Optimal. Leaf size=36 \[ \frac {3}{5} a^2 x^{5/3}+\frac {3}{4} a b x^{8/3}+\frac {3}{11} b^2 x^{11/3} \]
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Rubi [A]
time = 0.01, 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}{5} a^2 x^{5/3}+\frac {3}{4} a b x^{8/3}+\frac {3}{11} b^2 x^{11/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{2/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{2/3}+2 a b x^{5/3}+b^2 x^{8/3}\right ) \, dx\\ &=\frac {3}{5} a^2 x^{5/3}+\frac {3}{4} a b x^{8/3}+\frac {3}{11} b^2 x^{11/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 28, normalized size = 0.78 \begin {gather*} \frac {3}{220} x^{5/3} \left (44 a^2+55 a b x+20 b^2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.76, size = 24, normalized size = 0.67 \begin {gather*} \frac {3 x^{\frac {5}{3}} \left (44 a^2+55 a b x+20 b^2 x^2\right )}{220} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 25, normalized size = 0.69
method | result | size |
gosper | \(\frac {3 x^{\frac {5}{3}} \left (20 x^{2} b^{2}+55 a b x +44 a^{2}\right )}{220}\) | \(25\) |
derivativedivides | \(\frac {3 a^{2} x^{\frac {5}{3}}}{5}+\frac {3 a b \,x^{\frac {8}{3}}}{4}+\frac {3 b^{2} x^{\frac {11}{3}}}{11}\) | \(25\) |
default | \(\frac {3 a^{2} x^{\frac {5}{3}}}{5}+\frac {3 a b \,x^{\frac {8}{3}}}{4}+\frac {3 b^{2} x^{\frac {11}{3}}}{11}\) | \(25\) |
trager | \(\frac {3 x^{\frac {5}{3}} \left (20 x^{2} b^{2}+55 a b x +44 a^{2}\right )}{220}\) | \(25\) |
risch | \(\frac {3 x^{\frac {5}{3}} \left (20 x^{2} b^{2}+55 a b x +44 a^{2}\right )}{220}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 24, normalized size = 0.67 \begin {gather*} \frac {3}{11} \, b^{2} x^{\frac {11}{3}} + \frac {3}{4} \, a b x^{\frac {8}{3}} + \frac {3}{5} \, a^{2} x^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 27, normalized size = 0.75 \begin {gather*} \frac {3}{220} \, {\left (20 \, b^{2} x^{3} + 55 \, a b x^{2} + 44 \, a^{2} x\right )} x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 34, normalized size = 0.94 \begin {gather*} \frac {3 a^{2} x^{\frac {5}{3}}}{5} + \frac {3 a b x^{\frac {8}{3}}}{4} + \frac {3 b^{2} x^{\frac {11}{3}}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 51, normalized size = 1.42 \begin {gather*} \frac {3}{11} b^{2} \left (x^{\frac {1}{3}}\right )^{2} x^{3}+\frac {6 a b \left (x^{\frac {1}{3}}\right )^{2} x^{2}}{2\cdot 4}+\frac {3}{5} a^{2} \left (x^{\frac {1}{3}}\right )^{2} x \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^{5/3}\,\left (44\,a^2+55\,a\,b\,x+20\,b^2\,x^2\right )}{220} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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