Exercise 188Calculus › Single-variable calculus › Integration › Integration techniquesL1Added 31 Oct 2026

Integration by parts

#integrals#by parts

Statement

Compute $\displaystyle\int_0^1 x\,e^x\,dx$ .

Hint

Differentiate $x$ and integrate $e^x$ .

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Take $u=x$ and $v'=e^x$ , so $u'=1$ and $v=e^x$ . Then
$\int_0^1xe^x\,dx=\Big[xe^x\Big]_0^1-\int_0^1e^x\,dx=e-(e-1)=1.$