Question:
Evaluate the following integrals:
$\int x e^{x} d x$
Solution:
Let $I=\int x e^{x} d x$
Using integration by parts,
$I=x \int e^{x} d x-\int \frac{d}{d x} x \int e^{x} d x$
We know that, $\int e^{x} d x=e^{x}$ and $\frac{d}{d x} x=1$
$=x e^{x}-\int e^{x} d x$
$=x e^{x}-e^{x}+c$
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