Optimal. Leaf size=36 \[ \frac {3}{7} a^2 x^{7/3}+\frac {3}{5} a b x^{10/3}+\frac {3}{13} b^2 x^{13/3} \]
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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}{7} a^2 x^{7/3}+\frac {3}{5} a b x^{10/3}+\frac {3}{13} b^2 x^{13/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^{4/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{4/3}+2 a b x^{7/3}+b^2 x^{10/3}\right ) \, dx\\ &=\frac {3}{7} a^2 x^{7/3}+\frac {3}{5} a b x^{10/3}+\frac {3}{13} b^2 x^{13/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 28, normalized size = 0.78 \begin {gather*} \frac {3}{455} x^{7/3} \left (65 a^2+91 a b x+35 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 | \(\frac {3 x^{\frac {7}{3}} \left (35 x^{2} b^{2}+91 a b x +65 a^{2}\right )}{455}\) | \(25\) |
derivativedivides | \(\frac {3 a^{2} x^{\frac {7}{3}}}{7}+\frac {3 a b \,x^{\frac {10}{3}}}{5}+\frac {3 b^{2} x^{\frac {13}{3}}}{13}\) | \(25\) |
default | \(\frac {3 a^{2} x^{\frac {7}{3}}}{7}+\frac {3 a b \,x^{\frac {10}{3}}}{5}+\frac {3 b^{2} x^{\frac {13}{3}}}{13}\) | \(25\) |
trager | \(\frac {3 x^{\frac {7}{3}} \left (35 x^{2} b^{2}+91 a b x +65 a^{2}\right )}{455}\) | \(25\) |
risch | \(\frac {3 x^{\frac {7}{3}} \left (35 x^{2} b^{2}+91 a b x +65 a^{2}\right )}{455}\) | \(25\) |
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}{13} \, b^{2} x^{\frac {13}{3}} + \frac {3}{5} \, a b x^{\frac {10}{3}} + \frac {3}{7} \, a^{2} x^{\frac {7}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 29, normalized size = 0.81 \begin {gather*} \frac {3}{455} \, {\left (35 \, b^{2} x^{4} + 91 \, a b x^{3} + 65 \, a^{2} x^{2}\right )} x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.34, size = 34, normalized size = 0.94 \begin {gather*} \frac {3 a^{2} x^{\frac {7}{3}}}{7} + \frac {3 a b x^{\frac {10}{3}}}{5} + \frac {3 b^{2} x^{\frac {13}{3}}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.00, size = 24, normalized size = 0.67 \begin {gather*} \frac {3}{13} \, b^{2} x^{\frac {13}{3}} + \frac {3}{5} \, a b x^{\frac {10}{3}} + \frac {3}{7} \, a^{2} x^{\frac {7}{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^{7/3}\,\left (65\,a^2+91\,a\,b\,x+35\,b^2\,x^2\right )}{455} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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