Optimal. Leaf size=25 \[ \log \left (-x+\left (-e^{-2-2 x+e x}+x\right ) \log ^2(\log (3))\right ) \]
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Rubi [A]
time = 0.17, antiderivative size = 46, normalized size of antiderivative = 1.84, number of steps
used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6816}
\begin {gather*} \log \left (-e^{-2 x-2} \left (e^{2 x+2} x-e^{2 x+2} x \log ^2(\log (3))+e^{e x} \log ^2(\log (3))\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (-e^{-2-2 x} \left (e^{2+2 x} x+e^{e x} \log ^2(\log (3))-e^{2+2 x} x \log ^2(\log (3))\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 22, normalized size = 0.88 \begin {gather*} \log \left (x+\left (e^{-2+(-2+e) x}-x\right ) \log ^2(\log (3))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.56, size = 24, normalized size = 0.96
method | result | size |
derivativedivides | \(\ln \left (\left ({\mathrm e}^{x \,{\mathrm e}-2 x -2}-x \right ) \ln \left (\ln \left (3\right )\right )^{2}+x \right )\) | \(24\) |
default | \(\ln \left (\left ({\mathrm e}^{x \,{\mathrm e}-2 x -2}-x \right ) \ln \left (\ln \left (3\right )\right )^{2}+x \right )\) | \(24\) |
norman | \(\ln \left (\ln \left (\ln \left (3\right )\right )^{2} x -\ln \left (\ln \left (3\right )\right )^{2} {\mathrm e}^{x \,{\mathrm e}-2 x -2}-x \right )\) | \(30\) |
risch | \(2+\ln \left ({\mathrm e}^{x \,{\mathrm e}-2 x -2}-\frac {x \left (\ln \left (\ln \left (3\right )\right )^{2}-1\right )}{\ln \left (\ln \left (3\right )\right )^{2}}\right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 40, normalized size = 1.60 \begin {gather*} -2 \, x + \log \left (-\frac {{\left (\log \left (\log \left (3\right )\right )^{2} - 1\right )} x e^{\left (2 \, x + 2\right )} - e^{\left (x e\right )} \log \left (\log \left (3\right )\right )^{2}}{\log \left (\log \left (3\right )\right )^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 24, normalized size = 0.96 \begin {gather*} \log \left (-{\left (x - e^{\left (x e - 2 \, x - 2\right )}\right )} \log \left (\log \left (3\right )\right )^{2} + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 29, normalized size = 1.16 \begin {gather*} \log {\left (\frac {- x \log {\left (\log {\left (3 \right )} \right )}^{2} + x}{\log {\left (\log {\left (3 \right )} \right )}^{2}} + e^{- 2 x + e x - 2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 32, normalized size = 1.28 \begin {gather*} \log \left (x e^{2} \log \left (\log \left (3\right )\right )^{2} - e^{\left (x e - 2 \, x\right )} \log \left (\log \left (3\right )\right )^{2} - x e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.48, size = 28, normalized size = 1.12 \begin {gather*} \ln \left (x-x\,{\ln \left (\ln \left (3\right )\right )}^2+{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{x\,\mathrm {e}}\,{\ln \left (\ln \left (3\right )\right )}^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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