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If $m$ and $n$ are integers greater than one, does the function $f(t)=[\frac{m-n}{m+1}-t^{n+1}]^{-\frac{1}{m+1}}$ have an elementary indefinite integral?

I have tried to find the integral by trigonometric substitution but I could not find the answer, (supposing that the integral exists).

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Already for certain simple cases like $m=1$ and $n=2$ or $3$, definitely no elementary antiderivative. –  André Nicolas Oct 4 '12 at 13:59

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