# Cotangent Integral Formula

In this tutorial we will prove the formula of cotangent integral which is another important formula in integral calculus. This integral belongs to the trigonometric formulae.

The integration of the cotangent function is of the form

To prove this formula, consider

Using the derivative formula and , we have

Integrating both sides of equation (i) with respect to , we have

As we know that by definition integration is the inverse process of the derivative, the integral sign and on the right side will cancel each other out, i.e.

__Alternate Proof__

We substitute with

Here we have then

Using the formula of integration,

__Other Integral Formulae of the Cotangent Function__

The other formulae of cotangent integral with an angle of sine in the form of a function are given as

**1. **

**2. **

__Example__**:** Evaluate the integral with respect to

We have integral

Using the formula , we have