   Chapter 8.3, Problem 29E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral Involving Secant and Tangent In Exercises 21–34, find the indefinite integral. ∫ sec 5 x tan 3 x d x

To determine

To calculate: The indefinite integral of the following expression sec5xtan3xdx

Explanation

Given: The provided expression is sec5xtan3xdx

Formula Used:

The following trigonometric identity,

1+tan2x=sec2x

The following differential formula,

ddxsecx=tanxsecx

The following integral formula,

(yn)dy=yn+1n+1+C

Calculation:

Consider the provided integral, sec5xtan3xdx.

sec5xtan3xdx=sec4xtan2x(tanxsecx)dxsec5xtan3xdx=sec4x(sec2x1)(tanxsecx)dxsec5xtan3xdx=(sec6xsec4x)(tanxsecx)dx

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