Hello everyone!

I'm really stuck on this electromagnetics problem:

Determine the mutual inductance between an infinite wire and an equilateral triangle-shaped loop as shown in the figure.

Now, I tried putting current on the long wire so I get $\displaystyle \vec{B}=\frac{\mu_0 I}{2\pi r}\vec{a_{\phi}}$ or in cartesian coordinates $\displaystyle \vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}$.

Then I have to dot $\displaystyle \vec{B}$ with $\displaystyle \vec{dA}$ and integrate to find the flux, but that involves a lot of calculation and will carry an $\displaystyle \tan^{-1}$ somewhere, and non of the answers contain a $\displaystyle \tan^{-1}$ but rather a $\displaystyle \ln$.

So what to do?