Calculus Examples

$\int t e^{t} d t$

Step 1

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = t$ and $d v = e^{t}$ .

$t e^{t} - \int e^{t} d t$

Step 2

The integral of $e^{t}$ with respect to $t$ is $e^{t}$ .

$t e^{t} - (e^{t} + C)$

Step 3

Simplify.

$t e^{t} - e^{t} + C$