Engineering Board Exam Reviewer · Partial Fractions and Rational Integrals · medium

Evaluate: 3 x + 5≤ft(x - 1 )2 ≤ft(x + 1 ),dx

1. ≤ft|x + 1 |/2 - ≤ft|x - 1 |/2 - 4/x - 1+C
2. ≤ft|x + 1 |/2 - ≤ft|x - 1 |/2 + 4/x - 1+C
3. ≤ft|x + 1 |/2 + ≤ft|x - 1 |/2 - 4/x - 1+C
4. ≤ft|x + 1 | - ≤ft|x - 1 |/2 - 4/x - 1+C

Answer

A. ≤ft|x + 1 |/2 - ≤ft|x - 1 |/2 - 4/x - 1+C

Solution

Write 3x+5/(x-1)2(x+1)=A/x-1+B/(x-1)2+C/x+1. Then B=4 (at x=1), C= 12 (at x=-1), and A+C=0 gives A=- 12. Integrating: - 12 |x-1|-4/x-1+ 12 |x+1|+C.

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