Optimal. Leaf size=38 \[ \left (2-e^{-e^x+\frac {(2+2 x)^2}{e^{2+e^x x}-\log (5)}}\right ) x \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Aborted
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Mathematica [F] time = 126.13, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 e^{4+2 e^x x}-4 e^{2+e^x x} \log (5)+2 \log ^2(5)+e^{\frac {4-e^{2+x+e^x x}+8 x+4 x^2+e^x \log (5)}{e^{2+e^x x}-\log (5)}} \left (e^{4+2 e^x x} \left (-1+e^x x\right )+\left (8 x+8 x^2\right ) \log (5)-\log ^2(5)+e^x x \log ^2(5)+e^{2+e^x x} \left (-8 x-8 x^2+2 \log (5)+e^x \left (4 x+12 x^2+12 x^3+4 x^4-2 x \log (5)\right )\right )\right )}{e^{4+2 e^x x}-2 e^{2+e^x x} \log (5)+\log ^2(5)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.98, size = 60, normalized size = 1.58 \begin {gather*} -x e^{\left (-\frac {4 \, {\left (x^{2} + 2 \, x + 1\right )} e^{x} + e^{\left (2 \, x\right )} \log \relax (5) - e^{\left (x e^{x} + 2 \, x + 2\right )}}{e^{x} \log \relax (5) - e^{\left (x e^{x} + x + 2\right )}}\right )} + 2 \, x \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*} \int -\frac {{\left (x e^{x} \log \relax (5)^{2} + {\left (x e^{x} - 1\right )} e^{\left (2 \, x e^{x} + 4\right )} - 2 \, {\left (4 \, x^{2} - {\left (2 \, x^{4} + 6 \, x^{3} + 6 \, x^{2} - x \log \relax (5) + 2 \, x\right )} e^{x} + 4 \, x - \log \relax (5)\right )} e^{\left (x e^{x} + 2\right )} + 8 \, {\left (x^{2} + x\right )} \log \relax (5) - \log \relax (5)^{2}\right )} e^{\left (\frac {4 \, x^{2} + e^{x} \log \relax (5) + 8 \, x - e^{\left (x e^{x} + x + 2\right )} + 4}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)}\right )} - 4 \, e^{\left (x e^{x} + 2\right )} \log \relax (5) + 2 \, \log \relax (5)^{2} + 2 \, e^{\left (2 \, x e^{x} + 4\right )}}{2 \, e^{\left (x e^{x} + 2\right )} \log \relax (5) - \log \relax (5)^{2} - e^{\left (2 \, x e^{x} + 4\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 50, normalized size = 1.32
method | result | size |
risch | \(-x \,{\mathrm e}^{-\frac {-{\mathrm e}^{x +{\mathrm e}^{x} x +2}+{\mathrm e}^{x} \ln \relax (5)+4 x^{2}+8 x +4}{-{\mathrm e}^{{\mathrm e}^{x} x +2}+\ln \relax (5)}}+2 x\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.55, size = 104, normalized size = 2.74 \begin {gather*} -x e^{\left (\frac {4 \, x^{2}}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)} + \frac {e^{x} \log \relax (5)}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)} + \frac {8 \, x}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)} - \frac {e^{\left (x e^{x} + x + 2\right )}}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)} + \frac {4}{e^{\left (x e^{x} + 2\right )} - \log \relax (5)}\right )} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {2\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x+4}-4\,{\mathrm {e}}^{x\,{\mathrm {e}}^x+2}\,\ln \relax (5)+{\mathrm {e}}^{-\frac {8\,x+{\mathrm {e}}^x\,\ln \relax (5)-{\mathrm {e}}^{x\,{\mathrm {e}}^x+2}\,{\mathrm {e}}^x+4\,x^2+4}{\ln \relax (5)-{\mathrm {e}}^{x\,{\mathrm {e}}^x+2}}}\,\left (\ln \relax (5)\,\left (8\,x^2+8\,x\right )-{\mathrm {e}}^{x\,{\mathrm {e}}^x+2}\,\left (8\,x-2\,\ln \relax (5)-{\mathrm {e}}^x\,\left (4\,x-2\,x\,\ln \relax (5)+12\,x^2+12\,x^3+4\,x^4\right )+8\,x^2\right )-{\ln \relax (5)}^2+{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x+4}\,\left (x\,{\mathrm {e}}^x-1\right )+x\,{\mathrm {e}}^x\,{\ln \relax (5)}^2\right )+2\,{\ln \relax (5)}^2}{{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x+4}-2\,{\mathrm {e}}^{x\,{\mathrm {e}}^x+2}\,\ln \relax (5)+{\ln \relax (5)}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 8.04, size = 46, normalized size = 1.21 \begin {gather*} - x e^{\frac {4 x^{2} + 8 x - e^{x} e^{x e^{x} + 2} + e^{x} \log {\relax (5 )} + 4}{e^{x e^{x} + 2} - \log {\relax (5 )}}} + 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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