Solve \int \sec^n x dx for n0

Question:

Solve {eq}\int \sec^n \ x \ dx \ {/eq} for {eq}n>0 {/eq}

Indefinite Integral:

The indefinite integral of trigonometric functions can either be reduced to the standard form or can be applied with the trigonometric identity to form an integral in the standard result form.

Answer and Explanation:


As we know that the integral of:

{eq}\int \sec ^n\left(x\right)dx=\frac{\sec ^{n-1}\left(x\right)\sin \left(x\right)}{n-1}+\frac{n-2}{n-1}\int \sec ^{n-2}\left(x\right)dx\\ {/eq}

using the standard result.


Learn more about this topic:

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Indefinite Integral: Definition, Rules & Examples

from Calculus: Tutoring Solution

Chapter 7 / Lesson 14
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