Many definite integrals are made much easier by taking the
domain to be
complex, making up an appropriate
contour, and performing
contour integration with the aid of
complex analysis (
Cauchy's integral theorem,
residue calculus,
Jordan's lemma, etc.)
Not suprising, as complex analysis was invented in part to tackle all the gross integrals coming out of fluid mechanics, electromagnetism, and other scientific fields in the 1800s...