Optimal. Leaf size=21 \[ \frac {3}{8} a x^{8/3}+\frac {3}{11} b x^{11/3} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ \frac {3}{8} a x^{8/3}+\frac {3}{11} b x^{11/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^{5/3} (a+b x) \, dx &=\int \left (a x^{5/3}+b x^{8/3}\right ) \, dx\\ &=\frac {3}{8} a x^{8/3}+\frac {3}{11} b x^{11/3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.81 \[ \frac {3}{88} x^{8/3} (11 a+8 b x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 18, normalized size = 0.86 \[ \frac {3}{88} \, {\left (8 \, b x^{3} + 11 \, a x^{2}\right )} x^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 13, normalized size = 0.62 \[ \frac {3}{11} \, b x^{\frac {11}{3}} + \frac {3}{8} \, a x^{\frac {8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.67 \[ \frac {3 \left (8 b x +11 a \right ) x^{\frac {8}{3}}}{88} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 13, normalized size = 0.62 \[ \frac {3}{11} \, b x^{\frac {11}{3}} + \frac {3}{8} \, a x^{\frac {8}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.62 \[ \frac {3\,x^{8/3}\,\left (11\,a+8\,b\,x\right )}{88} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.01, size = 19, normalized size = 0.90 \[ \frac {3 a x^{\frac {8}{3}}}{8} + \frac {3 b x^{\frac {11}{3}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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