Cubic elliptic integral

Asked Aug 11 '20 at 09:34

Active Aug 11 '20 at 10:40

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I search a close form about integral of $\frac{1}{\sqrt{(x^3+a^3)\cdot (x^3+b^3)}}$ between $0$ and $+\infty$.

I know There are already a subject about this but i want a particular answer: which is the close form in terms of complete elliptic integral of the first kind $K$ ?

It seems apparently that the beginning of close form is $\frac{4 \cdot \sqrt{3}*K(X)}{(9*a*b)}$ but what is $X$ ? I don't see the formula what i want.

Thanks.

edited Aug 11 '20 at 10:40

asked Aug 11 '20 at 09:34

Raptor

Where did you find $\frac{4 , \sqrt{3},K(X)}{(9ab)}$ ? – Claude Leibovici Aug 11 '20 at 10:18
I experiment with MAPLE and if i put a=b and X=0,it's right. – Raptor Aug 11 '20 at 10:22

Cubic elliptic integral

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