Calculus Examples

$\int \frac{\tan^{3} (x)}{\cos^{3} (x)} d x$

Step 1

Convert from $\frac{1}{\cos^{3} (x)}$ to $\sec^{3} (x)$ .

$\frac{d}{d x} [\int \tan^{3} (x) \sec^{3} (x) d x]$

Step 2

$\int \tan^{3} (x) \sec^{3} (x) d x$ is an antiderivative of $\tan^{3} (x) \sec^{3} (x)$ , so by definition $\frac{d}{d x} [\int \tan^{3} (x) \sec^{3} (x) d x]$ is $\tan^{3} (x) \sec^{3} (x)$ .

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

Step 3

Reorder the factors of $\tan^{3} (x) \sec^{3} (x)$ .

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