Reduction Formula for Cosine Powers

Rarely Tested

Reduction Formula for Cosine Powers

Define:

$$I_n=\int\cos^n x\,dx$$

Then:

$$I_n=\frac{\sin x\cos^{n-1}x}{n}+\frac{n-1}{n}I_{n-2}$$

Usage

- Used to reduce an integral involving a high power of cosine.

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