[DTube] Reduction Formula for Integral of ∫sin^n(x)dx

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

We can approach this problem with integration by parts. The first step is to rewrite the integral as:

∫sinⁿ(x)dx = ∫sin^n-1(x)sin(x)dx

Thus we have 2 parts to the integral, where:

u = sin^n-1(x)
dv = sin(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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Integration: Reduction Formulas

1. Reduction Formula for Integral of ∫sin^n(x)dx
2. Reduction Formula for Integral of ∫cos^n(x)dx
3. Reduction Formula for Integral of ∫tan^n(x)dx

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