Compute the following integral.
First, we can factor the denominator,
Next, we want to simplify the expression. In particular, we want the numerator to be a polynomial of smaller degree than the denominator. Dividing the numerator by the denominator we obtain
Therefore, we can start evaluating the integral,
Now we need to use partial fractions to evaluate this last integral on the right. To that end we write,
Therefore, we have the equation
Substituting the values , , and we obtain the following values
So, then we can continue evaluating the integral,