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cos^3 x
= (cos^2 x)(cos x)
= (1-sin^2 x)(cos x)
= cos x - (sin^2 x)(cos x)
after integration,
it become:
= -sin x - (1/3)(sin^3 x) + c
I started the same way - (I didn't know it was called substitution, i had been calling it by-parts)
The correct answer, or the one at the back of the book is,
1/3sinx (3cos^2 x + 2sin^2 x)