Optimal. Leaf size=51 \[ \frac{9}{10} a^2 b x^{10/3}+\frac{3}{7} a^3 x^{7/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3} \]
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Rubi [A] time = 0.0109155, antiderivative size = 51, normalized size of antiderivative = 1., 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} \[ \frac{9}{10} a^2 b x^{10/3}+\frac{3}{7} a^3 x^{7/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{4/3} (a+b x)^3 \, dx &=\int \left (a^3 x^{4/3}+3 a^2 b x^{7/3}+3 a b^2 x^{10/3}+b^3 x^{13/3}\right ) \, dx\\ &=\frac{3}{7} a^3 x^{7/3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{3}{16} b^3 x^{16/3}\\ \end{align*}
Mathematica [A] time = 0.0112979, size = 39, normalized size = 0.76 \[ \frac{3 x^{7/3} \left (2184 a^2 b x+1040 a^3+1680 a b^2 x^2+455 b^3 x^3\right )}{7280} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.7 \begin{align*}{\frac{1365\,{b}^{3}{x}^{3}+5040\,a{b}^{2}{x}^{2}+6552\,{a}^{2}bx+3120\,{a}^{3}}{7280}{x}^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.4617, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{16} \, b^{3} x^{\frac{16}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{3}{7} \, a^{3} x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47577, size = 107, normalized size = 2.1 \begin{align*} \frac{3}{7280} \,{\left (455 \, b^{3} x^{5} + 1680 \, a b^{2} x^{4} + 2184 \, a^{2} b x^{3} + 1040 \, a^{3} x^{2}\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 5.23708, size = 49, normalized size = 0.96 \begin{align*} \frac{3 a^{3} x^{\frac{7}{3}}}{7} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \frac{3 b^{3} x^{\frac{16}{3}}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05051, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{16} \, b^{3} x^{\frac{16}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{3}{7} \, a^{3} x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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