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 = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.85, size = 15, normalized size = 0.54 \[ \frac {3}{40} \, {\left (5 \, x^{2} - 8 \, x + 60\right )} x^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 0.57 \[ \frac {3}{8} \, x^{\frac {8}{3}} - \frac {3}{5} \, x^{\frac {5}{3}} + \frac {9}{2} \, x^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 0.57 \[ \frac {3 \left (5 x^{2}-8 x +60\right ) x^{\frac {2}{3}}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 16, normalized size = 0.57 \[ \frac {3}{8} \, x^{\frac {8}{3}} - \frac {3}{5} \, x^{\frac {5}{3}} + \frac {9}{2} \, x^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.54 \[ \frac {3\,x^{2/3}\,\left (5\,x^2-8\,x+60\right )}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.46, size = 24, normalized size = 0.86 \[ \frac {3 x^{\frac {8}{3}}}{8} - \frac {3 x^{\frac {5}{3}}}{5} + \frac {9 x^{\frac {2}{3}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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