Chapter 7.5, Problem 15E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Evaluate the integral.15. ∫ x sec x tan x   d x

To determine

To evaluate: The integral function xsecxtanxdx.

Explanation

Given information:

The integral function is âˆ«xsecxtanxâ€‰dx.

Calculation:

Show the integral function as follows:

âˆ«xsecxtanxâ€‰dx (1)

Consider u=x (2)

Differentiate both sides of the equation (2).

dudx=1du=dx

Consider dv=secxtanxâ€‰dx (3)

Integrate both sides of Equation (3).

âˆ«dv=âˆ«secxtanxâ€‰dx (4)

Show the formula for integration.

âˆ«secxtanxâ€‰dx=secx (5)

Apply Equation (5) in Equation (4).

âˆ«dv=âˆ«secxtanxâ€‰dx=secxv=secx

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