



 
Hi Ascher, Write sin^{3}(2x) as sin^{2}(2x) sin(2x) and then use the fact that sin^{2}(y) + cos^{2}(y) = 1. Write back if you need more help, Penny
Remember how recipes say "set one egg aside"? Well, set one of the sines aside: integral of sin^{2} (2x) sin(2x) dx Now use the Pythagorean identity to rewrite in cosines: integral of (1  cos^{2}(2x)) sin(2x) dx and integrate by substitution, using u = cos(2x), (1/2)du = sin(x)dx. This or a similar trick can be used whenever you have: an odd power of sine and any power of cosine Only the cases with sin^{even} cos^{even} and tan^{even} sec^{odd} need special methods. Good Hunting!  


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