How do you find the integral of $\int {sec}^{n} (x)$ $int sec^n(x)$ if m or n is an integer?

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How do you find the integral of $\int {sec}^{n} (x)$ $int sec^n(x)$ if m or n is an integer?

1 Answer

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Answer 1 · 2018-03-26T02:42:15

See Explanation

Explanation:

The proof for this is pretty lengthy, but I've found a good explanation showing it here: https://www.enotes.com/homework-help/integral-sec-n-x-dx-722738

In essence, it comes down to this formula (also known as integral reduction)

$\int {sec}^{n} d x = \frac{{sec}^{n - 1} sin x}{n - 1} + \frac{n - 2}{n - 1} \int {sec}^{n - 2} d x$ $intsec^ndx=(sec^(n-1)sinx)/(n-1)+(n-2)/(n-1)intsec^(n-2)dx$

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How do you find the integral of $\int {sec}^{n} (x)$ $int sec^n(x)$ if m or n is an integer?

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Explanation:

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How do you find the integral of ∫secn(x)int sec^n(x) if m or n is an integer?

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How do you find the integral of $\int {sec}^{n} (x)$ $int sec^n(x)$ if m or n is an integer?