   Chapter 7.8, Problem 30E

Chapter
Section
Textbook Problem

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∫ − 1 2 x ( x + 1 ) 2   d x

To determine

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

Explanation

Given:

12x(x+1)2dx

Formula used:

1xdx=logx+cxndx=xn+1n+1+c

Let I=12x(x+1)2dx

By partial fraction method:

x(x+1)2=A(x+1)+B(x+1)2 (I)

x=A(x+1)+Bx=Ax+(A+B)A=1B+A=0

Therefore,

B=1

Substitute values of A and B in equation (I)

I=121x+1dx121(x+1)2dx

Since integral is not defined at x=1

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