Optimal. Leaf size=25 \[ \log \left (\log \left (\frac {1}{2-e^3+e^3 \log \left (\frac {2-x}{x}\right )}\right )\right ) \]
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Rubi [A]
time = 0.05, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 76, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12, 6816}
\begin {gather*} \log \left (\log \left (\frac {1}{e^3 \log \left (\frac {2-x}{x}\right )-e^3+2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 e^3\right ) \int \frac {1}{\left (-4 x+2 x^2+e^3 \left (2 x-x^2\right )+e^3 \left (-2 x+x^2\right ) \log \left (\frac {2-x}{x}\right )\right ) \log \left (\frac {1}{2-e^3+e^3 \log \left (\frac {2-x}{x}\right )}\right )} \, dx\right )\\ &=\log \left (\log \left (\frac {1}{2-e^3+e^3 \log \left (\frac {2-x}{x}\right )}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 23, normalized size = 0.92 \begin {gather*} \log \left (\log \left (\frac {1}{2-e^3+e^3 \log \left (-1+\frac {2}{x}\right )}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 11.77, size = 24, normalized size = 0.96
method | result | size |
norman | \(\ln \left (\ln \left (\frac {1}{{\mathrm e}^{3} \ln \left (\frac {2-x}{x}\right )-{\mathrm e}^{3}+2}\right )\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 0.92 \begin {gather*} \log \left (\log \left (-e^{3} \log \left (x\right ) + e^{3} \log \left (-x + 2\right ) - e^{3} + 2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 22, normalized size = 0.88 \begin {gather*} \log \left (\log \left (\frac {1}{e^{3} \log \left (-\frac {x - 2}{x}\right ) - e^{3} + 2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 19, normalized size = 0.76 \begin {gather*} \log {\left (\log {\left (\frac {1}{e^{3} \log {\left (\frac {2 - x}{x} \right )} - e^{3} + 2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 24.68, size = 22, normalized size = 0.88 \begin {gather*} \ln \left (\ln \left (\frac {1}{{\mathrm {e}}^3\,\ln \left (-\frac {x-2}{x}\right )-{\mathrm {e}}^3+2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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