Optimal. Leaf size=19 \[ 3 b \sqrt [3]{x}-\frac{3 a}{2 x^{2/3}} \]
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Rubi [A] time = 0.0035201, antiderivative size = 19, 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} \[ 3 b \sqrt [3]{x}-\frac{3 a}{2 x^{2/3}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^{5/3}} \, dx &=\int \left (\frac{a}{x^{5/3}}+\frac{b}{x^{2/3}}\right ) \, dx\\ &=-\frac{3 a}{2 x^{2/3}}+3 b \sqrt [3]{x}\\ \end{align*}
Mathematica [A] time = 0.0052261, size = 19, normalized size = 1. \[ 3 b \sqrt [3]{x}-\frac{3 a}{2 x^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.6 \begin{align*} -{\frac{-6\,bx+3\,a}{2}{x}^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00163, size = 18, normalized size = 0.95 \begin{align*} 3 \, b x^{\frac{1}{3}} - \frac{3 \, a}{2 \, x^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4177, size = 34, normalized size = 1.79 \begin{align*} \frac{3 \,{\left (2 \, b x - a\right )}}{2 \, x^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.486049, size = 17, normalized size = 0.89 \begin{align*} - \frac{3 a}{2 x^{\frac{2}{3}}} + 3 b \sqrt [3]{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05946, size = 18, normalized size = 0.95 \begin{align*} 3 \, b x^{\frac{1}{3}} - \frac{3 \, a}{2 \, x^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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