# Integration of Tangent Inverse

Tangent inverse function ${\tan ^{ - 1}}x$ 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 ${\tan ^{ - 1}}x$, now consider second function as $1$. Now the integration becomes

Take first function is ${\tan ^{ - 1}}x$ and second function will be $1$
Using formula for integration by parts, we have

Equation (i) becomes using above formula, we have

Multiplying and dividing by 2, we have

Using formula

we have

Now further we can use this integration of tangent inverse as a formula.