Evaluating ∫₀¹ ln(1+x)/(1+x²) dx

Rats_N_Cats · Dec 18, 2009

Homework Statement

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

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.

dirk_mec1 · Dec 18, 2009

Handwritten-style typeset solution: identity (1) integral from 0 to a of f(x) dx equals integral from 0 to a of f(a - x) dx, then Problem 2 evaluating integral from 0 to 1 of ln(x+1)/(x^2+1) dx, with the trigonometric substitution x = tan t and the derivation reaching I = (pi/8) ln 2.

Rats_N_Cats · Dec 18, 2009

Okay, I got that. Thanks.
I knew of the identity, but didn't know I'd have to use it after making a substitution.

Evaluating ∫₀¹ ln(1+x)/(1+x²) dx

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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