Reduction Formula for Integral of ∫cot^n(x)dx

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

We can approach this problem by first reserving a cot^2(x), so we write:

cot^n(x) = cot^(n-2)(x)cott^2(x)

Then by the Pythagorean Identity, we can express cot^2(x) as csc^2(x) - 1, so...

cot^n(x) = cot^(n-2)(x)[csc^2(x) - 1] = cot^(n-2)(x)csc^2(x) - cot^(n-2)(x)

Thus we end up with 2 integrals.

Please watch the video for the full tutorial.

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