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.