How to do integrals involving Gauss function and cosine function?

How can I calculate the integral: $$\int_{-\infty}^{+\infty}e^{-\frac{(x-a)^2}{0.01}}\cos(bx)dx$$ I can not find in the references. Excuse my bad English.

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You could expand the cosine in a Taylor series around $x=a$... –  Fabian Oct 19 '12 at 16:21

$$\cos(bx)=\frac12\left(\mathrm e^{\mathrm ibx}+\mathrm e^{-\mathrm ibx}\right)\;,$$
A reference is Rudin, Principles of mathematical analysis, Example 9.43. Here the integral $$\int_{-\infty}^{\infty}e^{-x^2}\cos(xt)\,dx$$ is calculated using the theory of ordinary differential equations. The integral is $$\sqrt{\pi}\exp\left(-\frac{t^2}{4} \right).$$ (Hint) In your integral after introducing new variable you should calculate $$\int_{-\infty}^{\infty}e^{-z^2}\cos(cz)\,dz$$ and $$\int_{-\infty}^{\infty}e^{-z^2}\sin(cz)\,dz.$$