# Help with a troublesome integral

1. Mar 8, 2015

### mmzaj

We have the integral:
$$I(s)=\int_{0}^{\infty}\log\left(1+\frac{s^{2}}{4\pi^{2}} \log^{2}(1+ix)\right ) e^{-2\pi nx}dx$$
Where $s$ is a complex parameter, and $n$ is a positive integer.
Things i tried:
Set $\log(1+ix)=y$, so that
$$I(s)=-i\int_{c}\log\left(1+\frac{s^{2}}{4\pi^{2}}y^{2} \right )\exp\left(2\pi in e^{y} \right )e^{y}dy$$
Where the path $c$ has to be defined !!

2. Mar 12, 2015