   Chapter 6.2, Problem 52E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Indefinite Integrals Using Two Methods In Exercises 51–54, find the indefinite integral (a) using the integration table in Appendix C and (b) using integration by parts. ∫ 4 x e 4 x   d x

(a)

To determine

To calculate: The solution of indefinite integral 4xe4xdx using integration table in Appendix C.

Explanation

Given Information:

The expression is provided as:

4xe4xdx

Formula used:

The formula for the integral ueudu is:

ueudu=(u1)eu+C

The general power differentiation Rule is;

ddx[un]=nun1dudx

Calculation:

Consider u=4x.

Differentiate the considered function with respect to x using power rule of differentiation.

du=4dx

Consider the provided expression:

4xe4xdx

Multiply and divide by 4.

4xe4xdx=14(4xe4x)4dx

Substitute u for 4x, and du for 4dx

(b)

To determine

To calculate: The solution of indefinite integral 4xe4xdx using integration by parts.

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