Tuesday, July 19, 2016

calculus - How to evaluate intsin3xcos3x:dx without a reduction formula?




We have the integral sin3xcos3xdx. You can do this using the reduction formula, but I wonder if there's another (perhaps simpler) way to do this, like for example with a substitution?


Answer



Hint. You may write
sin3xcos3x=sinx(1cos2x)cos3x=sinx(cos3xcos5x)


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