Calculus Examples

$\int t \cos (t) d t$

Step 1

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = t$ and $d v = \cos (t)$ .

$t \sin (t) - \int \sin (t) d t$

Step 2

The integral of $\sin (t)$ with respect to $t$ is $- \cos (t)$ .

$t \sin (t) - (- \cos (t) + C)$

Step 3

Rewrite $t \sin (t) - (- \cos (t) + C)$ as $t \sin (t) + \cos (t) + C$ .

$t \sin (t) + \cos (t) + C$