I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on the computation of
Part 1: Introduction.
Part 2: Factoring the denominator using De Moivre’s Theorem.
Part 3: Factoring the denominator using the difference of two squares.
Part 4: The partial fractions decomposition of the integrand.
Part 5: Partial evaluation of the resulting integrals.
Part 6: Evaluation of the remaining integrals.
Part 7: An apparent simplification using a trigonometric identity.
Part 8: Discussion of the angles for which the identity holds.
Part 9: Proof of the angles for which the identity holds.
Part 10: Implications for using this identity when computing definite integrals.