Optimal. Leaf size=19 \[ -\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
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Rubi [A] time = 0.003261, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^2}{x^2} \, dx &=-\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x}\\ \end{align*}
Mathematica [A] time = 0.0037742, size = 19, normalized size = 1. \[ -\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 25, normalized size = 1.3 \begin{align*} -{\frac{{a}^{2}}{x}}-3\,{\frac{ab}{{x}^{2/3}}}-3\,{\frac{{b}^{2}}{\sqrt [3]{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.972983, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44842, size = 57, normalized size = 3. \begin{align*} -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.82251, size = 26, normalized size = 1.37 \begin{align*} - \frac{a^{2}}{x} - \frac{3 a b}{x^{\frac{2}{3}}} - \frac{3 b^{2}}{\sqrt [3]{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11324, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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