   Chapter 5.4, Problem 3E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Verify by differentiation that the formula is correct. ∫ tan 2 x   d x = tan x − x + C

To determine

To verify: The integral function using differentiation.

Explanation

Given information:

The integral function is tan2xdx=tanxx+C (1)

Verify the integral function using the procedure as follows:

• Differentiate the right side function with respect to x.
• Check whether the differential value matches with the left side function.
• If it matches, then the solution is correct, otherwise it is incorrect.

Take the right side function in Equation (1) and differentiate with respect to x.

ddx[tanxx+C]=sec2x1+0=

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Study Guide for Stewart's Multivariable Calculus, 8th 