# What is the integral of #cos^5(x)#?

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Gaurav
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Dec 16, 2014

Explanation :

From trigonometric identity, which is

#cos^2x+sin^2x=1# ,#=>cos^2x=1-sin2x#

let's assume

#sinx = t# ,#=> (cosx) dx= dt# substituting this in the

#(i)# , we get

Now using expansion of

#(1-y)^2=1+y^2-2y# , yields,

now substituting

#t# back gives,

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