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 or in cartesian coordinates .

Then I have to dot with and integrate to find the flux, but that involves a lot of calculation and will carry an somewhere, and non of the answers contain a but rather a .

So what to do?