Optimal. Leaf size=24 \[ e^{e^{-4+e^{2 (-2+x) x^2}+(x-\log (5))^2}} \]
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Rubi [F]
time = 7.37, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \exp \left (-4+e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)+\log ^2(5)\right ) \left (2 x+e^{-4 x^2+2 x^3} \left (-8 x+6 x^2\right )-2 \log (5)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) \left (2 x+e^{-4 x^2+2 x^3} \left (-8 x+6 x^2\right )-2 \log (5)\right ) \, dx\\ &=\int \left (2 \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x+2 \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x (-4+3 x)-2 \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) \log (5)\right ) \, dx\\ &=2 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x \, dx+2 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x (-4+3 x) \, dx-(2 \log (5)) \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) \, dx\\ &=2 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x \, dx+2 \int \left (-4 \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x+3 \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x^2\right ) \, dx-(2 \log (5)) \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) \, dx\\ &=2 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x \, dx+6 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x^2 \, dx-8 \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2+2 (-2+x) x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) x \, dx-(2 \log (5)) \int \exp \left (e^{-4 x^2+2 x^3}+\exp \left (-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)\right )+x^2-2 x \log (5)-4 \left (1-\frac {\log ^2(5)}{4}\right )\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 1.45, size = 0, normalized size = 0.00 \begin {gather*} \int e^{-4+e^{-4 x^2+2 x^3}+e^{-4+e^{-4 x^2+2 x^3}+x^2-2 x \log (5)+\log ^2(5)}+x^2-2 x \log (5)+\log ^2(5)} \left (2 x+e^{-4 x^2+2 x^3} \left (-8 x+6 x^2\right )-2 \log (5)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.63, size = 29, normalized size = 1.21
method | result | size |
risch | \({\mathrm e}^{\left (\frac {1}{25}\right )^{x} {\mathrm e}^{{\mathrm e}^{2 \left (x -2\right ) x^{2}}+\ln \left (5\right )^{2}-4+x^{2}}}\) | \(25\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 x^{3}-4 x^{2}}+\ln \left (5\right )^{2}-2 x \ln \left (5\right )+x^{2}-4}}\) | \(29\) |
default | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 x^{3}-4 x^{2}}+\ln \left (5\right )^{2}-2 x \ln \left (5\right )+x^{2}-4}}\) | \(29\) |
norman | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 x^{3}-4 x^{2}}+\ln \left (5\right )^{2}-2 x \ln \left (5\right )+x^{2}-4}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.98, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (e^{\left (x^{2} - 2 \, x \log \left (5\right ) + \log \left (5\right )^{2} + e^{\left (2 \, x^{3} - 4 \, x^{2}\right )} - 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (e^{\left (x^{2} - 2 \, x \log \left (5\right ) + \log \left (5\right )^{2} + e^{\left (2 \, x^{3} - 4 \, x^{2}\right )} - 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.68, size = 31, normalized size = 1.29 \begin {gather*} e^{e^{x^{2} - 2 x \log {\left (5 \right )} + e^{2 x^{3} - 4 x^{2}} - 4 + \log {\left (5 \right )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.20, size = 34, normalized size = 1.42 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{{\ln \left (5\right )}^2}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x^3}\,{\mathrm {e}}^{-4\,x^2}}}{5^{2\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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