Optimal. Leaf size=18 \[ \frac {1}{4} \log \left (-e^2+x-\log (-1+x)\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6741, 12, 6684} \begin {gather*} \frac {1}{4} \log \left (-x+\log (x-1)+e^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2+x}{4 (1-x) \left (e^2-x+\log (-1+x)\right )} \, dx\\ &=\frac {1}{4} \int \frac {-2+x}{(1-x) \left (e^2-x+\log (-1+x)\right )} \, dx\\ &=\frac {1}{4} \log \left (e^2-x+\log (-1+x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 18, normalized size = 1.00 \begin {gather*} \frac {1}{4} \log \left (-e^2+x-\log (-1+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{4} \, \log \left (-x + e^{2} + \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{4} \, \log \left (-x + e^{2} + \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 14, normalized size = 0.78
method | result | size |
norman | \(\frac {\ln \left (-x +{\mathrm e}^{2}+\ln \left (x -1\right )\right )}{4}\) | \(14\) |
risch | \(\frac {\ln \left (-x +{\mathrm e}^{2}+\ln \left (x -1\right )\right )}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{4} \, \log \left (-x + e^{2} + \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.71, size = 15, normalized size = 0.83 \begin {gather*} \frac {\ln \left (x-\ln \left (x-1\right )-{\mathrm {e}}^2\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 12, normalized size = 0.67 \begin {gather*} \frac {\log {\left (- x + \log {\left (x - 1 \right )} + e^{2} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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