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

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


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 


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




Watch the following video for explanations.