# How to evaluate $\int_0^1 {\log x \log(1-x) \log^2(1+x) \over x} \,dx$ [duplicate]

Solve that the following integral: $$\int_0^1 {\log x \log(1-x) \log^2(1+x) \over x} \,dx.$$

I haven't solved it yet.

-

## marked as duplicate by Vladimir Reshetnikov, Jack D'Aurizio, Hakim, Omnomnomnom, user133281Sep 19 at 18:15

The is a definite integral, which has a numerical value, so in that sense, yes it is possible to express it in closed form, albeit depending on what you mean by closed form. –  pbs Nov 10 '13 at 9:28
$0.1099416891.$ –  user64494 Nov 10 '13 at 9:38
Notice that the integrand is undefined at $x=0$ and $x=1$ or at any $x$ between $0$ and $1$. –  user40615 Nov 10 '13 at 9:54
$$\ln(1-x)=\sum_{n=1}^\infty\frac{x^n}n$$ –  Lucian Nov 10 '13 at 10:50