Calculus Examples

$\int (\csc (x) \cot (x) + 3) d x$

Step 1

Remove parentheses.

$\int \csc (x) \cot (x) + 3 d x$

Step 2

Split the single integral into multiple integrals.

$\int \csc (x) \cot (x) d x + \int 3 d x$

Step 3

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

$- \csc (x) + C + \int 3 d x$

Step 4

Apply the constant rule.

$- \csc (x) + C + 3 x + C$

Step 5

Simplify.

$- \csc (x) + 3 x + C$