Evaluate
You need to first factor the denominator, which is
You need to find the coefficients
You should end up with
The integral you then need to compute is
Evaluate
What is the partial fraction decomposition for this function?
The decomposition is
You can plug in
The integral you need to compute is
Compute
The partial fraction decomposition here is of the form
You should end up with
The integral to be evaluated is then
Your answer should have two logarithm terms and one inverse tangent term.
Compute
We can't go right into partial fractions here, because the degree in the numerator is higher than the degree in the denominator. How do we fix this?
Long division gives that
Then we evaluate the integral; the first part is a polynomial and the second is a logarithm.
Compute
Here we have a repeated quadratic factor, so what does that mean for the partial fraction decomposition of this function?
The decomposition you should use is
Solving out for the coefficients should give
You'll need to use trigonometric substitution on the
Compute
Compute