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 = {43} \[ \frac {3}{7} a^2 x^{7/3}+\frac {3}{5} a b x^{10/3}+\frac {3}{13} b^2 x^{13/3} \]
Antiderivative was successfully verified.
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Rule 43
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 \[ \frac {3}{455} x^{7/3} \left (65 a^2+91 a b x+35 b^2 x^2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 29, normalized size = 0.81 \[ \frac {3}{455} \, {\left (35 \, b^{2} x^{4} + 91 \, a b x^{3} + 65 \, a^{2} x^{2}\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 24, normalized size = 0.67 \[ \frac {3}{13} \, b^{2} x^{\frac {13}{3}} + \frac {3}{5} \, a b x^{\frac {10}{3}} + \frac {3}{7} \, a^{2} x^{\frac {7}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.69 \[ \frac {3 \left (35 b^{2} x^{2}+91 a b x +65 a^{2}\right ) x^{\frac {7}{3}}}{455} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 24, normalized size = 0.67 \[ \frac {3}{13} \, b^{2} x^{\frac {13}{3}} + \frac {3}{5} \, a b x^{\frac {10}{3}} + \frac {3}{7} \, a^{2} x^{\frac {7}{3}} \]
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 \[ \frac {3\,x^{7/3}\,\left (65\,a^2+91\,a\,b\,x+35\,b^2\,x^2\right )}{455} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.65, size = 34, normalized size = 0.94 \[ \frac {3 a^{2} x^{\frac {7}{3}}}{7} + \frac {3 a b x^{\frac {10}{3}}}{5} + \frac {3 b^{2} x^{\frac {13}{3}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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