Question

Find:
$\int \frac{x{e}^x}{(1+x{)}^2}dx$

Answer 1

$y=\int \frac{x{e}^x}{(1+x{)}^2}dx$

$y=\int [\frac{1}{1+x}-\frac{1}{(1+x{)}^2}]dx$

We know $\int e^x\left[f\right(x)-f(x\left)\right]=e^{x}f\left(x\right)$

then

$y=\int e^x[\frac{1}{1+x}-\frac{1}{(1+x{)}^2}]dx=\frac{e^x}{1+x}+c$