The tangent inverse function it is an important integral function, but it has no direct method to find it. We shall find the integration of tangent inverse by using the integration by parts method.
The integration of tangent 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 tangent inverse as a formula.