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

Evaluate: 1x2 ≤ft(x + 1 ),dx (assume x>0)

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

Answer

C. - x + ≤ft|x + 1 | - 1/x+C

Solution

Write 1/x2(x+1)=- 1x+1/x2+1/x+1. Integrating: - x- 1x+ (x+1)+C for x>0.

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