Calculus Examples

$4 \cos (x) + \sec^{2} (x)$

Step 1

Split the single integral into multiple integrals.

$\int 4 \cos (x) d x + \int \sec^{2} (x) d x$

Step 2

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int \cos (x) d x + \int \sec^{2} (x) d x$

Step 3

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

$4 (\sin (x) + C) + \int \sec^{2} (x) d x$

Step 4

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

$4 (\sin (x) + C) + \tan (x) + C$

Step 5

Simplify.

$4 \sin (x) + \tan (x) + C$