Calculus Examples

$\int \cot^{2} (x) d x$

Step 1

Using the Pythagorean Identity, rewrite $\cot^{2} (x)$ as $- 1 + \csc^{2} (x)$ .

$\int - 1 + \csc^{2} (x) d x$

Step 2

Split the single integral into multiple integrals.

$\int - 1 d x + \int \csc^{2} (x) d x$

Step 3

Apply the constant rule.

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

Step 4

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

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

Step 5

Simplify.

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