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 = {1607, 78}
\begin {gather*} -\frac {3}{x}-\log (1-x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rule 1607
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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Maple [A]
time = 0.42, size = 15, normalized size = 0.94
method | result | size |
default | \(-\ln \left (x -1\right )+\ln \left (x \right )-\frac {3}{x}\) | \(15\) |
norman | \(-\ln \left (x -1\right )+\ln \left (x \right )-\frac {3}{x}\) | \(15\) |
risch | \(-\ln \left (x -1\right )+\ln \left (x \right )-\frac {3}{x}\) | \(15\) |
meijerg | \(-\ln \left (1-x \right )+\ln \left (x \right )+i \pi -\frac {3}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 14, normalized size = 0.88 \begin {gather*} -\frac {3}{x} - \log \left (x - 1\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.22, size = 18, normalized size = 1.12 \begin {gather*} -\frac {x \log \left (x - 1\right ) - x \log \left (x\right ) + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.62 \begin {gather*} \log {\left (x \right )} - \log {\left (x - 1 \right )} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, 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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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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