In this video I go over another example on integration by parts and proof the reduction formula for integrating sinⁿ(x) where n is any integer greater than or equal to 2.

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Integration by Parts: Example 6

Example: Prove the reduction formula:

Solution:

Note: This equation is called a reduction formula because the exponent n has been reduced to n - 1 and n - 2.

The reduction formula is useful because we could eventually express: