Optimal. Leaf size=28 \[ e^{-7+x-\left (2 x+x \left (e^{3+x}+x\right )\right ) (2-\log (\log (\log (x))))} \]
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Rubi [F] time = 37.35, 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 \frac {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\exp \left (-4-2 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x))+\log (x) \log (\log (x)) \log (\log (\log (x)))+x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))}+\frac {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2 x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))}\right ) \, dx\\ &=\int \frac {\exp \left (-4-2 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x))+\log (x) \log (\log (x)) \log (\log (\log (x)))+x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx+\int \frac {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2 x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx\\ &=\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1+(1+x) \log (x) \log (\log (x)) (-2+\log (\log (\log (x)))))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x+\log (x) \log (\log (x)) (-3-4 x+2 (1+x) \log (\log (\log (x)))))}{\log (x)} \, dx\\ &=\int \left (\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x)))}{\log (x)}+2 e^{-7-3 x-2 e^{3+x} x-2 x^2} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx+\int \left (\frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x)))}{\log (x)}+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx\\ &=2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x)))}{\log (x)} \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x)))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \left (e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))+e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 (1+x) \log (x) \log (\log (x)))}{\log (x)} \, dx+\int \left (\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} (2+x) \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}-e^{-7-3 x-2 e^{3+x} x-2 x^2} (3+4 x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int \left (e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx\\ &=2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} (2+x) \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-\int e^{-7-3 x-2 e^{3+x} x-2 x^2} (3+4 x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \left (\frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}-2 e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=-\left (2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx\right )+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \left (\frac {2 e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}+\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}\right ) \, dx-\int \left (3 e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))+4 e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-2 \int \left (e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx-3 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-4 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx-3 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-4 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.23, size = 35, normalized size = 1.25 \begin {gather*} e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{x \left (2+e^{3+x}+x\right )}(\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.49, size = 36, normalized size = 1.29 \begin {gather*} e^{\left (-2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + {\left (x^{2} + x e^{\left (x + 3\right )} + 2 \, x\right )} \log \left (\log \left (\log \relax (x)\right )\right ) - 3 \, x - 7\right )} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 33, normalized size = 1.18
method | result | size |
risch | \(\ln \left (\ln \relax (x )\right )^{\left ({\mathrm e}^{3+x}+x +2\right ) x} {\mathrm e}^{-7-2 \,{\mathrm e}^{3+x} x -2 x^{2}-3 x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 43, normalized size = 1.54 \begin {gather*} e^{\left (x^{2} \log \left (\log \left (\log \relax (x)\right )\right ) + x e^{\left (x + 3\right )} \log \left (\log \left (\log \relax (x)\right )\right ) - 2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + 2 \, x \log \left (\log \left (\log \relax (x)\right )\right ) - 3 \, x - 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.44, size = 38, normalized size = 1.36 \begin {gather*} {\ln \left (\ln \relax (x)\right )}^{2\,x+x^2+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-7}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 20.40, size = 39, normalized size = 1.39 \begin {gather*} e^{- 2 x^{2} - 2 x e^{x + 3} - 3 x + \left (x^{2} + x e^{x + 3} + 2 x\right ) \log {\left (\log {\left (\log {\relax (x )} \right )} \right )} - 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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