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Mathematics
Laila Podlesny's user avatar
Laila Podlesny's user avatar
Laila Podlesny's user avatar
Laila Podlesny
  • Member for 11 years, 2 months
  • Last seen more than 6 years ago
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595
Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$
Nov 11, 2013
69
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
May 13, 2013
53
Integral $\int_0^\infty\frac{\operatorname{arccot}\left(\sqrt{x}-2\,\sqrt{x+1}\right)}{x+1}\mathrm dx$
Nov 8, 2013
51
Integral $\int_0^{\pi/2}\arctan^2\left(\frac{6\sin x}{3+\cos 2x}\right)\mathrm dx$
Nov 13, 2013
50
Closed form of $\prod_{n=1}^\infty\sqrt[2^n]{\frac{\Gamma(2^n+\frac{1}{2})}{\Gamma(2^n)}}$
May 12, 2013
42
Calculate the following infinite sum in a closed form $\sum_{n=1}^\infty(n\ \text{arccot}\ n-1)$?
May 16, 2013
41
$\int_0^1\arctan\,_4F_3\left(\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x}{64}\right)\,\mathrm dx$
May 11, 2013
41
Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$
Oct 14, 2013
41
How to find ${\large\int}_1^\infty\frac{1-x+\ln x}{x \left(1+x^2\right) \ln^2 x} \mathrm dx$? [closed]
Aug 22, 2014
40
A closed form of $\int_0^\infty\frac{\sqrt[\phi]{x}\ \arctan x}{\left(x^\phi+1\right)^2}dx$
Oct 9, 2013
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34
How to get all 24 rotations of a 3-dimensional array?
17
Integer lattice points on a hypersphere
15
What are Root objects with multiple polynomials?
10
How do I expand StirlingS2[n, 10] in terms of elementary functions?
10
Find a generalized hypergeometric-based function yielding certain ratios of fifth-degree polynomials