Optimal. Leaf size=19 \[ 3 a \sqrt [3]{x}+\frac{3}{4} b x^{4/3} \]
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Rubi [A] time = 0.0034785, 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} \[ 3 a \sqrt [3]{x}+\frac{3}{4} b x^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^{2/3}} \, dx &=\int \left (\frac{a}{x^{2/3}}+b \sqrt [3]{x}\right ) \, dx\\ &=3 a \sqrt [3]{x}+\frac{3}{4} b x^{4/3}\\ \end{align*}
Mathematica [A] time = 0.0045585, size = 16, normalized size = 0.84 \[ \frac{3}{4} \sqrt [3]{x} (4 a+b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \begin{align*}{\frac{3\,bx+12\,a}{4}\sqrt [3]{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01697, size = 18, normalized size = 0.95 \begin{align*} \frac{3}{4} \, b x^{\frac{4}{3}} + 3 \, a x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53769, size = 34, normalized size = 1.79 \begin{align*} \frac{3}{4} \,{\left (b x + 4 \, a\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.14289, size = 17, normalized size = 0.89 \begin{align*} 3 a \sqrt [3]{x} + \frac{3 b x^{\frac{4}{3}}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05519, size = 18, normalized size = 0.95 \begin{align*} \frac{3}{4} \, b x^{\frac{4}{3}} + 3 \, a x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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