How can this definite integral be represented in the form of $\beta$ function ?
$ \int_0^1 \frac{x dx}{\sqrt{1-x^5}} $
The answer is $\frac{1}{5}\beta (\frac{2}{5}, \frac{1}{2})$ but I am not sure how to reach here
2026-03-28 06:05:48.1774677948
Express the integral as beta function
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Perform the substitution $u= x^5$, $x = u^{1/5}$, $dx = (1/5)u^{-4/5}$.