What is the integral of #sin(2x)cos^2(2x)dx#?

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Answer 1 · 2016-08-05T06:51:07

#int sin(2x)*cos^2(2x) d x=-1/6cos^3(2x)+C#

#int sin(2x)*cos^2(2x) d x=?#

#"Substitute "u=cos(2x)" ; "d u=-2sin(2x)*d x#

#int sin(2x)*cos^2(2x) d x=-1/2 int u^2*d u#

#"So ;" int u^n d u=1/(n+1)u^(n+1)#

#"Apply "n=2#

#int sin(2x)*cos^2(2x) d x=-1/2*1/3 u^3#

#"Now ;undo substitution"#

#int sin(2x)*cos^2(2x) d x=-1/6cos^3(2x)+C#