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I have trouble with Calculation of the following integral: for $0 and $p>1$

$$\int_0^{\sqrt 6} \left(\frac{t^4}{390}-\frac{t^2}{6}+1\right)^p\;dt.$$

Which substitution would work here?

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    Nothing pleasant unfortunately. If $p$ is a positive integer we can expand and integrate term by term. If $p$ is not an integer, we don't even have that, and should use a numerical method.2011-12-22
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    [cross posting](http://mymathforum.com/viewtopic.php?f=15&t=25875)2011-12-23
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    If $p$ is a half-integer, your integral is expressible in terms of the elliptic integrals.2011-12-23
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    It quite depends on p.2011-12-23
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    Start simplifying it to $$ \left(\left(\frac{t^2}{12}+1 \right)^2 - \left(\frac{t^2}{12}\frac{\sqrt{41}}{\sqrt{65}}\right)^2\right)^p $$2012-03-03

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