Calculus Examples

$\int x \cdot \cos (x) d x$

Step 1

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

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

Step 2

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

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

Step 3

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

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