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WZ
Numerade Educator

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Problem 54 Hard Difficulty

Use integration by parts to prove the reduction formula.

$ \displaystyle \int \sec^n x dx = \frac{\tan x \sec^{n - 2} x}{n - 1} + \frac{n - 2}{n - 1} \displaystyle \int \sec^{n - 2} x dx (n \neq 1) $

Answer

$ \tan x \sec ^{n-2} x +(n-2) \int \sec ^{n-1} x d x $

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Video Transcript

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