Evaluate the indefinite integral of xe^x

by RoRi

November 10, 2015

Compute the following indefinite integral:

$\int xe^x \, dx.$

To evaluate this integral we use integration by parts, letting

$\begin{align*} u &= x, & du &= dx,\\ dv &= e^x \, dx, & dv &= e^x. \end{align*}$

Then we have,

$\begin{align*} \int xe^x , dx &= xe^x - \int e^x \, dx \\ &= xe^x - e^x + C \\ &= e^x (x-1) + C. \end{align*}$

Stumbling Robot