Optimal. Leaf size=17 \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
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Rubi [A] time = 0.0370496, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {1593, 1802} \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 1802
Rubi steps
\begin{align*} \int \frac{-9-9 x+2 x^2}{-9 x+x^3} \, dx &=\int \frac{-9-9 x+2 x^2}{x \left (-9+x^2\right )} \, dx\\ &=\int \left (\frac{1}{3-x}+\frac{1}{x}+\frac{2}{3+x}\right ) \, dx\\ &=-\log (3-x)+\log (x)+2 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0046504, size = 17, normalized size = 1. \[ -\log (3-x)+\log (x)+2 \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \begin{align*} -\ln \left ( -3+x \right ) +\ln \left ( x \right ) +2\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974869, size = 20, normalized size = 1.18 \begin{align*} 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44348, size = 49, normalized size = 2.88 \begin{align*} 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.115618, size = 14, normalized size = 0.82 \begin{align*} \log{\left (x \right )} - \log{\left (x - 3 \right )} + 2 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.41245, size = 24, normalized size = 1.41 \begin{align*} 2 \, \log \left ({\left | x + 3 \right |}\right ) - \log \left ({\left | x - 3 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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