415 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Cos[
      21 \[Theta]] Sin[(\[Pi] x)/100] A[1, 14][t] B[1, 7][t]^2 - 
    0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]]^2 A[1, 14][t] B[1, 7][
    t]^2 + 8.32376 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]]^2 A[1, 14][t] B[1, 7][t]^2 + 
   0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
     21 \[Theta]] A[1, 14][t] B[1, 7][t]^2 - 
      0.040995 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
    21 \[Theta]] A[1, 14][t] B[1, 7][t]^2 + 
    52.6477 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][t]^3 - 
    52.6477 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
    7 \[Theta]] B[1, 7][t]^3 - 
    0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][
    t]^3 + 39.1352 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] B[1, 14][t] + 
    0.987777 Cos[(\[Pi] x)/100] Sin[14 \[Theta]] A[1, 0][t] B[1, 14][
      t] - 3438.75 Sin[(\[Pi] x)/200]^2 Sin[14 \[Theta]] A[1, 0][
     t] B[1, 14][t] + 
    0.533983 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 0][t]^2 B[1, 14][
    t] - 0.484011 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] A[1, 0][t]^2 B[1, 14][t] + 
    13.5898 Cos[(\[Pi] x)/100] Sin[7 \[Theta]] A[1, 7][t] B[1, 14][t] - 
    8.43363 Cos[(\[Pi] x)/200]^2 Cos[14 \[Theta]] Sin[
     7 \[Theta]] A[1, 7][t] B[1, 14][t] - 
    10.542 Cos[7 \[Theta]] Sin[(\[Pi] x)/200]^2 Sin[14 \[Theta]] A[1, 7][
     t] B[1, 14][t] + 
   0.0257425 Cos[(\[Pi] x)/100] Sin[21 \[Theta]] A[1, 7][t] B[1, 14][
    t] + 0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 0][
     t] A[1, 7][t] B[1, 14][t] - 
     1.66475 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
      7 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 14][t] + 
    3.92758 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
      7 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 14][t] + 
    1.06797 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 0][
        t] A[1, 7][t] B[1, 14][t] - 
     7.25708 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
       14 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 14][t] + 
     0.266991 Sin[(\[Pi] x)/200] Sin[21 \[Theta]] A[1, 0][t] A[1, 7][
     t] B[1, 14][t] - 
     0.0283811 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
    21 \[Theta]] A[1, 0][t] A[1, 7][t] B[1, 14][t] + 
     0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][
     t]^2 B[1, 14][t] - 
   8.32376 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]] A[1, 7][t]^2 B[1, 14][t] + 
     6.65901 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
      7 \[Theta]] A[1, 7][t]^2 B[1, 14][t] + 
   0.0378415 Cos[(\[Pi] x)/200] Cos[21 \[Theta]] Sin[(\[Pi] x)/100] Sin[
    7 \[Theta]] A[1, 7][t]^2 B[1, 14][t] + 
      210.591 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 7][t]^2 B[1, 14][
      t] - 210.591 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] A[1, 7][t]^2 B[1, 14][t] + 
    0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      14 \[Theta]] A[1, 7][t]^2 B[1, 14][t] + 
      0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[21 \[Theta]] A[1, 7][
     t]^2 B[1, 14][t] - 
     0.040995 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      21 \[Theta]] A[1, 7][t]^2 B[1, 14][t] - 
     2.12567 Cos[(\[Pi] x)/200]^2 Cos[14 \[Theta]] Sin[
      14 \[Theta]] A[1, 14][t] B[1, 14][t] - 
     2.12567 Cos[14 \[Theta]] Sin[(\[Pi] x)/200]^2 Sin[
     14 \[Theta]] A[1, 14][t] B[1, 14][t] + 
     1.06797 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 0][
      t] A[1, 14][t] B[1, 14][t] - 
      4.84011 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 14][t] + 
      3.87208 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
      14 \[Theta]] A[1, 0][t] A[1, 14][t] B[1, 14][t] + 
      0.266991 Sin[(\[Pi] x)/200] Sin[28 \[Theta]] A[1, 0][t] A[1, 14][
      t] B[1, 14][t] + 
      0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] A[1, 7][
     t] A[1, 14][t] B[1, 14][t] - 
     28.3008 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
     13.318 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
      7 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
     0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 7][
     t] A[1, 14][t] B[1, 14][t] - 
    28.3008 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
    0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] - 
    0.0788365 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
    14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
    13.318 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
    14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
    0.075683 Cos[(\[Pi] x)/200] Cos[21 \[Theta]] Sin[(\[Pi] x)/100] Sin[
    14 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
    0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     21 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] - 
     0.0788365 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     21 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
     0.075683 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
       21 \[Theta]] A[1, 7][t] A[1, 14][t] B[1, 14][t] + 
     0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[28 \[Theta]] A[1, 7][
      t] A[1, 14][t] B[1, 14][t] + 
     842.364 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] A[1, 14][t]^2 B[1, 14][
     t] - 842.364 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
      14 \[Theta]] A[1, 14][t]^2 B[1, 14][t] + 
      0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      14 \[Theta]] A[1, 14][t]^2 B[1, 14][t] + 
      0.266991 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      28 \[Theta]] A[1, 14][t]^2 B[1, 14][t] + 
      13.5898 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] B[1, 7][t] B[1, 14][t] + 
      8.43363 Cos[(\[Pi] x)/200]^2 Cos[7 \[Theta]] Cos[
      14 \[Theta]] B[1, 7][t] B[1, 14][t] - 
      0.0257425 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] B[1, 7][t] B[1, 14][
      t] - 10.542 Sin[(\[Pi] x)/200]^2 Sin[7 \[Theta]] Sin[
       14 \[Theta]] B[1, 7][t] B[1, 14][t] + 
      0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] B[1, 7][
      t] B[1, 14][t] - 
       1.66475 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
      200] A[1, 0][t] B[1, 7][t] B[1, 14][t] - 
      0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] B[1, 7][
       t] B[1, 14][t] + 
       0.0283811 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/
       200] A[1, 0][t] B[1, 7][t] B[1, 14][t] - 
      3.92758 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Cos[
      14 \[Theta]] Sin[(\[Pi] x)/100] A[1, 0][t] B[1, 7][t] B[1, 14][
     t] + 1.06797 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
       14 \[Theta]] A[1, 0][t] B[1, 7][t] B[1, 14][t] - 
     7.25708 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
      14 \[Theta]] A[1, 0][t] B[1, 7][t] B[1, 14][t] + 
      0.266991 Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/200] A[1, 7][t] B[1, 7][
        t] B[1, 14][t] - 
        8.32376 Cos[(\[Pi] x)/100] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
        200] A[1, 7][t] B[1, 7][t] B[1, 14][t] - 
         0.266991 Cos[7 \[Theta]] Cos[21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
         t] B[1, 7][t] B[1, 14][t] + 
        0.040995 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Cos[
           21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] B[1, 7][t] B[1, 14][
           t] - 6.65901 Cos[(\[Pi] x)/200] Cos[7 \[Theta]]^2 Sin[(\[Pi] x)/
          100] A[1, 7][t] B[1, 7][t] B[1, 14][t] - 
        0.0378415 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Cos[
       21 \[Theta]] Sin[(\[Pi] x)/100] A[1, 7][t] B[1, 7][t] B[1, 14][
          t] + 0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]]^2 A[1, 7][
        t] B[1, 7][t] B[1, 14][t] - 
       8.32376 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]]^2 A[1, 7][t] B[1, 7][t] B[1, 14][t] - 
     6.65901 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[
      7 \[Theta]]^2 A[1, 7][t] B[1, 7][t] B[1, 14][t] + 
     0.266991 Sin[(\[Pi] x)/200] Sin[14 \[Theta]]^2 A[1, 7][t] B[1, 7][
     t] B[1, 14][t] + 
   0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[21 \[Theta]] A[1, 7][
    t] B[1, 7][t] B[1, 14][t] - 
   0.040995 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
         21 \[Theta]] A[1, 7][t] B[1, 7][t] B[1, 14][t] + 
      0.0378415 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[7 \[Theta]] Sin[
     21 \[Theta]] A[1, 7][t] B[1, 7][t] B[1, 14][t] + 
    0.266991 Cos[7 \[Theta]] Cos[14 \[Theta]] Sin[(\[Pi] x)/
     200] A[1, 14][t] B[1, 7][t] B[1, 14][t] - 
      28.3008 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Cos[
      14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t] B[1, 7][t] B[1, 14][
    t] - 0.266991 Cos[14 \[Theta]] Cos[21 \[Theta]] Sin[(\[Pi] x)/
        200] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
      0.0788365 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Cos[
     21 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t] B[1, 7][t] B[1, 14][
     t] + 13.318 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Cos[
     14 \[Theta]] Sin[(\[Pi] x)/100] A[1, 14][t] B[1, 7][t] B[1, 14][
      t] - 0.075683 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Cos[
       21 \[Theta]] Sin[(\[Pi] x)/100] A[1, 14][t] B[1, 7][t] B[1, 14][
       t] - 0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
     14 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
    28.3008 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
              14 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] - 
    13.318 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[7 \[Theta]] Sin[
    14 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
  0.266991 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] Sin[
   21 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] - 
   0.0788365 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] Sin[
     21 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
  0.075683 Cos[(\[Pi] x)/200] Sin[(\[Pi] x)/100] Sin[14 \[Theta]] Sin[
    21 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
   0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
    28 \[Theta]] A[1, 14][t] B[1, 7][t] B[1, 14][t] + 
    0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][
    t]^2 B[1, 14][t] - 
   8.32376 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
   7 \[Theta]] B[1, 7][t]^2 B[1, 14][t] - 
   0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][
     t]^2 B[1, 14][t] + 
    0.040995 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      7 \[Theta]] B[1, 7][t]^2 B[1, 14][t] + 
    6.65901 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
     7 \[Theta]] B[1, 7][t]^2 B[1, 14][t] + 
   210.591 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] B[1, 7][t]^2 B[1, 14][
    t] - 210.591 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
    14 \[Theta]] B[1, 7][t]^2 B[1, 14][t] - 
   0.133496 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] B[1, 7][t]^2 B[1, 14][t] - 
     0.0378415 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Sin[(\[Pi] x)/100] Sin[
    21 \[Theta]] B[1, 7][t]^2 B[1, 14][t] - 429.778 B[1, 14][t]^2 + 
   429.778 Cos[(\[Pi] x)/100] B[1, 14][t]^2 + 
   1.06283 Cos[(\[Pi] x)/200]^2 Cos[14 \[Theta]]^2 B[1, 14][t]^2 - 
   1.06283 Sin[(\[Pi] x)/200]^2 Sin[14 \[Theta]]^2 B[1, 14][t]^2 - 
  0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] A[1, 0][t] B[1, 14][
t]^2 - 1.93604 Cos[(\[Pi] x)/200] Cos[14 \[Theta]]^2 Sin[(\[Pi] x)/
 100] A[1, 0][t] B[1, 14][t]^2 + 
 0.533983 Sin[(\[Pi] x)/200] Sin[14 \[Theta]]^2 A[1, 0][t] B[1, 14][
 t]^2 - 
  2.42005 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]]^2 A[1, 0][t] B[1, 14][t]^2 + 
   210.591 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][t] B[1, 14][
      t]^2 - 210.591 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/
      200] A[1, 7][t] B[1, 14][t]^2 - 
     0.133496 Cos[7 \[Theta]] Cos[28 \[Theta]] Sin[(\[Pi] x)/200] A[1, 7][
      t] B[1, 14][t]^2 - 
    13.318 Cos[(\[Pi] x)/200] Cos[7 \[Theta]] Cos[
      14 \[Theta]] Sin[(\[Pi] x)/100] A[1, 7][t] B[1, 14][t]^2 - 
    0.075683 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Cos[
     21 \[Theta]] Sin[(\[Pi] x)/100] A[1, 7][t] B[1, 14][t]^2 + 
   0.266991 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[14 \[Theta]] A[1, 7][
  t] B[1, 14][t]^2 - 
     28.3008 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] Sin[
        14 \[Theta]] A[1, 7][t] B[1, 14][t]^2 + 
     0.266991 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] Sin[
     21 \[Theta]] A[1, 7][t] B[1, 14][t]^2 - 
     0.0788365 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] Sin[
      21 \[Theta]] A[1, 7][t] B[1, 14][t]^2 + 
     842.364 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] A[1, 14][t] B[1, 14][
     t]^2 - 842.364 Cos[(\[Pi] x)/100] Cos[14 \[Theta]] Sin[(\[Pi] x)/
      200] A[1, 14][t] B[1, 14][t]^2 - 
    0.133496 Cos[14 \[Theta]] Cos[28 \[Theta]] Sin[(\[Pi] x)/
     200] A[1, 14][t] B[1, 14][t]^2 + 
     0.266991 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] Sin[
      28 \[Theta]] A[1, 14][t] B[1, 14][t]^2 + 
    210.591 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][t] B[1, 14][
    t]^2 - 210.591 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
     7 \[Theta]] B[1, 7][t] B[1, 14][t]^2 - 
     0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] Sin[7 \[Theta]] B[1, 7][
    t] B[1, 14][t]^2 + 
    13.318 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
      7 \[Theta]] B[1, 7][t] B[1, 14][t]^2 + 
    0.266991 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[14 \[Theta]] B[1, 7][
      t] B[1, 14][t]^2 - 
     28.3008 Cos[(\[Pi] x)/100] Cos[7 \[Theta]] Sin[(\[Pi] x)/200] Sin[
    14 \[Theta]] B[1, 7][t] B[1, 14][t]^2 - 
    0.266991 Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
    14 \[Theta]] B[1, 7][t] B[1, 14][t]^2 + 
    0.0788365 Cos[(\[Pi] x)/100] Cos[21 \[Theta]] Sin[(\[Pi] x)/200] Sin[
      14 \[Theta]] B[1, 7][t] B[1, 14][t]^2 - 
    0.075683 Cos[(\[Pi] x)/200] Cos[14 \[Theta]] Sin[(\[Pi] x)/100] Sin[
    21 \[Theta]] B[1, 7][t] B[1, 14][t]^2 + 
   842.364 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] B[1, 14][t]^3 - 
      842.364 Cos[(\[Pi] x)/100] Sin[(\[Pi] x)/200] Sin[
   14 \[Theta]] B[1, 14][t]^3 - 
   0.133496 Cos[28 \[Theta]] Sin[(\[Pi] x)/200] Sin[
     14 \[Theta]] B[1, 14][t]^3 + 6.90612*10^-7 Sin[(\[Pi] x)/200] 
 \!\(\*SuperscriptBox[
  RowBox[{"A", "[", 
  RowBox[{"1", ",", "0"}], "]"}], "\[Prime]\[Prime]",
    MultilineFunction->None]\)[t] + 
      6.90612*10^-7 Cos[7 \[Theta]] Sin[(\[Pi] x)/200] 
    \!\(\*SuperscriptBox[
      RowBox[{"A", "[", 
           RowBox[{"1", ",", "7"}], "]"}], "\[Prime]\[Prime]",
       MultilineFunction->None]\)[t] + 
        6.90612*10^-7 Cos[14 \[Theta]] Sin[(\[Pi] x)/200] 
      \!\(\*SuperscriptBox[
       RowBox[{"A", "[", 
      RowBox[{"1", ",", "14"}], "]"}], "\[Prime]\[Prime]",
    MultilineFunction->None]\)[t] + 
       6.90612*10^-7 Sin[(\[Pi] x)/200] Sin[7 \[Theta]] 
       \!\(\*SuperscriptBox[
        RowBox[{"B", "[", 
      RowBox[{"1", ",", "7"}], "]"}], "\[Prime]\[Prime]",
    MultilineFunction->None]\)[t] + 
        6.90612*10^-7 Sin[(\[Pi] x)/200] Sin[14 \[Theta]] 
    \!\(\*SuperscriptBox[
      RowBox[{"B", "[", 
    RowBox[{"1", ",", "14"}], "]"}], "\[Prime]\[Prime]",
      MultilineFunction->None]\)[t]
8
  • No they won't be....A is an unknown function and the value of L has already been substituted, that is why there is no "L" appearing in the output...!!
    – user1099153
    Commented Dec 19, 2011 at 7:17
  • Well, you haven't provided the magic value for L
    – abcd
    Commented Dec 19, 2011 at 7:25
  • 1
    Please post the full expression for Resi. To shorten it you could simplify it by Collect[Resi, A[, _][], Chop[Simplify[#]] &] . Also: the interchange of integrations does not necessarily have to be the same: After all you have endpoint singularities, so you have to be careful. I would try to do the integration not from 0 but from L0 and then take the explicit limit before doing the second integration. Integrate has never been good with slightly more involved multiple integrations, or better put: it is difficult to catch all mathematical gotchas automatically. So human brain is still needed.
    – Rolf Mertig
    Commented Dec 19, 2011 at 7:32
  • 1
    Harmeet: At the moment, the code you pasted is not copy/paste-able into Mathematica and I doubt anyone is going to spend too much time playing with it. I suggest you try to narrow down what is causing the problem. E.g., try to keep removing terms from Resi until the problem goes away. Then you'll either discover the cause of the problem yourself or reduce it down to a minimal size that allows other people to look at it.
    – Simon
    Commented Dec 19, 2011 at 9:33
  • 1
    In order to diagnose the problem, and just verify if this is a bug or not, we do need the full Resi expression. What you posted does not paste correctly. Please paste it like this: 1. Evaluate Resi to get it as an output cell. 2. Select the output cell. 3. Right click its cell bracket and select Copy As -> Input string. Then paste the result here, try to copy it back into Mathematica, and verify that it is identical to your original Resi with the === operator.
    – Szabolcs
    Commented Dec 19, 2011 at 9:45

1 Answer 1

Reset to default
7

Mathematica 8 works just fine here. Suppose I interprete Resi as follows (no idea if it is correct, but maybe):

  Resi = 1754.2*Sin[(Pi*x)/200]*A[1, 0][t] + 6.64531*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t] + 3.01996*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*
     A[1, 0][t]*A[1, 7][t] - 861.531*Cos[7*\[Theta]]*Sin[(Pi*x)/200]^2*
     A[1, 0][t]*A[1, 7][t] + 0.533983*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 0][t]^2*A[1, 7][t] - 0.369945*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]^2*A[1, 7][t] - 107.444*A[1, 7][t]^2 + 
    107.444*Cos[(Pi*x)/100]*A[1, 7][t]^2 - 3.95111*Cos[7*\[Theta]]^2*
     Sin[(Pi*x)/200]^2*A[1, 7][t]^2 + 3.95111*Cos[(Pi*x)/200]^2*
     Sin[7*\[Theta]]^2*A[1, 7][t]^2 + 0.533983*Cos[7*\[Theta]]^2*Sin[(Pi*x)/200]*
     A[1, 0][t]*A[1, 7][t]^2 - 1.84972*Cos[(Pi*x)/100]*Cos[7*\[Theta]]^2*
     Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 7][t]^2 + 0.133496*Cos[14*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 7][t]^2 - 1.47978*Cos[(Pi*x)/200]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]^2*A[1, 0][t]*A[1, 7][t]^2 + 
    52.6477*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]^3 - 
    52.6477*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]^3 + 
    0.133496*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]^3 + 
    39.1352*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t] + 
    0.987777*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*A[1, 0][t]*A[1, 14][t] - 
    3438.75*Cos[14*\[Theta]]*Sin[(Pi*x)/200]^2*A[1, 0][t]*A[1, 14][t] + 
    0.533983*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]^2*A[1, 14][t] - 
    0.484011*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]^2*
     A[1, 14][t] + 13.5898*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*A[1, 7][t]*
     A[1, 14][t] + 0.0257425*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*A[1, 7][t]*
     A[1, 14][t] - 10.542*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]^2*
     A[1, 7][t]*A[1, 14][t] + 8.43363*Cos[(Pi*x)/200]^2*Sin[7*\[Theta]]*
     Sin[14*\[Theta]]*A[1, 7][t]*A[1, 14][t] + 0.266991*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 7][t]*A[1, 14][t] - 
    1.66475*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*
     A[1, 7][t]*A[1, 14][t] + 1.06797*Cos[7*\[Theta]]*Cos[14*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 7][t]*A[1, 14][t] - 
    7.25708*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 0][t]*A[1, 7][t]*A[1, 14][t] + 0.266991*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 7][t]*A[1, 14][t] - 
    0.0283811*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*
     A[1, 7][t]*A[1, 14][t] - 3.92758*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*
     Sin[7*\[Theta]]*Sin[14*\[Theta]]*A[1, 0][t]*A[1, 7][t]*A[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 7][t]^2*A[1, 14][t] - 
    8.32376*Cos[(Pi*x)/100]*Cos[7*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 7][t]^2*
     A[1, 14][t] + 210.591*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]^2*
     A[1, 14][t] - 210.591*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 7][t]^2*A[1, 14][t] + 0.133496*Cos[14*\[Theta]]^2*Sin[(Pi*x)/200]*
     A[1, 7][t]^2*A[1, 14][t] + 0.266991*Cos[7*\[Theta]]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]^2*A[1, 14][t] - 
    0.040995*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 7][t]^2*A[1, 14][t] - 6.65901*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*
     Sin[7*\[Theta]]^2*A[1, 7][t]^2*A[1, 14][t] - 0.0378415*Cos[(Pi*x)/200]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]*Sin[21*\[Theta]]*A[1, 7][t]^2*A[1, 14][t] - 
    429.778*A[1, 14][t]^2 + 429.778*Cos[(Pi*x)/100]*A[1, 14][t]^2 - 
    1.06283*Cos[14*\[Theta]]^2*Sin[(Pi*x)/200]^2*A[1, 14][t]^2 + 
    1.06283*Cos[(Pi*x)/200]^2*Sin[14*\[Theta]]^2*A[1, 14][t]^2 + 
    0.533983*Cos[14*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 0][t]*A[1, 14][t]^2 - 
    2.42005*Cos[(Pi*x)/100]*Cos[14*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 0][t]*
     A[1, 14][t]^2 + 0.133496*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*
     A[1, 14][t]^2 - 1.93604*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*
     Sin[14*\[Theta]]^2*A[1, 0][t]*A[1, 14][t]^2 + 210.591*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]*A[1, 14][t]^2 - 
    210.591*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*
     A[1, 14][t]^2 + 0.266991*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 7][t]*A[1, 14][t]^2 - 28.3008*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*A[1, 14][t]^2 + 
    0.266991*Cos[14*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*
     A[1, 14][t]^2 - 0.0788365*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]*A[1, 14][t]^2 + 
    0.133496*Cos[7*\[Theta]]*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*
     A[1, 14][t]^2 - 13.318*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*
     Sin[14*\[Theta]]*A[1, 7][t]*A[1, 14][t]^2 - 0.075683*Cos[(Pi*x)/200]*
     Sin[(Pi*x)/100]*Sin[14*\[Theta]]*Sin[21*\[Theta]]*A[1, 7][t]*A[1, 14][t]^2 + 
    842.364*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]^3 - 
    842.364*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]^3 + 
    0.133496*Cos[14*\[Theta]]*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]^3 + 
    6.64531*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t] + 
    3.01996*Cos[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 0][t]*B[1, 7][t] - 
    861.531*Sin[(Pi*x)/200]^2*Sin[7*\[Theta]]*A[1, 0][t]*B[1, 7][t] + 
    0.533983*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 0][t]^2*B[1, 7][t] - 
    0.369945*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 0][t]^2*
     B[1, 7][t] - 7.90221*Cos[(Pi*x)/200]^2*Cos[7*\[Theta]]*Sin[7*\[Theta]]*
     A[1, 7][t]*B[1, 7][t] - 7.90221*Cos[7*\[Theta]]*Sin[(Pi*x)/200]^2*
     Sin[7*\[Theta]]*A[1, 7][t]*B[1, 7][t] + 1.06797*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 0][t]*A[1, 7][t]*B[1, 7][t] - 
    3.69945*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 0][t]*A[1, 7][t]*B[1, 7][t] + 2.95956*Cos[(Pi*x)/200]*
     Cos[7*\[Theta]]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 0][t]*A[1, 7][t]*
     B[1, 7][t] + 0.266991*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 0][t]*
     A[1, 7][t]*B[1, 7][t] + 52.6477*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 7][t]^2*B[1, 7][t] - 52.6477*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 7][t]^2*B[1, 7][t] + 0.133496*Cos[14*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]^2*B[1, 7][t] + 
    0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]^2*
     B[1, 7][t] - 13.5898*Cos[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 14][t]*
     B[1, 7][t] - 10.542*Cos[14*\[Theta]]*Sin[(Pi*x)/200]^2*Sin[7*\[Theta]]*
     A[1, 14][t]*B[1, 7][t] - 8.43363*Cos[(Pi*x)/200]^2*Cos[7*\[Theta]]*
     Sin[14*\[Theta]]*A[1, 14][t]*B[1, 7][t] + 0.0257425*Cos[(Pi*x)/100]*
     Sin[21*\[Theta]]*A[1, 14][t]*B[1, 7][t] - 0.266991*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 0][t]*A[1, 14][t]*B[1, 7][t] + 
    1.66475*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 0][t]*
     A[1, 14][t]*B[1, 7][t] + 1.06797*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 0][t]*A[1, 14][t]*B[1, 7][t] - 
    7.25708*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 0][t]*A[1, 14][t]*B[1, 7][t] + 3.92758*Cos[(Pi*x)/200]*
     Cos[7*\[Theta]]*Sin[(Pi*x)/100]*Sin[14*\[Theta]]*A[1, 0][t]*A[1, 14][t]*
     B[1, 7][t] + 0.266991*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*A[1, 0][t]*
     A[1, 14][t]*B[1, 7][t] - 0.0283811*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[21*\[Theta]]*A[1, 0][t]*A[1, 14][t]*B[1, 7][t] + 
    0.*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*
     B[1, 7][t] + 0.*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 7][t] + 
    0.266991*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 7][t] - 0.040995*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 7][t] + 
    0.*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 7][t] + 0.0378415*Cos[(Pi*x)/200]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 7][t] + 
    0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 7][t] + 0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[21*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 7][t] - 
    0.040995*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*
     A[1, 7][t]*A[1, 14][t]*B[1, 7][t] + 0.0378415*Cos[(Pi*x)/200]*
     Cos[7*\[Theta]]*Sin[(Pi*x)/100]*Sin[21*\[Theta]]*A[1, 7][t]*A[1, 14][t]*
     B[1, 7][t] + 210.591*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 14][t]^2*
     B[1, 7][t] - 210.591*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 14][t]^2*B[1, 7][t] - 0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 14][t]^2*B[1, 7][t] + 28.3008*Cos[(Pi*x)/100]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 14][t]^2*B[1, 7][t] + 
    0.133496*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 14][t]^2*
     B[1, 7][t] - 13.318*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Sin[(Pi*x)/100]*
     Sin[14*\[Theta]]*A[1, 14][t]^2*B[1, 7][t] + 0.075683*Cos[(Pi*x)/200]*
     Cos[21*\[Theta]]*Sin[(Pi*x)/100]*Sin[14*\[Theta]]*A[1, 14][t]^2*B[1, 7][t] + 
    0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*A[1, 14][t]^2*
     B[1, 7][t] - 0.0788365*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[21*\[Theta]]*A[1, 14][t]^2*B[1, 7][t] - 107.444*B[1, 7][t]^2 + 
    107.444*Cos[(Pi*x)/100]*B[1, 7][t]^2 + 3.95111*Cos[(Pi*x)/200]^2*
     Cos[7*\[Theta]]^2*B[1, 7][t]^2 - 3.95111*Sin[(Pi*x)/200]^2*Sin[7*\[Theta]]^2*
     B[1, 7][t]^2 - 0.133496*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*
     B[1, 7][t]^2 - 1.47978*Cos[(Pi*x)/200]*Cos[7*\[Theta]]^2*Sin[(Pi*x)/100]*
     A[1, 0][t]*B[1, 7][t]^2 + 0.533983*Sin[(Pi*x)/200]*Sin[7*\[Theta]]^2*
     A[1, 0][t]*B[1, 7][t]^2 - 1.84972*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]^2*A[1, 0][t]*B[1, 7][t]^2 + 52.6477*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]*B[1, 7][t]^2 - 52.6477*Cos[(Pi*x)/100]*
     Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*B[1, 7][t]^2 - 
    0.133496*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*
     B[1, 7][t]^2 + 0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[14*\[Theta]]*
     A[1, 7][t]*B[1, 7][t]^2 + 210.591*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 14][t]*B[1, 7][t]^2 - 210.591*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 14][t]*B[1, 7][t]^2 - 
    0.133496*Cos[14*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 14][t]*B[1, 7][t]^2 + 
    6.65901*Cos[(Pi*x)/200]*Cos[7*\[Theta]]^2*Sin[(Pi*x)/100]*A[1, 14][t]*
     B[1, 7][t]^2 - 0.0378415*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/100]*A[1, 14][t]*B[1, 7][t]^2 - 
    0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]^2*A[1, 14][t]*B[1, 7][t]^2 + 
    8.32376*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]^2*A[1, 14][t]*
     B[1, 7][t]^2 + 0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[21*\[Theta]]*
     A[1, 14][t]*B[1, 7][t]^2 - 0.040995*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*Sin[21*\[Theta]]*A[1, 14][t]*B[1, 7][t]^2 + 
    52.6477*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]^3 - 
    52.6477*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]^3 - 
    0.133496*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]^3 + 
    39.1352*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*B[1, 14][t] + 
    0.987777*Cos[(Pi*x)/100]*Sin[14*\[Theta]]*A[1, 0][t]*B[1, 14][t] - 
    3438.75*Sin[(Pi*x)/200]^2*Sin[14*\[Theta]]*A[1, 0][t]*B[1, 14][t] + 
    0.533983*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 0][t]^2*B[1, 14][t] - 
    0.484011*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 0][t]^2*
     B[1, 14][t] + 13.5898*Cos[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 7][t]*
     B[1, 14][t] - 8.43363*Cos[(Pi*x)/200]^2*Cos[14*\[Theta]]*Sin[7*\[Theta]]*
     A[1, 7][t]*B[1, 14][t] - 10.542*Cos[7*\[Theta]]*Sin[(Pi*x)/200]^2*
     Sin[14*\[Theta]]*A[1, 7][t]*B[1, 14][t] + 0.0257425*Cos[(Pi*x)/100]*
     Sin[21*\[Theta]]*A[1, 7][t]*B[1, 14][t] + 0.266991*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*A[1, 0][t]*A[1, 7][t]*B[1, 14][t] - 
    1.66475*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 0][t]*
     A[1, 7][t]*B[1, 14][t] + 3.92758*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 0][t]*A[1, 7][t]*B[1, 14][t] + 
    1.06797*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 0][t]*A[1, 7][t]*
     B[1, 14][t] - 7.25708*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*A[1, 0][t]*A[1, 7][t]*B[1, 14][t] + 
    0.266991*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*A[1, 0][t]*A[1, 7][t]*
     B[1, 14][t] - 0.0283811*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*
     A[1, 0][t]*A[1, 7][t]*B[1, 14][t] + 0.266991*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]^2*B[1, 14][t] - 
    8.32376*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 7][t]^2*B[1, 14][t] + 6.65901*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]*A[1, 7][t]^2*B[1, 14][t] + 
    0.0378415*Cos[(Pi*x)/200]*Cos[21*\[Theta]]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*
     A[1, 7][t]^2*B[1, 14][t] + 210.591*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     A[1, 7][t]^2*B[1, 14][t] - 210.591*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*A[1, 7][t]^2*B[1, 14][t] + 0.133496*Cos[14*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]^2*B[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*A[1, 7][t]^2*
     B[1, 14][t] - 0.040995*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[21*\[Theta]]*A[1, 7][t]^2*B[1, 14][t] - 2.12567*Cos[(Pi*x)/200]^2*
     Cos[14*\[Theta]]*Sin[14*\[Theta]]*A[1, 14][t]*B[1, 14][t] - 
    2.12567*Cos[14*\[Theta]]*Sin[(Pi*x)/200]^2*Sin[14*\[Theta]]*A[1, 14][t]*
     B[1, 14][t] + 1.06797*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     A[1, 0][t]*A[1, 14][t]*B[1, 14][t] - 4.84011*Cos[(Pi*x)/100]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 0][t]*A[1, 14][t]*
     B[1, 14][t] + 3.87208*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     Sin[14*\[Theta]]*A[1, 0][t]*A[1, 14][t]*B[1, 14][t] + 
    0.266991*Sin[(Pi*x)/200]*Sin[28*\[Theta]]*A[1, 0][t]*A[1, 14][t]*
     B[1, 14][t] + 0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     A[1, 7][t]*A[1, 14][t]*B[1, 14][t] - 28.3008*Cos[(Pi*x)/100]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*
     B[1, 14][t] + 13.318*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     Sin[7*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 14][t] - 28.3008*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 14][t] + 
    0.266991*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 14][t] - 0.0788365*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 14][t] + 
    13.318*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Sin[(Pi*x)/100]*Sin[14*\[Theta]]*
     A[1, 7][t]*A[1, 14][t]*B[1, 14][t] + 0.075683*Cos[(Pi*x)/200]*
     Cos[21*\[Theta]]*Sin[(Pi*x)/100]*Sin[14*\[Theta]]*A[1, 7][t]*A[1, 14][t]*
     B[1, 14][t] + 0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*
     A[1, 7][t]*A[1, 14][t]*B[1, 14][t] - 0.0788365*Cos[(Pi*x)/100]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[21*\[Theta]]*A[1, 7][t]*A[1, 14][t]*
     B[1, 14][t] + 0.075683*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     Sin[21*\[Theta]]*A[1, 7][t]*A[1, 14][t]*B[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[28*\[Theta]]*A[1, 7][t]*
     A[1, 14][t]*B[1, 14][t] + 842.364*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     A[1, 14][t]^2*B[1, 14][t] - 842.364*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*A[1, 14][t]^2*B[1, 14][t] + 0.133496*Cos[28*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[14*\[Theta]]*A[1, 14][t]^2*B[1, 14][t] + 
    0.266991*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[28*\[Theta]]*A[1, 14][t]^2*
     B[1, 14][t] + 13.5898*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*B[1, 7][t]*
     B[1, 14][t] + 8.43363*Cos[(Pi*x)/200]^2*Cos[7*\[Theta]]*Cos[14*\[Theta]]*
     B[1, 7][t]*B[1, 14][t] - 0.0257425*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*
     B[1, 7][t]*B[1, 14][t] - 10.542*Sin[(Pi*x)/200]^2*Sin[7*\[Theta]]*
     Sin[14*\[Theta]]*B[1, 7][t]*B[1, 14][t] + 0.266991*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 0][t]*B[1, 7][t]*B[1, 14][t] - 
    1.66475*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*
     B[1, 7][t]*B[1, 14][t] - 0.266991*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 0][t]*B[1, 7][t]*B[1, 14][t] + 0.0283811*Cos[(Pi*x)/100]*
     Cos[21*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*B[1, 7][t]*B[1, 14][t] - 
    3.92758*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     A[1, 0][t]*B[1, 7][t]*B[1, 14][t] + 1.06797*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*Sin[14*\[Theta]]*A[1, 0][t]*B[1, 7][t]*B[1, 14][t] - 
    7.25708*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[14*\[Theta]]*
     A[1, 0][t]*B[1, 7][t]*B[1, 14][t] + 0.266991*Cos[7*\[Theta]]^2*
     Sin[(Pi*x)/200]*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] - 
    8.32376*Cos[(Pi*x)/100]*Cos[7*\[Theta]]^2*Sin[(Pi*x)/200]*A[1, 7][t]*
     B[1, 7][t]*B[1, 14][t] - 0.266991*Cos[7*\[Theta]]*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] + 
    0.040995*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 7][t]*B[1, 7][t]*B[1, 14][t] - 6.65901*Cos[(Pi*x)/200]*
     Cos[7*\[Theta]]^2*Sin[(Pi*x)/100]*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] - 
    0.0378415*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/100]*
     A[1, 7][t]*B[1, 7][t]*B[1, 14][t] + 0.266991*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]^2*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] - 
    8.32376*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]^2*A[1, 7][t]*
     B[1, 7][t]*B[1, 14][t] - 6.65901*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*
     Sin[7*\[Theta]]^2*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] + 
    0.266991*Sin[(Pi*x)/200]*Sin[14*\[Theta]]^2*A[1, 7][t]*B[1, 7][t]*
     B[1, 14][t] + 0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[21*\[Theta]]*
     A[1, 7][t]*B[1, 7][t]*B[1, 14][t] - 0.040995*Cos[(Pi*x)/100]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[21*\[Theta]]*A[1, 7][t]*B[1, 7][t]*
     B[1, 14][t] + 0.0378415*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*
     Sin[21*\[Theta]]*A[1, 7][t]*B[1, 7][t]*B[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*
     B[1, 7][t]*B[1, 14][t] - 28.3008*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*B[1, 7][t]*B[1, 14][t] - 
    0.266991*Cos[14*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*
     B[1, 7][t]*B[1, 14][t] + 0.0788365*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*
     Cos[21*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 
    13.318*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     A[1, 14][t]*B[1, 7][t]*B[1, 14][t] - 0.075683*Cos[(Pi*x)/200]*
     Cos[14*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/100]*A[1, 14][t]*B[1, 7][t]*
     B[1, 14][t] - 0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[14*\[Theta]]*
     A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 28.3008*Cos[(Pi*x)/100]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[14*\[Theta]]*A[1, 14][t]*B[1, 7][t]*
     B[1, 14][t] - 13.318*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*Sin[7*\[Theta]]*
     Sin[14*\[Theta]]*A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 
    0.266991*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*Sin[21*\[Theta]]*A[1, 14][t]*
     B[1, 7][t]*B[1, 14][t] - 0.0788365*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*Sin[21*\[Theta]]*A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 
    0.075683*Cos[(Pi*x)/200]*Sin[(Pi*x)/100]*Sin[14*\[Theta]]*Sin[21*\[Theta]]*
     A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 0.266991*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*Sin[28*\[Theta]]*A[1, 14][t]*B[1, 7][t]*B[1, 14][t] + 
    0.266991*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]^2*
     B[1, 14][t] - 8.32376*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*B[1, 7][t]^2*B[1, 14][t] - 0.266991*Cos[21*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]^2*B[1, 14][t] + 
    0.040995*Cos[(Pi*x)/100]*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     B[1, 7][t]^2*B[1, 14][t] + 6.65901*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*
     Sin[(Pi*x)/100]*Sin[7*\[Theta]]*B[1, 7][t]^2*B[1, 14][t] + 
    210.591*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*B[1, 7][t]^2*B[1, 14][t] - 
    210.591*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*B[1, 7][t]^2*
     B[1, 14][t] - 0.133496*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     B[1, 7][t]^2*B[1, 14][t] - 0.0378415*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*
     Sin[(Pi*x)/100]*Sin[21*\[Theta]]*B[1, 7][t]^2*B[1, 14][t] - 
    429.778*B[1, 14][t]^2 + 429.778*Cos[(Pi*x)/100]*B[1, 14][t]^2 + 
    1.06283*Cos[(Pi*x)/200]^2*Cos[14*\[Theta]]^2*B[1, 14][t]^2 - 
    1.06283*Sin[(Pi*x)/200]^2*Sin[14*\[Theta]]^2*B[1, 14][t]^2 - 
    0.133496*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*A[1, 0][t]*B[1, 14][t]^2 - 
    1.93604*Cos[(Pi*x)/200]*Cos[14*\[Theta]]^2*Sin[(Pi*x)/100]*A[1, 0][t]*
     B[1, 14][t]^2 + 0.533983*Sin[(Pi*x)/200]*Sin[14*\[Theta]]^2*A[1, 0][t]*
     B[1, 14][t]^2 - 2.42005*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]^2*A[1, 0][t]*B[1, 14][t]^2 + 210.591*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*A[1, 7][t]*B[1, 14][t]^2 - 
    210.591*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*A[1, 7][t]*
     B[1, 14][t]^2 - 0.133496*Cos[7*\[Theta]]*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 7][t]*B[1, 14][t]^2 - 13.318*Cos[(Pi*x)/200]*Cos[7*\[Theta]]*
     Cos[14*\[Theta]]*Sin[(Pi*x)/100]*A[1, 7][t]*B[1, 14][t]^2 - 
    0.075683*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Cos[21*\[Theta]]*Sin[(Pi*x)/100]*
     A[1, 7][t]*B[1, 14][t]^2 + 0.266991*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*
     Sin[14*\[Theta]]*A[1, 7][t]*B[1, 14][t]^2 - 28.3008*Cos[(Pi*x)/100]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*Sin[14*\[Theta]]*A[1, 7][t]*B[1, 14][t]^2 + 
    0.266991*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*Sin[21*\[Theta]]*A[1, 7][t]*
     B[1, 14][t]^2 - 0.0788365*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*Sin[21*\[Theta]]*A[1, 7][t]*B[1, 14][t]^2 + 
    842.364*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*B[1, 14][t]^2 - 
    842.364*Cos[(Pi*x)/100]*Cos[14*\[Theta]]*Sin[(Pi*x)/200]*A[1, 14][t]*
     B[1, 14][t]^2 - 0.133496*Cos[14*\[Theta]]*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*
     A[1, 14][t]*B[1, 14][t]^2 + 0.266991*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     Sin[28*\[Theta]]*A[1, 14][t]*B[1, 14][t]^2 + 210.591*Sin[(Pi*x)/200]*
     Sin[7*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 - 210.591*Cos[(Pi*x)/100]*
     Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 - 
    0.133496*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*Sin[7*\[Theta]]*B[1, 7][t]*
     B[1, 14][t]^2 + 13.318*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*
     Sin[7*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 + 0.266991*Cos[7*\[Theta]]*
     Sin[(Pi*x)/200]*Sin[14*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 - 
    28.3008*Cos[(Pi*x)/100]*Cos[7*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     B[1, 7][t]*B[1, 14][t]^2 - 0.266991*Cos[21*\[Theta]]*Sin[(Pi*x)/200]*
     Sin[14*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 + 0.0788365*Cos[(Pi*x)/100]*
     Cos[21*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*B[1, 7][t]*B[1, 14][t]^2 - 
    0.075683*Cos[(Pi*x)/200]*Cos[14*\[Theta]]*Sin[(Pi*x)/100]*Sin[21*\[Theta]]*
     B[1, 7][t]*B[1, 14][t]^2 + 842.364*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     B[1, 14][t]^3 - 842.364*Cos[(Pi*x)/100]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     B[1, 14][t]^3 - 0.133496*Cos[28*\[Theta]]*Sin[(Pi*x)/200]*Sin[14*\[Theta]]*
     B[1, 14][t]^3 + ((6.90612*Sin[(Pi*x)/200])/10^7)*
     Derivative[2][A[1, 0]][t] + ((6.90612*Cos[7*\[Theta]]*Sin[(Pi*x)/200])/
      10^7)*Derivative[2][A[1, 7]][t] + 
    ((6.90612*Cos[14*\[Theta]]*Sin[(Pi*x)/200])/10^7)*Derivative[2][A[1, 14]][
      t] + ((6.90612*Sin[(Pi*x)/200]*Sin[7*\[Theta]])/10^7)*
     Derivative[2][B[1, 7]][t] + ((6.90612*Sin[(Pi*x)/200]*Sin[14*\[Theta]])/
      10^7)*Derivative[2][B[1, 14]][t];

Then:

    With[{L = 200}, 
  Print[AbsoluteTiming[r1 = ExpandAll[Chop[Integrate[Resi*Cos[7*1*\[Theta]]*Sin[(1*Pi*x)/L], {\[Theta], 0, 2*Pi}, 
         {x, 0, L}], 10^(-6)]]]]; 
   Print[AbsoluteTiming[r2 = ExpandAll[Chop[Integrate[Resi*Cos[7*1*\[Theta]]*Sin[(1*Pi*x)/L], {x, 0, L}, 
         {\[Theta], 0, 2*Pi}], 10^(-6)]]]]; r1 === r2]

gives, confirming yoda, :

    {36.7641028, 
 2087.69 A[1, 7][t] - 230144. A[1, 0][t] A[1, 7][t] + 
  225.867 A[1, 0][t]^2 A[1, 7][t] + 24830.6 A[1, 7][t]^3 - 
  2655.33 A[1, 7][t] A[1, 14][t] + 
  774.631 A[1, 0][t] A[1, 7][t] A[1, 14][t] + 
  100500. A[1, 7][t] A[1, 14][t]^2 + 
  24830.6 A[1, 7][t] B[1, 7][t]^2 - 2655.33 B[1, 7][t] B[1, 14][t] + 
  774.631 A[1, 0][t] B[1, 7][t] B[1, 14][t] + 
  100500. A[1, 7][t] B[1, 14][t]^2 + 
  0.000216962 (A[1, 7]^\[Prime]\[Prime])[t]}

{23.8343632, 
 2087.69 A[1, 7][t] - 230144. A[1, 0][t] A[1, 7][t] + 
  225.867 A[1, 0][t]^2 A[1, 7][t] + 24830.6 A[1, 7][t]^3 - 
  2655.33 A[1, 7][t] A[1, 14][t] + 
  774.631 A[1, 0][t] A[1, 7][t] A[1, 14][t] + 
  100500. A[1, 7][t] A[1, 14][t]^2 + 
  24830.6 A[1, 7][t] B[1, 7][t]^2 - 2655.33 B[1, 7][t] B[1, 14][t] + 
  774.631 A[1, 0][t] B[1, 7][t] B[1, 14][t] + 
  100500. A[1, 7][t] B[1, 14][t]^2 + 
  0.000216962 (A[1, 7]^\[Prime]\[Prime])[t]}

Of course, this really looks too slow. So if you help Integrate by rearranging the integrand a little bit, you can speed up things considerably:

    With[{L = 200}, 
  Print[AbsoluteTiming[rint0 = Expand[Collect[Expand[Resi*Cos[7*\[Theta]]*Sin[(Pi*x)/L], x] /. 
           p_Times /;  !FreeQ[p, x] :> Hold[Integrate][Select[p,  !FreeQ[#1, x] & ], {x, 0, L}]*
             Select[p, FreeQ[#1, x] & ], Hold[Integrate][_, _]] /. Hold[Integrate] -> Integrate, \[Theta]]; 
      rint1 = Chop[Expand[Collect[rint0 /. p_Times /;  !FreeQ[p, \[Theta]] :> Hold[Integrate][Select[p, 
                 !FreeQ[#1, \[Theta]] & ], {\[Theta], 0, 2*Pi}]*Select[p, FreeQ[#1, \[Theta]] & ], 
           Hold[Integrate][_, _]] /. Hold[Integrate] -> Integrate], 1/10^6]]]; 
   Print[AbsoluteTiming[tint1 = Expand[Collect[Expand[Resi*Cos[7*\[Theta]]*Sin[(Pi*x)/L], \[Theta]] /. 
           p_Times /;  !FreeQ[p, \[Theta]] :> Hold[Integrate][Select[p,  !FreeQ[#1, \[Theta]] & ], {\[Theta], 0, 2*Pi}]*
             Select[p, FreeQ[#1, \[Theta]] & ], Hold[Integrate][_, _]] /. Hold[Integrate] -> Integrate]; 
      tint2 = Chop[Expand[Collect[tint1 /. p_Times /;  !FreeQ[p, x] :> Hold[Integrate][Select[p, 
                 !FreeQ[#1, x] & ], {x, 0, L}]*Select[p, FreeQ[#1, x] & ], Hold[Integrate][_, _]] /. 
          Hold[Integrate] -> Integrate], 1/10^6]]]; Chop[rint1 - tint2, 1/10^6]]

Resulting in

    {1.5800904,2087.69 A[1,7][t]-230144. A[1,0][t] A[1,7][t]+225.867 A[1,0][t]^2 A[1,7][t]+24830.6 A[1,7][t]^3-2655.33 A[1,7][t] A[1,14][t]+774.631 A[1,0][t] A[1,7][t] A[1,14][t]+100500. A[1,7][t] A[1,14][t]^2+24830.6 A[1,7][t] B[1,7][t]^2-2655.33 B[1,7][t] B[1,14][t]+774.631 A[1,0][t] B[1,7][t] B[1,14][t]+100500. A[1,7][t] B[1,14][t]^2+0.000216962 (A[1,7]^\[Prime]\[Prime])[t]}

{1.5820904,2087.69 A[1,7][t]-230144. A[1,0][t] A[1,7][t]+225.867 A[1,0][t]^2 A[1,7][t]+24830.6 A[1,7][t]^3-2655.33 A[1,7][t] A[1,14][t]+774.631 A[1,0][t] A[1,7][t] A[1,14][t]+100500. A[1,7][t] A[1,14][t]^2+24830.6 A[1,7][t] B[1,7][t]^2-2655.33 B[1,7][t] B[1,14][t]+774.631 A[1,0][t] B[1,7][t] B[1,14][t]+100500. A[1,7][t] B[1,14][t]^2+0.000216962 (A[1,7]^\[Prime]\[Prime])[t]}
13
  • Hey Rolf.....the Problem still remains....I am using Mathematica 7. Here is the output that I got using the above code that you posted.I know I am sounding stupid but I simply don't understand what to do. But the code that you gave to increase the speed is working great...!! That solves my problem to a great extent...!!! Thanks a lot for that..!!!
    – user1099153
    Commented Dec 19, 2011 at 16:02
  • Mr. Rolf....You are GOD...!!! The program which took 16 hours to run now just takes a few minutes......!!!!! You have no Idea how much have you helped me....!!! My entire M.S. Thesis depends on it...!!! Thank You so much...!!!
    – user1099153
    Commented Dec 19, 2011 at 16:16
  • Rolf...If you don't mind could you just explain the code that you suggested for faster integration.....or if you could tell me some source from where I can get the meaning of this code that you provided....!!!
    – user1099153
    Commented Dec 19, 2011 at 16:18
  • @Harmeet: you are welcome. I had to do a lot of integrals when I was still active in physics, so I understand your pain. The idea here is to collect the basis integrals. I do this here by patternmatching and then using Collect. But originally I coded that kind of algorithms here: feyncalc.org/FeynCalcBook/Collect2
    – Rolf Mertig
    Commented Dec 19, 2011 at 18:30
  • @Harmeet: and, if you want to save even more time you could tabulate the basis integrals yourself. I did that in FeynCalc with feyncalc.org/FeynCalcBook/Integrate3 and feyncalc.org/FeynCalcBook/Integrate2
    – Rolf Mertig
    Commented Dec 19, 2011 at 18:32