Optimal. Leaf size=25 \[ \frac {9}{-2+\log \left (\frac {1}{5} \log \left (\frac {x}{4+e^{-6+2 x}}\right )\right )} \]
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Rubi [A] time = 0.60, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 3, number of rules used = 3, integrand size = 145, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {9}{2-\log \left (\frac {1}{5} \log \left (\frac {x}{e^{2 x-6}+4}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9 \left (-4 e^6+e^{2 x} (-1+2 x)\right )}{\left (4 e^6+e^{2 x}\right ) x \log \left (\frac {x}{4+e^{-6+2 x}}\right ) \left (2-\log \left (\frac {1}{5} \log \left (\frac {x}{4+e^{-6+2 x}}\right )\right )\right )^2} \, dx\\ &=9 \int \frac {-4 e^6+e^{2 x} (-1+2 x)}{\left (4 e^6+e^{2 x}\right ) x \log \left (\frac {x}{4+e^{-6+2 x}}\right ) \left (2-\log \left (\frac {1}{5} \log \left (\frac {x}{4+e^{-6+2 x}}\right )\right )\right )^2} \, dx\\ &=-\frac {9}{2-\log \left (\frac {1}{5} \log \left (\frac {x}{4+e^{-6+2 x}}\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 25, normalized size = 1.00 \begin {gather*} \frac {9}{-2+\log \left (\frac {1}{5} \log \left (\frac {x}{4+e^{-6+2 x}}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 22, normalized size = 0.88 \begin {gather*} \frac {9}{\log \left (\frac {1}{5} \, \log \left (\frac {x}{e^{\left (2 \, x - 6\right )} + 4}\right )\right ) - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 6.83, size = 129, normalized size = 5.16 \begin {gather*} -\frac {9 \, {\left (\log \left (\frac {x}{4 \, e^{6} + e^{\left (2 \, x\right )}}\right ) + 6\right )}}{\log \relax (5) \log \relax (x) - \log \relax (5) \log \left (4 \, e^{6} + e^{\left (2 \, x\right )}\right ) - \log \relax (x) \log \left (\log \left (\frac {x}{4 \, e^{6} + e^{\left (2 \, x\right )}}\right ) + 6\right ) + \log \left (4 \, e^{6} + e^{\left (2 \, x\right )}\right ) \log \left (\log \left (\frac {x}{4 \, e^{6} + e^{\left (2 \, x\right )}}\right ) + 6\right ) + 6 \, \log \relax (5) + 2 \, \log \relax (x) - 2 \, \log \left (4 \, e^{6} + e^{\left (2 \, x\right )}\right ) - 6 \, \log \left (\log \left (\frac {x}{4 \, e^{6} + e^{\left (2 \, x\right )}}\right ) + 6\right ) + 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.15, size = 98, normalized size = 3.92
method | result | size |
risch | \(\frac {9}{\ln \left (\frac {\ln \relax (x )}{5}-\frac {\ln \left ({\mathrm e}^{2 x -6}+4\right )}{5}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i x}{{\mathrm e}^{2 x -6}+4}\right ) \left (-\mathrm {csgn}\left (\frac {i x}{{\mathrm e}^{2 x -6}+4}\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (\frac {i x}{{\mathrm e}^{2 x -6}+4}\right )+\mathrm {csgn}\left (\frac {i}{{\mathrm e}^{2 x -6}+4}\right )\right )}{10}\right )-2}\) | \(98\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 27, normalized size = 1.08 \begin {gather*} -\frac {9}{\log \relax (5) - \log \left (\log \relax (x) - \log \left (4 \, e^{6} + e^{\left (2 \, x\right )}\right ) + 6\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.09, size = 25, normalized size = 1.00 \begin {gather*} \frac {9}{\ln \left (\frac {\ln \relax (x)}{5}-\frac {\ln \left ({\mathrm {e}}^{2\,x}+4\,{\mathrm {e}}^6\right )}{5}+\frac {6}{5}\right )-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.81, size = 17, normalized size = 0.68 \begin {gather*} \frac {9}{\log {\left (\frac {\log {\left (\frac {x}{e^{2 x - 6} + 4} \right )}}{5} \right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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