   Chapter 7.2, Problem 21E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ tan x sec 3 x   d x

To determine

To evaluate: The trigonometric integral tanxsec3xdx

Explanation

Trigonometric integral of the form tanmxsecnxdx can be solved using strategies depending on whether m and n are odd or even.

Formula used:

When power of tangent in the integral is odd, save one secxtanx factor and use the identity tan2x=sec2x1 to rewrite other terms in secant function form:

tan2k+1xsecnxdx=(sec2x1)ksecn1xsecxtanxdx

Then, use the substitution u=secx

Given:

The integral, tanxsec3xdx

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