Calculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

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

Step 4

Since the derivative of $- \cot (x)$ is $\csc^{2} (x)$ , the integral of $\csc^{2} (x)$ is $- \cot (x)$ .

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

Step 5

Simplify.

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