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How can one evaluate the following integral?

$$\int_{-c}^{c} e^{-ax^2}\cos^2(bx) \,\mathrm{d}x$$

Wolfram Alpha gives this. Is there not a more compact form?

If $\int_{-c}^{c} e^{-ax^2} \, \mathrm{d}x=k$, then can we express the first integral in terms of $k$? Thanks.

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    Your k is essentially erf, and erfi is defined in terms of erf, so when WolframAlpha represents the answer in terms of erf and erfi, it is essentially representing it in terms of your k.2011-10-16
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    @tzs: Thanks. I am not too familiar with erfs and erfis. What would the integral be then when written in $k$?2011-10-16
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    For a start, you would have $\text{Erf}[\sqrt{a} c] =k\sqrt{\frac{a}{\pi}}$2011-10-16
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    @Henry: Thanks. How do we deal with the erfi's?2011-10-16
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    $\text{erfi}(x) = -i \text{erf}(ix)$2011-10-16

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