Optimal. Leaf size=28 \[ \frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2} \]
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Rubi [A] time = 0.0044893, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {14} \[ \frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{3-x+x^2}{\sqrt [3]{x}} \, dx &=\int \left (\frac{3}{\sqrt [3]{x}}-x^{2/3}+x^{5/3}\right ) \, dx\\ &=\frac{9 x^{2/3}}{2}-\frac{3 x^{5/3}}{5}+\frac{3 x^{8/3}}{8}\\ \end{align*}
Mathematica [A] time = 0.0049692, size = 19, normalized size = 0.68 \[ \frac{3}{40} x^{2/3} \left (5 x^2-8 x+60\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 16, normalized size = 0.6 \begin{align*}{\frac{15\,{x}^{2}-24\,x+180}{40}{x}^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0002, size = 22, normalized size = 0.79 \begin{align*} \frac{3}{8} \, x^{\frac{8}{3}} - \frac{3}{5} \, x^{\frac{5}{3}} + \frac{9}{2} \, x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.182, size = 45, normalized size = 1.61 \begin{align*} \frac{3}{40} \,{\left (5 \, x^{2} - 8 \, x + 60\right )} x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.96746, size = 24, normalized size = 0.86 \begin{align*} \frac{3 x^{\frac{8}{3}}}{8} - \frac{3 x^{\frac{5}{3}}}{5} + \frac{9 x^{\frac{2}{3}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.891, size = 22, normalized size = 0.79 \begin{align*} \frac{3}{8} \, x^{\frac{8}{3}} - \frac{3}{5} \, x^{\frac{5}{3}} + \frac{9}{2} \, x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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