How do you solve $$ \int\sqrt{\sin(t)}dt $$ using the substitution method.
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that one is solved in a different way. – user103816 Oct 30 '13 at 14:49
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i did this in two more different ways a long time ago just cant recall that's why i put it as such. i was somehow able to convert this in a polynomial type. – user103816 Oct 30 '13 at 14:51
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You can get something like this: $\int_{0}^\frac{\pi}{2}\sqrt\sin x\sqrt\cos x dx$ in terms of the gamma function. Then use a simple trigonometric substitution. (See Whittaker and Watson p.256 . But it isn't elementary and it's a definite integral.) – Alan Oct 30 '13 at 16:04
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i think i can solve it i'll put answer after a few days. – user103816 Oct 30 '13 at 16:17
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https://archive.org/stream/courseofmodernan00whit#page/256/mode/2up ;) nice book. – user103816 Oct 30 '13 at 16:32
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Really duplicate to http://math.stackexchange.com/questions/177709? OP want this question to avoid using elliptic functions, while http://math.stackexchange.com/questions/177709 has not this restriction. – doraemonpaul Nov 01 '13 at 04:01