How do you integrate $int xe^xdx$ using integration by parts?

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Answer 1 · 2016-10-08T20:24:40

Remember the formula for IBP: $int u(dv)/dxdx=uv-intv(du)/dxdx$

Let $u=x=>(du)/dx=1$
Let $(dv)/dx=e^x=>v=e^x$

Substitute into the IBP equation:
$int xe^xdx=xe^x-int e^x(1)dx$
$:. int xe^xdx=xe^x-int e^xdx$
$:. int xe^xdx=xe^x-e^x+c$

How do you integrate int xe^xdxint xe^xdx using integration by parts?