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

Evaluate: 4 xx4 - 1,dx

1. - ≤ft(x2 + 1 ) + ≤ft|x2 - 1 |+C
2. ≤ft(x2 + 1 ) + ≤ft|x2 - 1 |+C
3. - ≤ft(x2 + 1 ) + 2 ≤ft|x2 - 1 |+C
4. - 2 ≤ft(x2 + 1 ) + ≤ft|x2 - 1 |+C

Answer

A. - ≤ft(x2 + 1 ) + ≤ft|x2 - 1 |+C

Solution

Factor x4-1=(x2-1)(x2+1): 4x/(x2-1)(x2+1)=2x/x2-1-2x/x2+1. Integrating: |x2-1|- (x2+1)+C.

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