Optimal. Leaf size=17 \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
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Rubi [A] time = 0.0050521, antiderivative size = 17, 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 = {14} \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+b \sqrt [3]{x}}{x^2} \, dx &=\int \left (\frac{a}{x^2}+\frac{b}{x^{5/3}}\right ) \, dx\\ &=-\frac{a}{x}-\frac{3 b}{2 x^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0062583, size = 17, normalized size = 1. \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{x}}-{\frac{3\,b}{2}{x}^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.978657, size = 20, normalized size = 1.18 \begin{align*} -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40431, size = 38, normalized size = 2.24 \begin{align*} -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.940901, size = 14, normalized size = 0.82 \begin{align*} - \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10605, size = 20, normalized size = 1.18 \begin{align*} -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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