Calculus Examples

$\int \tan^{2} (x) d x$

Step 1

Using the Pythagorean Identity, rewrite $\tan^{2} (x)$ as $- 1 + \sec^{2} (x)$ .

$\int - 1 + \sec^{2} (x) d x$

Step 2

Split the single integral into multiple integrals.

$\int - 1 d x + \int \sec^{2} (x) d x$

Step 3

Apply the constant rule.

$- x + C + \int \sec^{2} (x) d x$

Step 4

Since the derivative of $\tan (x)$ is $\sec^{2} (x)$ , the integral of $\sec^{2} (x)$ is $\tan (x)$ .

$- x + C + \tan (x) + C$

Step 5

Simplify.

$- x + \tan (x) + C$