The first three terms of an arithmetic sequence are as follows.
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You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form
You can use the "cover-up" method here to easily solve for . It involves fixing a value of
to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.
- If
, then
- If
, then
- If
, then
So the integral we want to compute is the same as
and each integral here is trivial. We end up with
which can be condensed as