   Chapter 7.4, Problem 21E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ d t ( t 2 − 1 ) 2

To determine

To evaluate the integral dt(t21)2

Explanation

Calculation: Given dt(t21)2

Resolve into partial fractions

1(t21)2=1(t1)2(t+1)2=At+1+B(t+1)2+Ct1+D(t1)21=A(t+1)(t1)2+B(t1)2+C(t+1)2(t1)+D(t+1)21=(A+C)t3+(A+B+C+D)t2+(A2BC+2D)t+(A+BC+D)A+C=0,A+B+C+D=0,A2BC+2D=0,A+BC+D=1on solving, we getA=14,B=14,C=14,D=141(t21)2=14t+1+14(t+1)</

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