Calculus Examples

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

Step 1

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

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

Step 2

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 3

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

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

Step 4

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

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