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

Evaluate: x2 + 1x ≤ft(x - 1 )2,dx (for x>1)

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

Answer

D. x - 2/x - 1+C

Solution

Write x2+1/x(x-1)2=A/x+B/x-1+C/(x-1)2. Then A=1, C=2, and comparing the x2 coefficients gives A+B=1, so B=0. Integrating 1x+2/(x-1)2 gives x-2/x-1+C.

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