Calculus Examples

$\int 9 θ \cos (θ) d θ$

Step 1

Since $9$ is constant with respect to $θ$ , move $9$ out of the integral.

$9 \int θ \cos (θ) d θ$

Step 2

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

$9 (θ \sin (θ) - \int \sin (θ) d θ)$

Step 3

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

$9 (θ \sin (θ) - (- \cos (θ) + C))$

Step 4

Rewrite $9 (θ \sin (θ) - (- \cos (θ) + C))$ as $9 (θ \sin (θ) + \cos (θ)) + C$ .

$9 (θ \sin (θ) + \cos (θ)) + C$