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[tex]\int cos^{8}(x)dx=\frac{1}{8}cos^{7}(x).sin(x)+\frac{7}{48}cos^{5}(x).sin(x)+\frac{35}{192}cos^{3}(x).sin(x)+\frac{35}{128}cos(x).sin(x)+\frac{35}{128}(x)+c[/tex]

I have looked through my text book and found a good example which will help me, the book uses a thing they are calling a recursive formula. I've done some research and I've seen the same formula from lots of different information sources.

Exhibit A: http://calc101.com/deriving_reduction_2.html

[STRIKE]They have all given demonstrations on how to get the formula, but when I try to do it myself I run into a problem when differentiating the first function [tex]cos^{n-1}(x)[/tex][/STRIKE]

Nevermind I was integrating haha, but still; obviously I am rusty on my differentiation techniques so if someone could check this for me that would be fantastic (mainly concerned with my procedure for communication marks etc.) :)

[tex]y=cos^{n-1}(x)[/tex]

Allow cos(x) to equal u

[tex]\frac{dy}{dx}=u^{n-1}.............1[/tex]

[tex]\frac{du}{dx}=-sin(x)[/tex]

[tex]\frac{du}{-sin(x)}=dx..............2[/tex]

Sub 2 into 1

[tex]\frac{dy}{\frac{du}{-sin(x)}}=u^{n-1}[/tex]

[tex]\frac{dy}{du}=(n-1)u^{n-1-1}.-sin(x)[/tex]

[tex]\frac{dy}{du}=(n-1)u^{n-2}.-sin(x)[/tex]

But u = cosx

[tex]\frac{dy}{du}=(n-1)cos^{n-2}(x).-sin(x)[/tex]