Optimal. Leaf size=17 \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
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Rubi [A] time = 0.0391746, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08, Rules used = {1594, 1628} \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 1594
Rule 1628
Rubi steps
\begin{align*} \int \frac{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx &=\int \frac{-3+5 x+6 x^2}{x \left (-3+2 x+x^2\right )} \, dx\\ &=\int \left (\frac{2}{-1+x}+\frac{1}{x}+\frac{3}{3+x}\right ) \, dx\\ &=2 \log (1-x)+\log (x)+3 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0058524, size = 17, normalized size = 1. \[ 2 \log (1-x)+\log (x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 16, normalized size = 0.9 \begin{align*} 2\,\ln \left ( x-1 \right ) +\ln \left ( x \right ) +3\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08153, size = 20, normalized size = 1.18 \begin{align*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48899, size = 51, normalized size = 3. \begin{align*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.11806, size = 15, normalized size = 0.88 \begin{align*} \log{\left (x \right )} + 2 \log{\left (x - 1 \right )} + 3 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.44645, size = 24, normalized size = 1.41 \begin{align*} 3 \, \log \left ({\left | x + 3 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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