AP Calculus ABmediummcq1 pt

Which of the following equals xxdx\int x\sqrt{x}\,dx?

A.25x5/2+C\frac{2}{5}x^{5/2}+C
B.23x3/2+C\frac{2}{3}x^{3/2}+C
C.x222x3/23+C\frac{x^2}{2}\cdot\frac{2x^{3/2}}{3}+C
D.25x5/2\frac{2}{5}x^{5/2}

Explanation

Core Concept

Rewrite as x3/2x^{3/2} and integrate: x5/25/2=25x5/2+C\frac{x^{5/2}}{5/2}=\frac{2}{5}x^{5/2}+C.

Correct Answer

A25x5/2+C\frac{2}{5}x^{5/2}+C

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