Tangent Substitution: Radical and x in the denominator: Find

Here we can use the Tangent Substitution Rule with :

Let , ,

and using the Tangent-Secant identity, .

Upon substitution, we have

Using the Secant-cosine and Tangent-sine-cosine identities, we get

We can use the Csc-Sine identity to get:

We now use the integral of the cosecant :

We can convert back to an expression in x, using the Tangent Diagram: , or , or

, . With this result, we finally get