Optimal. Leaf size=26 \[ e^{-1-e^x+e^{3+\log ^x(12)} (-4+x)^2-x} \]
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Rubi [F]
time = 4.74, 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 e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \left (-1-e^x+e^{3+\log ^x(12)} \left (-8+2 x+\left (16-8 x+x^2\right ) \log ^x(12) \log (\log (12))\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )}-e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )}+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \left (2-4 \log ^x(12) \log (\log (12))+x \log ^x(12) \log (\log (12))\right )\right ) \, dx\\ &=-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx+\int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \left (2-4 \log ^x(12) \log (\log (12))+x \log ^x(12) \log (\log (12))\right ) \, dx\\ &=-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx+\int \left (2 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)^2 \log ^x(12) \log (\log (12))\right ) \, dx\\ &=2 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \, dx+\log (\log (12)) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)^2 \log ^x(12) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ &=2 \int \left (-4 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right )+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x\right ) \, dx+\log (\log (12)) \int \left (16 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \log ^x(12)-8 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \log ^x(12)+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x^2 \log ^x(12)\right ) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ &=2 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \, dx-8 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \, dx+\log (\log (12)) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x^2 \log ^x(12) \, dx-(8 \log (\log (12))) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \log ^x(12) \, dx+(16 \log (\log (12))) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \log ^x(12) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 2.40, size = 26, normalized size = 1.00 \begin {gather*} e^{-1-e^x+e^{3+\log ^x(12)} (-4+x)^2-x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs.
\(2(25)=50\).
time = 0.17, size = 56, normalized size = 2.15
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\left (\ln \left (3\right )+2 \ln \left (2\right )\right )^{x}+3} x^{2}-8 \,{\mathrm e}^{\left (\ln \left (3\right )+2 \ln \left (2\right )\right )^{x}+3} x -{\mathrm e}^{x}+16 \,{\mathrm e}^{\left (\ln \left (3\right )+2 \ln \left (2\right )\right )^{x}+3}-x -1}\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (23) = 46\).
time = 0.89, size = 55, normalized size = 2.12 \begin {gather*} e^{\left (x^{2} e^{\left ({\left (\log \left (3\right ) + 2 \, \log \left (2\right )\right )}^{x} + 3\right )} - 8 \, x e^{\left ({\left (\log \left (3\right ) + 2 \, \log \left (2\right )\right )}^{x} + 3\right )} - x - e^{x} + 16 \, e^{\left ({\left (\log \left (3\right ) + 2 \, \log \left (2\right )\right )}^{x} + 3\right )} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 26, normalized size = 1.00 \begin {gather*} e^{\left ({\left (x^{2} - 8 \, x + 16\right )} e^{\left (\log \left (12\right )^{x} + 3\right )} - x - e^{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, size = 40, normalized size = 1.54 \begin {gather*} e^{\left (x^{2} e^{\left (\log \left (12\right )^{x} + 3\right )} - 8 \, x e^{\left (\log \left (12\right )^{x} + 3\right )} - x - e^{x} + 16 \, e^{\left (\log \left (12\right )^{x} + 3\right )} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.60, size = 45, normalized size = 1.73 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}}\,{\mathrm {e}}^{16\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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