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## Homework Statement

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

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

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?.

Thanks for your help.