Optimal. Leaf size=16 \[ -\frac {3}{x}-\log (1-x)+\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\frac {3}{x}-\log (1-x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rule 1593
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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3}{x}-\log (1-x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-3+2 x}{-x^2+x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 18, normalized size = 1.12 \begin {gather*} -\frac {x \log \left (x - 1\right ) - x \log \relax (x) + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 16, normalized size = 1.00 \begin {gather*} -\frac {3}{x} - \log \left ({\left | x - 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 0.94 \begin {gather*} \ln \relax (x )-\ln \left (x -1\right )-\frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.62, size = 14, normalized size = 0.88 \begin {gather*} -\frac {3}{x} - \log \left (x - 1\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 14, normalized size = 0.88 \begin {gather*} 2\,\mathrm {atanh}\left (2\,x-1\right )-\frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.62 \begin {gather*} \log {\relax (x )} - \log {\left (x - 1 \right )} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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