In this video, we work through the derivation of the reduction formula for the integral of cos^n(x) or [cos(x)]^n.
The first step is to rewrite the integral as:
∫cos^n(x)dx = ∫cos^n-1(x)cos(x)dx
Thus we have 2 parts to the integral, where:
u = cos^n-1(x)
dv = cos(x)dx
We can then proceed with integration by parts:
∫udv = uv - ∫vdu
Working through the substitutions and the steps, we eventually arrive at the reduction formula shown in the video.
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