Monthly Archives: October 2014

Real evaluation of an improper log integral

The problem posed in M.SE concerns real methods of evaluating $$\int_0^{\infty} dx\frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} $$ The place I started is the nifty result, proven here, that $$\frac{\sin{x}}{\cosh{t} – \cos{x}} = 2 \sum_{k=1}^{\infty} e^{-k t} \sin{k x} $$ Of course, the integral actually looks like $$\int_0^{\infty} dx \frac{\cos{x}}{\cosh{x} – \sin{x}} \log{x} $$ so we need to […]