Engineering Board Exam Reviewer · Integration by Substitution · medium

Evaluate: x≤ft(x + 1 )3,dx

1. - 1/x + 1 - 12 ≤ft(x + 1 )2+C
2. 1/x + 1 - 12 ≤ft(x + 1 )2+C
3. - 12 ≤ft(x + 1 )2+C
4. - 1/x + 1 + 12 ≤ft(x + 1 )2+C

Answer

D. - 1/x + 1 + 12 ≤ft(x + 1 )2+C

Solution

Let u=x+1, so x=u-1. Then -1/u3,du= ≤ft(u-2-u-3 )du=- 1u+1/2u2+C=-1/x+1+1/2(x+1)2+C.

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