   Chapter 7.8, Problem 22E

Chapter
Section
Textbook Problem

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∫ 1 ∞ ln x x 2   d x

To determine

whether the given integral is convergent or divergent, evaluate it if convergent.

Explanation

Given:

1lnxx2dx

Formula used

f(x)g(x)dx=f(x)g(x)dx[f'(x)g(x)dx]dxlimxex=0

Let I=1lnxx2dx

Assume:lnx=t when x=1;t=0x=;t=

Therefore,

x=et;dt=1xdx so the given integralI=0tetdt=0tetdt

To evaluate the associated ind

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