   Chapter 6.2, Problem 36E ### 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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# Using Integration Tables In Exercises 9-36, use the integration table in Appendix C to evaluate the definite integral. See Example 1, 2, 3, and 5. ∫ ( ln   x ) 3   d x

To determine

To calculate: The solution of indefinite integral (lnx)3dx.

Explanation

Given Information:

The expression is provided as;

(lnx)3dx

Formula used:

The formula for integral (lnu)2du is;

(lnu)2du=u[22lnu+(lnu)2]+C

The formula for integral (lnu)ndu is;

(lnu)ndu=u(lnu)nn(lnu)n1du

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x.

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

du=dx

Consider the provided expression:

(lnx)3dx

Substitute u for x, n for 3, and du for dx. as;

(lnx)3dx=(lnu)ndu

Use the formula (lnu)ndu=u(lnu)nn(lnu)n1

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