Calculus Examples

$\int \cot^{3} (x) d x$

Step 1

Apply the reduction formula.

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

Step 2

The integral of $\cot (x)$ with respect to $x$ is $\ln (| \sin (x) |)$ .

$- \frac{\cot^{2} (x)}{2} - (\ln (| \sin (x) |) + C)$

Step 3

Rewrite $- \frac{\cot^{2} (x)}{2} - (\ln (| \sin (x) |) + C)$ as $- \frac{1}{2} \cot^{2} (x) - \ln (| \sin (x) |) + C$ .

$- \frac{1}{2} \cot^{2} (x) - \ln (| \sin (x) |) + C$