How do you integrate $int xe^-x$ by integration by parts method?

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Answer 1 · 2016-11-27T17:30:57

$-e^-x(x+1)+C$

We have the integral $intxe^-xdx$ . We want to apply integration by parts, which fits the form $intudv=uv-intdvu$ . So for the given integral, let:

${(u=x,=>,du=dx),(dv=e^-xdx,=>,v=-e^-x):}$

To go from $dv$ to $v$ , the integration will require a substitution. Think for $inte^-xdx$ , let $t=-x$ .

So:

$intxe^-xdx=uv-intudv=-xe^-x+inte^-xdx$

We've already done this integral:

$intxe^-xdx=-xe^-x-e^-x$

$intxe^-xdx=-e^-x(x+1)+C$

How do you integrate int xe^-xint xe^-x by integration by parts method?