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{xe^x dx

integrate by parts let

f(x) = x so f'(x) = 1

and g(x) = e^x so g'(x) = e^x

so..

f(x)*g(x) - {(g(x)*f'(x)) dx

therefore xe^x - {(e^x * 1) dx

so..

xe^x - e^x + C

factorize so...

(x-1)e^x + C

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