Could someone please help me to calculate the integral of:
$\int_{-\infty}^{+\infty} \cos (at) e^{-bt^2} dt.$
a and b both real, b>0.
I have tried integration by parts, but I can't seem to simplify it to anything useful. Essentially, I would like to arrive at something that looks like: 7.4.6 here: textbook result