Finding antiderivative of cos^5(x)...  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Finding antiderivative of cos^5(x)...

Postby nuadre on Fri May 29, 2009 2:58 am

Hey can anyone help me with question 34 of exercise 9C. I've done it about 10 times and cant get it right.

FInd the antiderivative of:

cos ^5x or (cosx)^5

Ive been doing:

=(cosx)(cos^2x)^2
=(cosx)((cos2x+1)/2)^2
=cosx(1/4 + cos2x/2 + cos^2(2x)/4)

This is the point where I get stuck.
I've gone
= cosx/4 + cos3x/2 + cos^2(3x)/4
I know its not right. Can anyone help me get to the solution?
Answer: y= sinx -2/3sin^3(x) + 1/5sin^5(x)

Cheers! Been bugging me all yesterday because all the next questions are similar.
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Re: Finding antiderivative of cos^5(x)...  TOPIC_SOLVED

Postby Martingale on Fri May 29, 2009 4:18 am

nuadre wrote:Hey can anyone help me with question 34 of exercise 9C. I've done it about 10 times and cant get it right.

FInd the antiderivative of:

cos ^5x or (cosx)^5

Ive been doing:

=(cosx)(cos^2x)^2
=(cosx)((cos2x+1)/2)^2
=cosx(1/4 + cos2x/2 + cos^2(2x)/4)

This is the point where I get stuck.
I've gone
= cosx/4 + cos3x/2 + cos^2(3x)/4
I know its not right. Can anyone help me get to the solution?
Answer: y= sinx -2/3sin^3(x) + 1/5sin^5(x)

Cheers! Been bugging me all yesterday because all the next questions are similar.






now let
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