Hi WUrunner,

If we simplify what's inside the logarithm we should get

Now multiply this out to get

Now we know that the first integral is (see Gaussian integral - Wikipedia, the free encyclopedia). The second integral can be computed using a u-substitution or by noting that we're integrating an odd function about a symmetric interval. When we put all the pieces together (if I've done the computations correctly) we should get

Does this straighten things out? Let me know if anything is unclear. Good luck!