Chapter 7.2, Problem 49E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

# Evaluate the integral. ∫ x tan 2 x   d x

To determine

To evaluate: The trigonometric integral xtan2xdx

Explanation

Trigonometric integral can be solved using the various trigonometric identities which simplifies the integrand.

Formula used:

The identity cos2x=2cos2x1

and the identity sec2xtan2x=1

Given:

The integral, xtan2xdx.

Calculation:

Rewrite the given integral using the identity sec2xtan2x=1

xtan2xdx=x(sec2x1)dx

Solve the integral using integration by parts. Make the choice for u and dv such that the resulting integration from the formula above is easier to integrate. Let

u=x      dv=(sec2x1)dx

Then, the differentiation of u and antiderivative of dv will be

du=dx      v=tanxx

Substitute for variables in the formula above to get

xtan2xd

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Study Guide for Stewart's Multivariable Calculus, 8th