Optimal. Leaf size=19 \[ \frac {a x^3}{3}+\frac {3}{8} b x^{8/3} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \[ \frac {a x^3}{3}+\frac {3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) x^2 \, dx &=\int \left (b x^{5/3}+a x^2\right ) \, dx\\ &=\frac {3}{8} b x^{8/3}+\frac {a x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 19, normalized size = 1.00 \[ \frac {a x^3}{3}+\frac {3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 13, normalized size = 0.68 \[ \frac {1}{3} \, a x^{3} + \frac {3}{8} \, b x^{\frac {8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.68 \[ \frac {1}{3} \, a x^{3} + \frac {3}{8} \, b x^{\frac {8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.74 \[ \frac {a \,x^{3}}{3}+\frac {3 b \,x^{\frac {8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 15, normalized size = 0.79 \[ \frac {1}{24} \, {\left (8 \, a + \frac {9 \, b}{x^{\frac {1}{3}}}\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.68 \[ \frac {a\,x^3}{3}+\frac {3\,b\,x^{8/3}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 15, normalized size = 0.79 \[ \frac {a x^{3}}{3} + \frac {3 b x^{\frac {8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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