Question

Evaluate $\int \frac{log(1+x)}{1+x}dx$ on $(-1,\infty )$

Answer 1

$\int \frac{\log (1+x)}{1+x}dx$

$=\int \ln (1+x)d\left[\ln \right(1+x\left)\right]$, since $\frac{d}{dx}\log (1+x)=\frac{1}{1+x}$

$=\frac{\left[\log \right(1+x){]}^2}{2}+C$