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. 

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