Optimal. Leaf size=26 \[ 1+e^{x-x^2 \log ^2\left (\frac {1}{(4+\log (x-x \log (4)))^2}\right )} \]
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Rubi [A] time = 0.63, antiderivative size = 38, normalized size of antiderivative = 1.46, number of steps used = 2, number of rules used = 2, integrand size = 130, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {2444, 6706} \begin {gather*} \exp \left (x-x^2 \log ^2\left (\frac {1}{\log ^2(x (1-\log (4)))+8 \log (x (1-\log (4)))+16}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2444
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (x-x^2 \log ^2\left (\frac {1}{16+8 \log (x-x \log (4))+\log ^2(x-x \log (4))}\right )\right ) \left (4+\log (x-x \log (4))+4 x \log \left (\frac {1}{16+8 \log (x-x \log (4))+\log ^2(x-x \log (4))}\right )+(-8 x-2 x \log (x-x \log (4))) \log ^2\left (\frac {1}{16+8 \log (x-x \log (4))+\log ^2(x-x \log (4))}\right )\right )}{4+\log (x (1-\log (4)))} \, dx\\ &=\exp \left (x-x^2 \log ^2\left (\frac {1}{16+8 \log (x (1-\log (4)))+\log ^2(x (1-\log (4)))}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 24, normalized size = 0.92 \begin {gather*} e^{x-x^2 \log ^2\left (\frac {1}{(4+\log (x-x \log (4)))^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 35, normalized size = 1.35 \begin {gather*} e^{\left (-x^{2} \log \left (\frac {1}{\log \left (-2 \, x \log \relax (2) + x\right )^{2} + 8 \, \log \left (-2 \, x \log \relax (2) + x\right ) + 16}\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 2.10, size = 33, normalized size = 1.27 \begin {gather*} e^{\left (-x^{2} \log \left (\log \left (-2 \, x \log \relax (2) + x\right )^{2} + 8 \, \log \left (-2 \, x \log \relax (2) + x\right ) + 16\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.78, size = 280, normalized size = 10.77
method | result | size |
risch | \(\left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{4 i \pi \,\mathrm {csgn}\left (i \left (\ln \left (-\left (2 \ln \relax (2)-1\right ) x \right )+4\right )^{2}\right ) x^{2}} \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{-4 i \pi \,\mathrm {csgn}\left (i \left (\ln \left (-x \right )+\ln \left (2 \ln \relax (2)-1\right )+4\right )\right ) x^{2}} {\mathrm e}^{-\frac {x \left (-x \,\pi ^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}\right )^{6}+4 x \,\pi ^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}\right )^{5} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )\right )-6 x \,\pi ^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}\right )^{4} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )\right )^{2}+4 x \,\pi ^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}\right )^{3} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )\right )^{3}-x \,\pi ^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )\right )^{4}+16 x \ln \left (\ln \left (x -2 x \ln \relax (2)\right )+4\right )^{2}-4\right )}{4}}\) | \(280\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 22, normalized size = 0.85 \begin {gather*} e^{\left (-4 \, x^{2} \log \left (\log \relax (x) + \log \left (-2 \, \log \relax (2) + 1\right ) + 4\right )^{2} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.48, size = 36, normalized size = 1.38 \begin {gather*} {\mathrm {e}}^x\,{\mathrm {e}}^{-x^2\,{\ln \left (\frac {1}{{\ln \left (x-2\,x\,\ln \relax (2)\right )}^2+8\,\ln \left (x-2\,x\,\ln \relax (2)\right )+16}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.67, size = 36, normalized size = 1.38 \begin {gather*} e^{- x^{2} \log {\left (\frac {1}{\log {\left (- 2 x \log {\relax (2 )} + x \right )}^{2} + 8 \log {\left (- 2 x \log {\relax (2 )} + x \right )} + 16} \right )}^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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