# New to the method of steepest descent

## Homework Statement

I'm new to this approximation method and was wondering the best way to proceed with this function:

$$\int_{-\infty}^{+\infty} dx e^{\frac{ax^{2}}{2}}e^{ln[2cosh(b+cx)]}$$

I've found the saddle point (I think). But I was wondering if it would be best to expand the x squared term or the ln(cosh) term. If the latter, should I expand the cosh as a taylor series to get ln(expanded cosh) and then expand the logarithm (of the expanded cosh?) and simplify the result?.