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

Evaluate: x3 + 2x2 - 1,dx

1. x22 + ≤ft|x + 1 |/2 - 3 ≤ft|x - 1 |/2+C
2. x22 - 3 ≤ft|x + 1 |/2 + ≤ft|x - 1 |/2+C
3. x22 + ≤ft|x2 - 1 |+C
4. x22 - ≤ft|x + 1 |/2 + 3 ≤ft|x - 1 |/2+C

Answer

D. x22 - ≤ft|x + 1 |/2 + 3 ≤ft|x - 1 |/2+C

Solution

The degree of the numerator exceeds that of the denominator, so divide first: x3+2/x2-1=x+x+2/x2-1, and x+2/(x-1)(x+1)=3/2/x-1-1/2/x+1. Integrating: x2/2+ 32 |x-1|- 12 |x+1|+C.

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