0
$\begingroup$

How to perform $\int_0^1 \frac{\left(a_0\log(u)+a_1\log(1-u)+a_{2}\log(1-xu)\right)^9}{u-1} du $?

Method tried:

Intgration-by-parts

Series expansion

change of variable $\log(u)=x$

But I still can't work out.

One may use Mathematica, but it returns this integral just as your input.

The answer maybe some series of PolyLog and Single(multi-) zeta function.

$\endgroup$
2
  • 1
    $\begingroup$ $\int_{0}^{1} \ln(1-x)/(1-x) dx= \int_{0}^{1} \ln x/x dx$ does not converge. $\endgroup$
    – Z Ahmed
    Commented Nov 28, 2020 at 15:02
  • $\begingroup$ @ZAhmed I know it does not converge, but we can extract the finite part and regularize the divergence. $\endgroup$
    – YU MU
    Commented Nov 28, 2020 at 20:57

0

Reset to default

You must log in to answer this question.