DTube: Reduction Formula for Integral of ∫cos^n(x)dx

In this video, we work through the derivation of the reduction formula for the integral of cosⁿ(x) or [cos(x)]ⁿ.

The first step is to rewrite the integral as:

∫cosⁿ(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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