SOLUTION: Please help me solve this equation: Evaluate the integral {{{ int ( sin^2(3x)cos^5(3x), dx ) }}}

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Question 356868: Please help me solve this equation:
Evaluate the integral +int+%28+sin%5E2%283x%29cos%5E5%283x%29%2C+dx+%29+
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=3x, du=3dx

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%28sin%28u%29%29%5E2%2B%28cos%28u%29%29%5E2=1
%28cos%28u%29%29%5E2=1-%28sin%28u%29%29%5E2
%28cos%28u%29%29%5E4=1-%28sin%28u%29%29%5E4
Substitute,


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Let v=sin%28u%29, dv=cos%28u%29du



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Now the problem is reduced to a simple polynomial integration.
Integrate and then substitute back for v and then finally u.
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Additionally, this is not an algebra problem.