Calculus Examples

$\int [3 \sin (x) - 2 \sec^{2} (x)] d x$

Step 1

Remove parentheses.

$\int 3 \sin (x) - 2 \sec^{2} (x) d x$

Step 2

Split the single integral into multiple integrals.

$\int 3 \sin (x) d x + \int - 2 \sec^{2} (x) d x$

Step 3

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \sin (x) d x + \int - 2 \sec^{2} (x) d x$

Step 4

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

$3 (- \cos (x) + C) + \int - 2 \sec^{2} (x) d x$

Step 5

Since $- 2$ is constant with respect to $x$ , move $- 2$ out of the integral.

$3 (- \cos (x) + C) - 2 \int \sec^{2} (x) d x$

Step 6

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

$3 (- \cos (x) + C) - 2 (\tan (x) + C)$

Step 7

Simplify.

$- 3 \cos (x) - 2 \tan (x) + C$