How can I solve this integral?
$$\int \frac{dx}{\sqrt{a(1+x)^3+1}}$$
where $a>0$.
I have tried by using Mathematica, but it fails. Someone has any sugestion?
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1It's eliptic integral. It can't be written as an elementary function. – pointer Aug 19 '14 at 19:42
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For $x>0$ and $a>0$ the solution is $(1+x); _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-a(1+x)^3 \right)$ which contains a hypergeometric function. – Benedict W. J. Irwin Jun 01 '18 at 16:49