Tangent inverse function it is an important integral function, but it has no direct method to find we shall find the integration of tangent inverse by using integration by parts method.
The integration of tangent inverse is of the form
To solve this integration, it must have at least two functions, it in this function it has only one function that is , now consider second function as . Now the integration becomes
Take first function is and second function will be
Using formula for integration by parts, we have
Equation (i) becomes using above formula, we have
Multiplying and dividing by 2, we have
Now further we can use this integration of tangent inverse as a formula.