Optimal. Leaf size=28 \[ 5-x+\log \left (\frac {1}{\log (2) \left (2-x+\left (2-e^9\right ) \log (x)\right )}\right ) \]
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Rubi [A]
time = 0.26, antiderivative size = 22, normalized size of antiderivative = 0.79, number of steps
used = 4, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6873, 6874,
6816} \begin {gather*} -x-\log \left (-x+\left (2-e^9\right ) \log (x)+2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 \left (1-\frac {e^9}{2}\right )-x+x^2-\left (2 x-e^9 x\right ) \log (x)}{2 x-x^2-\left (-2 x+e^9 x\right ) \log (x)} \, dx\\ &=\int \left (-1+\frac {-2+e^9+x}{x \left (2-x+2 \left (1-\frac {e^9}{2}\right ) \log (x)\right )}\right ) \, dx\\ &=-x+\int \frac {-2+e^9+x}{x \left (2-x+2 \left (1-\frac {e^9}{2}\right ) \log (x)\right )} \, dx\\ &=-x-\log \left (2-x+\left (2-e^9\right ) \log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 23, normalized size = 0.82 \begin {gather*} -x-\log \left (2-x+2 \log (x)-e^9 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 4.00, size = 20, normalized size = 0.71
method | result | size |
default | \(-x -\ln \left (\ln \left (x \right ) {\mathrm e}^{9}-2 \ln \left (x \right )+x -2\right )\) | \(20\) |
norman | \(-x -\ln \left (\ln \left (x \right ) {\mathrm e}^{9}-2 \ln \left (x \right )+x -2\right )\) | \(20\) |
risch | \(-x -\ln \left (\ln \left (x \right )+\frac {x -2}{{\mathrm e}^{9}-2}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 24, normalized size = 0.86 \begin {gather*} -x - \log \left (\frac {{\left (e^{9} - 2\right )} \log \left (x\right ) + x - 2}{e^{9} - 2}\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 = 0.61 \begin {gather*} -x - \log \left ({\left (e^{9} - 2\right )} \log \left (x\right ) + x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 15, normalized size = 0.54 \begin {gather*} - x - \log {\left (\frac {x - 2}{-2 + e^{9}} + \log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 0.68 \begin {gather*} -x - \log \left (e^{9} \log \left (x\right ) + x - 2 \, \log \left (x\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.52, size = 19, normalized size = 0.68 \begin {gather*} -x-\ln \left (x-2\,\ln \left (x\right )+{\mathrm {e}}^9\,\ln \left (x\right )-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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