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 = {45}
\begin {gather*} \frac {3}{8} a x^{8/3}+\frac {3}{11} b x^{11/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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 \begin {gather*} \frac {3}{88} x^{8/3} (11 a+8 b x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.67
method | result | size |
gosper | \(\frac {3 x^{\frac {8}{3}} \left (8 b x +11 a \right )}{88}\) | \(14\) |
derivativedivides | \(\frac {3 a \,x^{\frac {8}{3}}}{8}+\frac {3 b \,x^{\frac {11}{3}}}{11}\) | \(14\) |
default | \(\frac {3 a \,x^{\frac {8}{3}}}{8}+\frac {3 b \,x^{\frac {11}{3}}}{11}\) | \(14\) |
trager | \(\frac {3 x^{\frac {8}{3}} \left (8 b x +11 a \right )}{88}\) | \(14\) |
risch | \(\frac {3 x^{\frac {8}{3}} \left (8 b x +11 a \right )}{88}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{11} \, b x^{\frac {11}{3}} + \frac {3}{8} \, a x^{\frac {8}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.75, size = 18, normalized size = 0.86 \begin {gather*} \frac {3}{88} \, {\left (8 \, b x^{3} + 11 \, a x^{2}\right )} x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.28, size = 19, normalized size = 0.90 \begin {gather*} \frac {3 a x^{\frac {8}{3}}}{8} + \frac {3 b x^{\frac {11}{3}}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.02, size = 13, normalized size = 0.62 \begin {gather*} \frac {3}{11} \, b x^{\frac {11}{3}} + \frac {3}{8} \, a x^{\frac {8}{3}} \end {gather*}
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 \begin {gather*} \frac {3\,x^{8/3}\,\left (11\,a+8\,b\,x\right )}{88} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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