# Cotangent Integral Formula

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

The integration of cotangent function is of the form

To prove this formula, consider

Using the derivative formulas 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 derivative, so the integral sign and on the right side will cancel each other, i.e.

__Alternate Proof__**:**

We have given integration of the form

Here we have then

Using the formula of integration,

__Other Integral Formulas of Cotangent Function__**:**

The other formulas of cotangent integral with angle of sine is in the form of function are given as

**1. **** **

**2. **** **

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

We have integral

Using the formula , we have