# How do you integrate int (xe^x)/((x+1)^2)dx using integration by parts?

Jan 28, 2016

You may try several other choices (I did) before you try $u = x {e}^{x}$ and $\mathrm{dv} = {\left(x + 1\right)}^{-} 2 \mathrm{dx}$

#### Explanation:

Following through on the choices above, we find that

$\mathrm{du} = \left({e}^{x} + x {e}^{x}\right) \mathrm{dx}$ and $v = - \frac{1}{x + 1}$

$\int \frac{x {e}^{x}}{{\left(x + 1\right)}^{2}} \mathrm{dx} = - \frac{x {e}^{x}}{x + 1} + \int {e}^{x}$

$= {e}^{x} / \left(x + 1\right) + C$