Calculus Examples

$\int 5 \tan^{2} (x) d x$

Step 1

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int \tan^{2} (x) d x$

Step 2

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

$5 \int - 1 + \sec^{2} (x) d x$

Step 3

Split the single integral into multiple integrals.

$5 (\int - 1 d x + \int \sec^{2} (x) d x)$

Step 4

Apply the constant rule.

$5 (- x + C + \int \sec^{2} (x) d x)$

Step 5

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

$5 (- x + C + \tan (x) + C)$

Step 6

Simplify.

$5 (- x + \tan (x)) + C$