how do i take antiderivative of (cosx)^3
antiderivative = integral
to get the integral of this, note that we can rewrite (cos x)^3 as (cos x)(cos x)^2 . then recall that (cos x)^2 = 1 - (sin x)^2 ,, rewriting:
integral of [ (cos x)(1 - (sin x)^2) ] dx
then we let
u = sin x ; and thus
du = cos x dx
substituting these,
integral [ (1 - u^2) ] du
we can integrate this right away:
u - (u^3)/3 + C
where C = inegration constant
substituting back the value of u:
sin x - [ (sin x)^3 ]/3 + C
hope this helps~ :)