Optimal. Leaf size=51 \[ \frac {3}{8} a^3 x^{8/3}+\frac {9}{11} a^2 b x^{11/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {3}{17} b^3 x^{17/3} \]
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Rubi [A]
time = 0.01, antiderivative size = 51, 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 = {45}
\begin {gather*} \frac {3}{8} a^3 x^{8/3}+\frac {9}{11} a^2 b x^{11/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {3}{17} b^3 x^{17/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{5/3} (a+b x)^3 \, dx &=\int \left (a^3 x^{5/3}+3 a^2 b x^{8/3}+3 a b^2 x^{11/3}+b^3 x^{14/3}\right ) \, dx\\ &=\frac {3}{8} a^3 x^{8/3}+\frac {9}{11} a^2 b x^{11/3}+\frac {9}{14} a b^2 x^{14/3}+\frac {3}{17} b^3 x^{17/3}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 39, normalized size = 0.76 \begin {gather*} \frac {3 x^{8/3} \left (1309 a^3+2856 a^2 b x+2244 a b^2 x^2+616 b^3 x^3\right )}{10472} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.71
method | result | size |
gosper | \(\frac {3 x^{\frac {8}{3}} \left (616 b^{3} x^{3}+2244 a \,b^{2} x^{2}+2856 a^{2} b x +1309 a^{3}\right )}{10472}\) | \(36\) |
derivativedivides | \(\frac {3 a^{3} x^{\frac {8}{3}}}{8}+\frac {9 a^{2} b \,x^{\frac {11}{3}}}{11}+\frac {9 a \,b^{2} x^{\frac {14}{3}}}{14}+\frac {3 b^{3} x^{\frac {17}{3}}}{17}\) | \(36\) |
default | \(\frac {3 a^{3} x^{\frac {8}{3}}}{8}+\frac {9 a^{2} b \,x^{\frac {11}{3}}}{11}+\frac {9 a \,b^{2} x^{\frac {14}{3}}}{14}+\frac {3 b^{3} x^{\frac {17}{3}}}{17}\) | \(36\) |
trager | \(\frac {3 x^{\frac {8}{3}} \left (616 b^{3} x^{3}+2244 a \,b^{2} x^{2}+2856 a^{2} b x +1309 a^{3}\right )}{10472}\) | \(36\) |
risch | \(\frac {3 x^{\frac {8}{3}} \left (616 b^{3} x^{3}+2244 a \,b^{2} x^{2}+2856 a^{2} b x +1309 a^{3}\right )}{10472}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 35, normalized size = 0.69 \begin {gather*} \frac {3}{17} \, b^{3} x^{\frac {17}{3}} + \frac {9}{14} \, a b^{2} x^{\frac {14}{3}} + \frac {9}{11} \, a^{2} b x^{\frac {11}{3}} + \frac {3}{8} \, a^{3} x^{\frac {8}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.61, size = 40, normalized size = 0.78 \begin {gather*} \frac {3}{10472} \, {\left (616 \, b^{3} x^{5} + 2244 \, a b^{2} x^{4} + 2856 \, a^{2} b x^{3} + 1309 \, a^{3} 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 = 0.59, size = 49, normalized size = 0.96 \begin {gather*} \frac {3 a^{3} x^{\frac {8}{3}}}{8} + \frac {9 a^{2} b x^{\frac {11}{3}}}{11} + \frac {9 a b^{2} x^{\frac {14}{3}}}{14} + \frac {3 b^{3} x^{\frac {17}{3}}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.87, size = 35, normalized size = 0.69 \begin {gather*} \frac {3}{17} \, b^{3} x^{\frac {17}{3}} + \frac {9}{14} \, a b^{2} x^{\frac {14}{3}} + \frac {9}{11} \, a^{2} b x^{\frac {11}{3}} + \frac {3}{8} \, a^{3} x^{\frac {8}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 35, normalized size = 0.69 \begin {gather*} \frac {3\,a^3\,x^{8/3}}{8}+\frac {3\,b^3\,x^{17/3}}{17}+\frac {9\,a^2\,b\,x^{11/3}}{11}+\frac {9\,a\,b^2\,x^{14/3}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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