Optimal. Leaf size=13 \[ -\frac{1}{\sqrt [3]{1-\frac{3}{x}}} \]
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Rubi [A] time = 0.0037591, antiderivative size = 13, 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 = {261} \[ -\frac{1}{\sqrt [3]{1-\frac{3}{x}}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (1-\frac{3}{x}\right )^{4/3} x^2} \, dx &=-\frac{1}{\sqrt [3]{1-\frac{3}{x}}}\\ \end{align*}
Mathematica [A] time = 0.0054422, size = 13, normalized size = 1. \[ -\frac{1}{\sqrt [3]{\frac{x-3}{x}}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 1.4 \begin{align*} -{\frac{-3+x}{x} \left ({\frac{-3+x}{x}} \right ) ^{-{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953112, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{{\left (-\frac{3}{x} + 1\right )}^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78042, size = 41, normalized size = 3.15 \begin{align*} -\frac{x \left (\frac{x - 3}{x}\right )^{\frac{2}{3}}}{x - 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.916459, size = 10, normalized size = 0.77 \begin{align*} - \frac{1}{\sqrt [3]{1 - \frac{3}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06431, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{{\left (-\frac{3}{x} + 1\right )}^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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