Complex Analysis: Theory and Applications · Problem 8.6.5

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · contour-integrals-residues

Problem

Use residues to compute the following integral:

\text{P.V.} \int_0^\infty \frac{\ln(x^2+1)}{x^2+1} \, dx.

Hint: Use the integrand

f(z) = \dfrac{\log(z+i)}{z^2+1}