Calculus Examples

$\sin (x) \cos^{2} (x)$

Let $u = \cos (x)$ . Then $d u = - \sin (x) d x$ , so $- \frac{1}{\sin (x)} d u = d x$ . Rewrite using $u$ and $d$ $u$ .

Tap for more steps...

Let $u = \cos (x)$ . Find $\frac{d u}{d x}$ .

Tap for more steps...

Differentiate $\cos (x)$ .

$\frac{d}{d x} [\cos (x)]$

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

$- \sin (x)$

Rewrite the problem using $u$ and $d u$ .

$\int - 1 u^{2} d u$

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

$- \int u^{2} d u$

By the Power Rule, the integral of $u^{2}$ with respect to $u$ is $\frac{1}{3} u^{3}$ .

$- (\frac{1}{3} u^{3} + C)$

Rewrite $- (\frac{1}{3} u^{3} + C)$ as $- \frac{1}{3} u^{3} + C$ .

$- \frac{1}{3} u^{3} + C$

Replace all occurrences of $u$ with $\cos (x)$ .

$- \frac{1}{3} \cos^{3} (x) + C$