   Chapter 8.1, Problem 104E

Chapter
Section
Textbook Problem

PUTNAM EXAM CHALLENGEEvaluate ∫ 2 4 ln ( 9 − x ) d x ln ( 9 − x ) + ln ( x + 3 ) . This problem was composed by the Committee on the Putnam Prize Competition.© The Mathematical Association of America. All rights reserved.

To determine

To calculate: The value of the integral, 24ln(9x)dxln(9x)+ln(x+3).

Explanation

Given:

The definite integral 24ln(9x)dxln(9x)+ln(x+3).

Formula used:

Definite Integral Property, abf(x)dx=abf(a+bx)dx.

Calculation:

Consider the following definite integral:

24ln(9x)dxln(9x)+ln(x+3)

Follow these steps to calculate the definite integral as follows:

Let, I=24ln(9x)dxln(9x)+ln(x+3) …… (1)

Use abf(x)dx=abf(a+bx)dx the definite integral (1) can be reduced as shown below:

I=24ln(9(6x))ln(9

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