Tuesday, 11 August 2015

calculus - Integrate intcos4x,mathrmdx.



cos4xdx=(1sin2x)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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