   Chapter 6.2, Problem 51E ### 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. ∫ ln   x 3 d x

(a)

To determine

To calculate: The solution of indefinite integral lnx3dx using integration table in Appendix C.

Explanation

Given Information:

The expression is provided as:

lnx3dx

Formula used:

The formula for the integral lnudu is:

lnudu=u(1+lnu)+C

The General power differentiation Rule;

ddx[un]=nun1dudx

Calculation:

Consider u=x3.

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

du=dx3

Consider the provided expression:

lnx3dx

Multiply and divide by 3.

lnx3dx=313lnx3dx=3(lnx3)dx3

Substitute u for x3, and du for dx3

(b)

To determine

To calculate: The solution of indefinite integral lnx3dx using integration by parts.

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