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How to calculate: $$\int \sqrt{(\cos{x})^2-a^2} \, dx$$

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    This seems distinctly nontrivial - I get elliptic integrals. I doubt it is expressible in elementary functions. Where did it come from? I can do 1 instead of $a^2$ though, pretty easily. That good enough?2011-06-27
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    I'm trying to find the probability that two cars be in reach after time $\tau$ .. I assumed a model and I'm stuck with that2011-06-27
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    Do you want the indefinite integral or do you need actually a certain definite integral? (very often in applications one need to integral from a point where the argument of the $\sqrt{\cdot}$ is zero to another point with these properties)2011-06-27
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    Is a bounded by anything?2011-06-27
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    Further - from this integral, how will you determine the probability? As this will likely have an imaginary component, will you just mod the answer?2011-06-27
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    Maybe you should post your probability problem too.2011-06-27

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