How do you find the antiderivative of $x^{\frac{3}{2}}$ $x^(3/2)$ ?

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Answer 1 · 2016-10-20T16:25:57

$\frac{2}{5} {\sqrt{x}}^{5}$ $2/5 sqrt x^5$ + c

$\int x^{\frac{3}{2}} d x$ $int x^(3/2) dx$

= $\frac{x^{\frac{3}{2} + 1}}{(\frac{3}{2} + 1)}$ $x^(3/2 + 1)/((3/2 +1)$

= $\frac{x^{\frac{5}{2}}}{\frac{5}{2}}$ $x^(5/2)/(5/2)$

= $\frac{2}{5} x^{\frac{5}{2}} + c$ $2/5x^(5/2) + c$

= $\frac{2}{5} {\sqrt{x}}^{5}$ $2/5 sqrt x^5$ + c

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