Solving Difficult Integral Homework: \int_0^1\frac{ln(1+x)}{1+x^{2}} dx

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Homework Statement



I'm stuck with this definite integral : \int_0^1\frac{ln(1+x)}{1+x^{2}} dx

Homework Equations



The various "standard integrals".

The Attempt at a Solution



I just don't know where to start, or how to do it. I tried various substitutions but none of them worked; I also tired doing it by parts but that didn't work either.
 
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Okay, I got that. Thanks.
I knew of the identity, but didn't know I'd have to use it after making a substitution.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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