Engineering Board Exam Reviewer · Integration by Substitution · medium

Evaluate: 1sqrt(x) ≤ft(sqrt(x) + 1 )3,dx

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

Answer

C. - 1≤ft(sqrt(x) + 1 )2+C

Solution

Let u=1+sqrt(x), du= dx2sqrt(x). Then 2,du/u3=-1/u2+C=- 1(1+sqrt(x))2+C.

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