# finding integral

I have trouble with Calculation of the following integral: for $0<t<\sqrt 6$ 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?

-
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. –  André Nicolas Dec 22 '11 at 23:57
cross posting –  The Chaz 2.0 Dec 23 '11 at 0:05
You can improve your accept rate by accepting answers. –  Paul Dec 23 '11 at 0:06
If $p$ is a half-integer, your integral is expressible in terms of the elliptic integrals. –  Ｊ. Ｍ. Dec 23 '11 at 0:27
It quite depends on p. –  Strin Dec 23 '11 at 9:27
show 1 more comment