Optimal. Leaf size=21 \[ \frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3} \]
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Rubi [A] time = 0.0035655, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{4/3} (a+b x) \, dx &=\int \left (a x^{4/3}+b x^{7/3}\right ) \, dx\\ &=\frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3}\\ \end{align*}
Mathematica [A] time = 0.0044912, size = 17, normalized size = 0.81 \[ \frac{3}{70} x^{7/3} (10 a+7 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \begin{align*}{\frac{21\,bx+30\,a}{70}{x}^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10987, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{3}{7} \, a x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53166, size = 47, normalized size = 2.24 \begin{align*} \frac{3}{70} \,{\left (7 \, b x^{3} + 10 \, a 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 = 1.46949, size = 19, normalized size = 0.9 \begin{align*} \frac{3 a x^{\frac{7}{3}}}{7} + \frac{3 b x^{\frac{10}{3}}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05425, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{3}{7} \, a x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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