Evaluate: ∫ x√(x + 2) dx
Evaluate: ∫ x√(x + 2) dx
- A. (2/5)(x+2)^(5/2) - (4/3)(x+2)^(3/2) + C
- B. (2/5)(x+2)^(5/2) + (4/3)(x+2)^(3/2) + C
- C. (x+2)^(5/2) - (x+2)^(3/2) + C
- D. (2/3)x(x+2)^(3/2) + C
Answer: A) (2/5)(x+2)^(5/2) - (4/3)(x+2)^(3/2) + C
Explanation: Let x + 2 = t. x = t - 2. dx = dt. ∫ (t - 2)√t dt = ∫ (t^(3/2) - 2t^(1/2)) dt = (2/5)t^(5/2) - (4/3)t^(3/2) + C.
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