Optimal. Leaf size=27 \[ e^{2-e^{2 \left (x+\left (x+\log \left (\frac {3}{2} x \log (x)\right )\right )^2\right )}-x} \]
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Rubi [A] time = 6.34, antiderivative size = 47, normalized size of antiderivative = 1.74, number of steps used = 1, number of rules used = 1, integrand size = 127, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {6706} \begin {gather*} \exp \left (-\left (\frac {3}{2}\right )^{4 x} e^{2 x^2+2 x+2 \log ^2\left (\frac {3}{2} x \log (x)\right )} (x \log (x))^{4 x}-x+2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (2-x-\left (\frac {3}{2}\right )^{4 x} e^{2 x+2 x^2+2 \log ^2\left (\frac {3}{2} x \log (x)\right )} (x \log (x))^{4 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.41, size = 39, normalized size = 1.44 \begin {gather*} e^{2-e^{2 \left (x+x^2+2 x \log \left (\frac {3}{2} x \log (x)\right )+\log ^2\left (\frac {3}{2} x \log (x)\right )\right )}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 37, normalized size = 1.37 \begin {gather*} e^{\left (-x - e^{\left (2 \, x^{2} + 4 \, x \log \left (\frac {3}{2} \, x \log \relax (x)\right ) + 2 \, \log \left (\frac {3}{2} \, x \log \relax (x)\right )^{2} + 2 \, x\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 81.81, size = 37, normalized size = 1.37 \begin {gather*} e^{\left (-x - e^{\left (2 \, x^{2} + 4 \, x \log \left (\frac {3}{2} \, x \log \relax (x)\right ) + 2 \, \log \left (\frac {3}{2} \, x \log \relax (x)\right )^{2} + 2 \, x\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.19, size = 631, normalized size = 23.37
method | result | size |
risch | \({\mathrm e}^{-\ln \relax (x )^{-4 \ln \relax (2)} \ln \relax (x )^{4 x} 3^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )} 2^{2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )} x^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )} x^{-4 \ln \relax (2)} \ln \relax (x )^{4 \ln \relax (x )} x^{4 \ln \relax (3)} 81^{x} \left (\frac {1}{16}\right )^{x} x^{4 x} 3^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right )} 2^{2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right )} x^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right )} \ln \relax (x )^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right )} \left (\frac {1}{16}\right )^{\ln \relax (3)} \ln \relax (x )^{4 \ln \relax (3)} \ln \relax (x )^{-2 i \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )} 3^{2 i \pi \,\mathrm {csgn}\left (i x \right )} 3^{2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right )} 2^{-2 i \pi \,\mathrm {csgn}\left (i x \right )} 2^{-2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right )} x^{2 i \pi \,\mathrm {csgn}\left (i x \right )} x^{2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right )} \ln \relax (x )^{2 i \pi \,\mathrm {csgn}\left (i x \right )} \ln \relax (x )^{2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right )} {\mathrm e}^{2 x +2 \ln \relax (3)^{2}+2 \ln \relax (2)^{2}+2 \ln \left (\ln \relax (x )\right )^{2}+2 \ln \relax (x )^{2}+2 x^{2}} {\mathrm e}^{2 i x \pi \mathrm {csgn}\left (i x \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )} {\mathrm e}^{2 i x \pi \mathrm {csgn}\left (i x \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i x \right )} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i x \ln \relax (x )\right )^{4}}{2}} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{5}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x \ln \relax (x )\right )^{4}}{2}} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{5}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i x \ln \relax (x )\right )^{2}}{2}} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{3}} {\mathrm e}^{\pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i x \ln \relax (x )\right )^{3}} {\mathrm e}^{-2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{4}} {\mathrm e}^{-2 i x \pi \mathrm {csgn}\left (i x \ln \relax (x )\right )^{3}} {\mathrm e}^{-\frac {\pi ^{2} \mathrm {csgn}\left (i x \ln \relax (x )\right )^{6}}{2}} {\mathrm e}^{-2 i x \pi \,\mathrm {csgn}\left (i x \ln \relax (x )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right )}+2-x}\) | \(631\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.17, size = 105, normalized size = 3.89 \begin {gather*} e^{\left (-x - \frac {e^{\left (2 \, x^{2} + 4 \, x \log \relax (3) + 2 \, \log \relax (3)^{2} - 4 \, x \log \relax (2) + 2 \, \log \relax (2)^{2} + 4 \, x \log \relax (x) + 4 \, \log \relax (3) \log \relax (x) - 4 \, \log \relax (2) \log \relax (x) + 2 \, \log \relax (x)^{2} + 4 \, x \log \left (\log \relax (x)\right ) + 4 \, \log \relax (3) \log \left (\log \relax (x)\right ) - 4 \, \log \relax (2) \log \left (\log \relax (x)\right ) + 4 \, \log \relax (x) \log \left (\log \relax (x)\right ) + 2 \, \log \left (\log \relax (x)\right )^{2} + 2 \, x\right )}}{2^{4 \, \log \relax (3)}} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.50, size = 76, normalized size = 2.81 \begin {gather*} {\mathrm {e}}^{-\frac {1}{2^{4\,x+4\,\ln \relax (3)}}\,{81}^x\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{2\,{\ln \left (x\,\ln \relax (x)\right )}^2}\,{\mathrm {e}}^{2\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{2\,{\ln \relax (3)}^2}\,{\mathrm {e}}^{2\,x^2}\,{\left (x\,\ln \relax (x)\right )}^{4\,x-4\,\ln \relax (2)+4\,\ln \relax (3)}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.18, size = 41, normalized size = 1.52 \begin {gather*} e^{- x - e^{2 x^{2} + 4 x \log {\left (\frac {3 x \log {\relax (x )}}{2} \right )} + 2 x + 2 \log {\left (\frac {3 x \log {\relax (x )}}{2} \right )}^{2}} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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