Optimal. Leaf size=20 \[ \log \left (\frac {3 e^{-e^{48} x}}{2 x^2 \log (x)}\right ) \]
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Rubi [A] time = 0.20, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 9, number of rules used = 6, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {12, 6741, 6742, 43, 2302, 29} \begin {gather*} -e^{48} x-2 \log (x)-\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 43
Rule 2302
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-e^2+\left (-2 e^2-e^{50} x\right ) \log (x)}{x \log (x)} \, dx}{e^2}\\ &=\frac {\int \frac {e^2 \left (-1-2 \log (x)-e^{48} x \log (x)\right )}{x \log (x)} \, dx}{e^2}\\ &=\int \frac {-1-2 \log (x)-e^{48} x \log (x)}{x \log (x)} \, dx\\ &=\int \left (\frac {-2-e^{48} x}{x}-\frac {1}{x \log (x)}\right ) \, dx\\ &=\int \frac {-2-e^{48} x}{x} \, dx-\int \frac {1}{x \log (x)} \, dx\\ &=\int \left (-e^{48}-\frac {2}{x}\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-e^{48} x-2 \log (x)-\log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.80 \begin {gather*} -e^{48} x-2 \log (x)-\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 15, normalized size = 0.75 \begin {gather*} -x e^{48} - 2 \, \log \relax (x) - \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 21, normalized size = 1.05 \begin {gather*} -{\left (x e^{50} + 2 \, e^{2} \log \relax (x) + e^{2} \log \left (\log \relax (x)\right )\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.80
method | result | size |
risch | \(-{\mathrm e}^{48} x -2 \ln \relax (x )-\ln \left (\ln \relax (x )\right )\) | \(16\) |
norman | \(-2 \ln \relax (x )-{\mathrm e}^{50} x \,{\mathrm e}^{-2}-\ln \left (\ln \relax (x )\right )\) | \(22\) |
default | \({\mathrm e}^{-2} \left (-x \,{\mathrm e}^{50}-2 \,{\mathrm e}^{2} \ln \relax (x )-{\mathrm e}^{2} \ln \left (\ln \relax (x )\right )\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 21, normalized size = 1.05 \begin {gather*} -{\left (x e^{50} + 2 \, e^{2} \log \relax (x) + e^{2} \log \left (\log \relax (x)\right )\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.09, size = 15, normalized size = 0.75 \begin {gather*} -\ln \left (\ln \relax (x)\right )-2\,\ln \relax (x)-x\,{\mathrm {e}}^{48} \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 = 0.75 \begin {gather*} - x e^{48} - 2 \log {\relax (x )} - \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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