Calculus Examples

$\int \cos (x) - \sin (x) d x$

Step 1

Split the single integral into multiple integrals.

$\int \cos (x) d x + \int - \sin (x) d x$

Step 2

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

$\sin (x) + C + \int - \sin (x) d x$

Step 3

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$\sin (x) + C - \int \sin (x) d x$

Step 4

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

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

Step 5

Simplify.

$\sin (x) + \cos (x) + C$