# Integration by Parts|Principles of Integral Evaluation| Integral of xe^xdx|

##### Use integration by parts to evaluate $\int \:xe^xdx$

Solution:

In this case, the integrand is the product of an algebraic function x with the exponential function $e^x$. According to LIATE we should let

$u=x\:\:\:\:\:and\:\:\:\:\:\:dv=e^xdx$

so that

$du=dx\:\:\:\:\:\:\:\:\:\:and\:\:\:\:\:\:\:\:\:\:v=\int \:e^xdx=e^x$

Thus from the Integration by Parts (IBP) Formula

$=uv-\int \:vdu$

$=xe^x-\int \:e^xdx$

$=xe^x-e^x+C$

Watch the following video for explanations.