Question

What is the integration of $cotx$?

Answer 1

Find the integration of $cotx$.

$\int cotxdx=\int \frac{\cos x}{\sin x}dx...\left(1\right)$

Let $\sin x=u$

So, $\cos xdx=du$.

Put the above values in the equation$\left(1\right)$:

$$\begin{gathered} \int \cot xdx=\int \frac{du}{u} \\ \int \cot xdx=\ln \left|u\right|+C \\ \int \cot xdx=\ln \left|\left(\sin x\right)\right|+C \end{gathered}$$

Hence, the required integral is $\int \cot xdx=\ln \left|\left(\sin x\right)\right|+C$ where $C$ is a constant of integration .