∫cos4xdx=∫(1−sin2x)2dx.
I tried using cos2(x)+sin2(x) = 1. This was on the integration by parts section of my textbook.
The integral I came out with is given me a hard time. I double checked my work and I feel I am on the right track but I feel stuck. I tried u substitution but there is no cosx to leverage with.
Answer
This is really the effect of what AWertheim is saying, and not that difficult.
cos4x=(cos2x)2=(1+cos(2x)2)2=14(1+2cos(2x)+cos2(2x))=14(1+2cos(2x)+1+cos(4x)2)=14+cos(2x)2+18+cos(4x)8=38+cos(2x)2+cos(4x)8.
The sole advantage here being that this form is very simple to integrate.
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