Optimal. Leaf size=19 \[ \frac {a x^4}{4}+\frac {3}{11} b x^{11/3} \]
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Rubi [A] time = 0.01, 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} \[ \frac {a x^4}{4}+\frac {3}{11} b x^{11/3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) x^3 \, dx &=\int \left (b x^{8/3}+a x^3\right ) \, dx\\ &=\frac {3}{11} b x^{11/3}+\frac {a x^4}{4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {a x^4}{4}+\frac {3}{11} b x^{11/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 13, normalized size = 0.68 \[ \frac {1}{4} \, a x^{4} + \frac {3}{11} \, b x^{\frac {11}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 13, normalized size = 0.68 \[ \frac {1}{4} \, a x^{4} + \frac {3}{11} \, b x^{\frac {11}{3}} \]
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 \[ \frac {a \,x^{4}}{4}+\frac {3 b \,x^{\frac {11}{3}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 15, normalized size = 0.79 \[ \frac {1}{44} \, {\left (11 \, a + \frac {12 \, b}{x^{\frac {1}{3}}}\right )} x^{4} \]
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 \[ \frac {a\,x^4}{4}+\frac {3\,b\,x^{11/3}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.24, size = 15, normalized size = 0.79 \[ \frac {a x^{4}}{4} + \frac {3 b x^{\frac {11}{3}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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