Optimal. Leaf size=16 \[ -\frac{3}{x}-\log (1-x)+\log (x) \]
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Rubi [A] time = 0.0136957, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1593, 77} \[ -\frac{3}{x}-\log (1-x)+\log (x) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 77
Rubi steps
\begin{align*} \int \frac{-3+2 x}{-x^2+x^3} \, dx &=\int \frac{-3+2 x}{(-1+x) x^2} \, dx\\ &=\int \left (\frac{1}{1-x}+\frac{3}{x^2}+\frac{1}{x}\right ) \, dx\\ &=-\frac{3}{x}-\log (1-x)+\log (x)\\ \end{align*}
Mathematica [A] time = 0.0032564, size = 16, normalized size = 1. \[ -\frac{3}{x}-\log (1-x)+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.051, size = 15, normalized size = 0.9 \begin{align*} \ln \left ( x \right ) -3\,{x}^{-1}-\ln \left ( -1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12229, size = 19, normalized size = 1.19 \begin{align*} -\frac{3}{x} - \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 = 2.06159, size = 46, normalized size = 2.88 \begin{align*} -\frac{x \log \left (x - 1\right ) - x \log \left (x\right ) + 3}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.147027, size = 10, normalized size = 0.62 \begin{align*} \log{\left (x \right )} - \log{\left (x - 1 \right )} - \frac{3}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24333, size = 22, normalized size = 1.38 \begin{align*} -\frac{3}{x} - \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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