Evaluate : ∫ x/ (x+1)^2 dx.

Question

Evaluate :

\(\int\,\frac{x}{(x+1)^2}dx.\)

Answer 1

\(\int\,\frac{x}{(x+1)^2}dx\)

\(=\int\,\left[\frac{1}{x+1}-\frac{1}{(x+1)^2}\right]dx\)

\(=log |x+1|+\frac{1}{(x+1)}+c.\)