   Chapter 6.2, Problem 54E ### 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. ∫ 7 x   ln   7 x   d x

(a)

To determine

To calculate: The solution of indefinite integral 7xln7xdx using integration table in Appendix C.

Explanation

Given Information:

The expression is provided as:

7xln7xdx

Formula used:

The formula for the integral ulnudu is:

ulnudu=u24(1+2(lnu))+C.

The General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=7x.

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

du=7dx

Consider the provided expression:

7xln7xdx

Multiply and divide by 7.

7xln7xdx=17(7xln7x)7dx

Substitute u for 7x, and du for 7dx

(b)

To determine

To calculate: The solution of indefinite integral 7xln7xdx using integration by parts.

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