[SOLVED] Amath 567, homework 4

1. Problem 1: Using residue calculus, calculate
I =
Z ∞
−∞
sin x
sinh x
dx2. Problem 2: Using residue calculus, calculate
I =
Z ∞
−∞
1 + cos(x)
(x − π)
2
d3. Problem 3: Evaluate the following integral using residue calculus
I =
Z ∞
0
x
a
a + 2x cos b + x
2
dx
where −1 < a < 1, a ̸= 0, and −π < b < π, b ̸= 0. Justify all key steps. Do not use
the general formula for this integral.