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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 5

Use the integration table in Appendix C to find ( ln x ) 3 d x .

To determine

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

Explanation

Given Information:

The integral is provided as:

(lnx)3dx

Formula used:

(1) The formula 44 for integral (lnu)2du is:

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

(2) The formula 45 for integral (lnu)ndu is:

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

(3) 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 integral:

(lnx)3dx

Substitute x=u, 3=n, and dx=du.

(lnx)3dx=(lnu)ndu

Use the formula 45 and solve the above integral as:

(lnx)3dx=u(lnu)nn(lnu)n1du

Substitute x for u and 3 for n

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