Substitution of Variables (by parts and simple partial fractions)

In order to evaluate this integral, we will need to use partial fraction decomposition.

Multiply both sides of the equation by the common denominator, which is

This means that must equal 1, and

The answer is .

To integrate, we must first make the following substitution:

Rewriting the integral in terms of u and integrating, we get

The following rule was used to integrate:

Finally, we replace u with our original x term: