This is intended to be an example of an elliptic integral but I'm not sure how to go about showing it. I'm not sure which identities to start with, any tips would be greatly appreciated!
2026-03-28 06:00:33.1774677633
Show that $\int_0^{\pi/2} \frac{dt}{\sqrt{\sin t}}=\int_0^1 \frac{dx}{\sqrt{x-x^3}}$
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Use the u-sub $x = \sin(t)$, $dx = \cos(t)\, dt$. A little cancellation makes the whole thing work.