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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.2012-10-04

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If $m=n$:

$$f(t)=\left(-t^{n+1}\right)^{-\frac{1}{n+1}}$$

$$=(-1)^{-\frac{1}{n+1}}t^{-1}$$

$$\int (-1)^{-\frac{1}{n+1}}t^{-1}dt=(-1)^{-\frac{1}{n+1}}\ln(t)+c$$