Question

$\int\limits_{0}^{1} \frac{\log (1+x)}{1+x^{2}} d x$

• A. $\frac{1}{2}$
• B. $\frac{\pi}{8} \log 2$
• C. $\frac{\pi}{2} \log 2$
• D. $\frac{\pi}{4} \log 2$

Answer 1

Answer: (B)

By substituting $x=\tan \theta$
$I=\int\limits_{0}^{\frac{\pi}{4}} \log (1+\tan \theta) d \theta$
$=\frac{\pi}{8} \log 2$