Optimal. Leaf size=24 \[ -4+x+\log \left (\frac {x}{3 (-3+(5-x) (-3+2 x))}\right ) \]
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Rubi [A]
time = 0.05, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1608, 1642}
\begin {gather*} x-\log (9-2 x)-\log (2-x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1608
Rule 1642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18+18 x-15 x^2+2 x^3}{x \left (18-13 x+2 x^2\right )} \, dx\\ &=\int \left (1+\frac {1}{2-x}+\frac {1}{x}-\frac {2}{-9+2 x}\right ) \, dx\\ &=x-\log (9-2 x)-\log (2-x)+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 0.71 \begin {gather*} x+\log (x)-\log \left (18-13 x+2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 19, normalized size = 0.79
method | result | size |
risch | \(x +\ln \left (x \right )-\ln \left (2 x^{2}-13 x +18\right )\) | \(18\) |
default | \(x -\ln \left (x -2\right )-\ln \left (2 x -9\right )+\ln \left (x \right )\) | \(19\) |
norman | \(x -\ln \left (x -2\right )-\ln \left (2 x -9\right )+\ln \left (x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.75 \begin {gather*} x - \log \left (2 \, x - 9\right ) - \log \left (x - 2\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 17, normalized size = 0.71 \begin {gather*} x - \log \left (2 \, x^{2} - 13 \, x + 18\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 15, normalized size = 0.62 \begin {gather*} x + \log {\left (x \right )} - \log {\left (2 x^{2} - 13 x + 18 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 21, normalized size = 0.88 \begin {gather*} x - \log \left ({\left | 2 \, x - 9 \right |}\right ) - \log \left ({\left | x - 2 \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 = 0.08, size = 15, normalized size = 0.62 \begin {gather*} x-\ln \left (x^2-\frac {13\,x}{2}+9\right )+\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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