Calculus Examples

$\int (1 - \csc (x) \cot (x)) d x$

Step 1

Remove parentheses.

$\int 1 - \csc (x) \cot (x) d x$

Step 2

Split the single integral into multiple integrals.

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

Step 3

Apply the constant rule.

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

Step 4

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

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

Step 5

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

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

Step 6

Simplify.

$x + \csc (x) + C$