   Chapter 6.2, Problem 17QY ### 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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# In Exercises 16–21, use integration by parts or the integration table in Appendix C to evaluate the definite integral. ∫ 1 2 5 x   ln   x   d x

To determine

To calculate: The value of definite integral 125xlnxdx.

Explanation

Given Information:

The definite integral is,

125xlnxdx

Formula used:

(1) The formula 42 for integral ulnudu is:

ulnudu=u24[1+2lnu]+C

(2) General power differentiation Rule:

ddx[un]=nun1dudx

Here, n is the any number.

Calculation:

Consider u=x.

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

du=dx

Consider the provided integral:

125xlnxdx

Rewrite.

125xlnxdx=512xlnxdx

Substitute u for x, and du for dx

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