Question

Evaluate : ∫(log|1 + x|)/(1 + x²) dx, x ∈ [0,1]

Answer 1

 Let I be the integral given to us.

\(\therefore I = \int \limits_0^1 \frac{\log 1 + x}{1 + x^2} dx\)

Substitute x = tan t

⇒ dx = sec²t dt

Now, as \(\int\limits_0^a f(x)dx = \int\limits_0^a f(a - x)dx\), we have

Answer 2

Given integral