Engineering Board Exam Reviewer · Integration by Substitution · easy

Evaluate: x + 1x2 + 2 x + 5,dx

1. ≤ft(x2 + 2 x + 5 )2+C
2. ≤ft(x2 + 2 x + 5 )+C
3. ≤ft(x/2 + 1/2 )2+C
4. ≤ft(x2 + 2 x + 5 )4+C

Answer

A. ≤ft(x2 + 2 x + 5 )2+C

Solution

The numerator is half the derivative of the denominator: with u=x2+2x+5, du=(2x+2),dx, so +1/x2+2x+5,dx= 12 (x2+2x+5)+C.

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6. Evaluate: x/x,dx
7. Evaluate: x/ex+1,dx
8. Evaluate: x2(x3-2)4,dx
9. Evaluate: 1sqrt(x) ≤ft(sqrt(x) + 1 )3,dx
10. Evaluate: ≤ft(x )≤ft( ≤ft(x ) + 1 )3,dx

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