The integral of cotangent inverse it is an important integral function, but it has no direct method to find it. We shall find the integration of cotangent inverse by using the integration by parts method.
The integral of cotangent inverse is of the form
To solve this integration it must have at least two functions, however it has only one function: . So consider the second function as . Now the integration becomes
The first function is and the second function is .
Using the formula for integration by parts, we have
Using the formula above, equation (i) becomes
Multiplying and dividing by 2, we have
Now we can also use this integration of cotangent inverse as a formula.