Calculus Examples

$\int 2 \sin (x) + 3 \cos (x) d x$

Step 1

Split the single integral into multiple integrals.

$\int 2 \sin (x) d x + \int 3 \cos (x) d x$

Step 2

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

$2 \int \sin (x) d x + \int 3 \cos (x) d x$

Step 3

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

$2 (- \cos (x) + C) + \int 3 \cos (x) d x$

Step 4

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

$2 (- \cos (x) + C) + 3 \int \cos (x) d x$

Step 5

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

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

Step 6

Simplify.

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