Calculus Examples

$\sec^{3} (x) \tan (x)$

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

Tap for more steps...

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

Tap for more steps...

Differentiate $\sec (x)$ .

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

The derivative of $\sec (x)$ with respect to $x$ is $\sec (x) \tan (x)$ .

$\sec (x) \tan (x)$

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

$\int u^{2} d u$

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

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

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

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