Evaluate: $\int_0^1 \frac{1-x}{(1+x)\log(x)}\, dx$

Asked Jun 23 '15 at 19:47

Active Jun 23 '15 at 19:48

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Evaluate:

$$\int_0^1 \frac{1-x}{(1+x)\log(x)}\, dx$$

Wolfram alpha gives an answer of $\log(2/\pi)$, but I have been unable to prove this. Help appreciated.

edited Jun 23 '15 at 19:48

asked Jun 23 '15 at 19:47

goonfiend

the result should be $\frac{2}{\pi}$ – Dr. Sonnhard Graubner Jun 23 '15 at 19:57

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