Optimal. Leaf size=36 \[ \frac {3}{8} a^2 x^{8/3}+\frac {6}{11} a b x^{11/3}+\frac {3}{14} b^2 x^{14/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 36, 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^2 x^{8/3}+\frac {6}{11} a b x^{11/3}+\frac {3}{14} b^2 x^{14/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{5/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{5/3}+2 a b x^{8/3}+b^2 x^{11/3}\right ) \, dx\\ &=\frac {3}{8} a^2 x^{8/3}+\frac {6}{11} a b x^{11/3}+\frac {3}{14} b^2 x^{14/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 28, normalized size = 0.78 \begin {gather*} \frac {3}{616} x^{8/3} \left (77 a^2+112 a b x+44 b^2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 25, normalized size = 0.69
method | result | size |
gosper | \(\frac {3 x^{\frac {8}{3}} \left (44 x^{2} b^{2}+112 a b x +77 a^{2}\right )}{616}\) | \(25\) |
derivativedivides | \(\frac {3 a^{2} x^{\frac {8}{3}}}{8}+\frac {6 a b \,x^{\frac {11}{3}}}{11}+\frac {3 b^{2} x^{\frac {14}{3}}}{14}\) | \(25\) |
default | \(\frac {3 a^{2} x^{\frac {8}{3}}}{8}+\frac {6 a b \,x^{\frac {11}{3}}}{11}+\frac {3 b^{2} x^{\frac {14}{3}}}{14}\) | \(25\) |
trager | \(\frac {3 x^{\frac {8}{3}} \left (44 x^{2} b^{2}+112 a b x +77 a^{2}\right )}{616}\) | \(25\) |
risch | \(\frac {3 x^{\frac {8}{3}} \left (44 x^{2} b^{2}+112 a b x +77 a^{2}\right )}{616}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 24, normalized size = 0.67 \begin {gather*} \frac {3}{14} \, b^{2} x^{\frac {14}{3}} + \frac {6}{11} \, a b x^{\frac {11}{3}} + \frac {3}{8} \, a^{2} x^{\frac {8}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.65, size = 29, normalized size = 0.81 \begin {gather*} \frac {3}{616} \, {\left (44 \, b^{2} x^{4} + 112 \, a b x^{3} + 77 \, a^{2} 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 = 0.42, size = 34, normalized size = 0.94 \begin {gather*} \frac {3 a^{2} x^{\frac {8}{3}}}{8} + \frac {6 a b x^{\frac {11}{3}}}{11} + \frac {3 b^{2} x^{\frac {14}{3}}}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.63, size = 24, normalized size = 0.67 \begin {gather*} \frac {3}{14} \, b^{2} x^{\frac {14}{3}} + \frac {6}{11} \, a b x^{\frac {11}{3}} + \frac {3}{8} \, a^{2} 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 = 24, normalized size = 0.67 \begin {gather*} \frac {3\,x^{8/3}\,\left (77\,a^2+112\,a\,b\,x+44\,b^2\,x^2\right )}{616} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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