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As far as that first integral, i would just replace (sin x)^3 with (1-(cos x)^2)(sin x) and sub in with u=cos x
Hey, I know how to solve it now, too!
Your question is so inspiring! I used to think this kinda trig and derivative mix is my last-to-solve.
It's solved now. Thanks George, even though it's not what I was looking for... again.
I've written the proof or the derivation in post 3, following Ricky's fomula, so you can check my procedure and simply duplicate it before showing the formula. And that will make your solution complete.
Since the equation is not seperable and not homogenous, I don't believe there is any other way to solve it.
I've learned to not use formulas straight off like that, I learn nothing from it. Kinda ugly, yeah. But thanks anyway for showing that formula, might get in handy, though I preferably do everything from scratch.
http://www.mathsisfun.com/forum/viewtop … 635#p32635
This ugly equation comes out to be: