Optimal. Leaf size=22 \[ e^{\left (2 \left (-10+e^{3+e^{e^x} x}\right )+\log (x)\right )^2} \]
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Rubi [B] time = 3.22, antiderivative size = 209, normalized size of antiderivative = 9.50, number of steps used = 1, number of rules used = 1, integrand size = 125, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2288} \begin {gather*} \frac {\left (4 e^{2 e^{e^x} x+e^x+6} \left (e^x x^2+x\right )+2 e^{e^{e^x} x+3} \left (1-e^{e^x} \left (20 e^x x^2-\left (e^x x^2+x\right ) \log (x)+20 x\right )\right )+\log (x)\right ) \exp \left (4 e^{2 e^{e^x} x+6}+\log ^2(x)-4 e^{e^{e^x} x+3} (20-\log (x))+400\right )}{x^{41} \left (4 e^{2 e^{e^x} x+6} \left (e^{x+e^x} x+e^{e^x}\right )+\frac {2 e^{e^{e^x} x+3}}{x}-2 e^{e^{e^x} x+3} \left (e^{x+e^x} x+e^{e^x}\right ) (20-\log (x))+\frac {\log (x)}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\exp \left (400+4 e^{6+2 e^{e^x} x}-4 e^{3+e^{e^x} x} (20-\log (x))+\log ^2(x)\right ) \left (4 e^{6+e^x+2 e^{e^x} x} \left (x+e^x x^2\right )+\log (x)+2 e^{3+e^{e^x} x} \left (1-e^{e^x} \left (20 x+20 e^x x^2-\left (x+e^x x^2\right ) \log (x)\right )\right )\right )}{x^{41} \left (\frac {2 e^{3+e^{e^x} x}}{x}+4 e^{6+2 e^{e^x} x} \left (e^{e^x}+e^{e^x+x} x\right )-2 e^{3+e^{e^x} x} \left (e^{e^x}+e^{e^x+x} x\right ) (20-\log (x))+\frac {\log (x)}{x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.44, size = 42, normalized size = 1.91 \begin {gather*} e^{4 \left (-10+e^{3+e^{e^x} x}\right )^2+\log ^2(x)} x^{-40+4 e^{3+e^{e^x} x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 36, normalized size = 1.64 \begin {gather*} e^{\left (4 \, {\left (\log \relax (x) - 20\right )} e^{\left (x e^{\left (e^{x}\right )} + 3\right )} + \log \relax (x)^{2} + 4 \, e^{\left (2 \, x e^{\left (e^{x}\right )} + 6\right )} - 40 \, \log \relax (x) + 400\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*} \int \frac {2 \, {\left (4 \, {\left (x^{2} e^{x} + x\right )} e^{\left (2 \, x e^{\left (e^{x}\right )} + e^{x} + 6\right )} - 2 \, {\left ({\left (20 \, x^{2} e^{x} - {\left (x^{2} e^{x} + x\right )} \log \relax (x) + 20 \, x\right )} e^{\left (e^{x}\right )} - 1\right )} e^{\left (x e^{\left (e^{x}\right )} + 3\right )} + \log \relax (x) - 20\right )} e^{\left (4 \, {\left (\log \relax (x) - 20\right )} e^{\left (x e^{\left (e^{x}\right )} + 3\right )} + \log \relax (x)^{2} + 4 \, e^{\left (2 \, x e^{\left (e^{x}\right )} + 6\right )} - 40 \, \log \relax (x) + 400\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.13, size = 45, normalized size = 2.05
method | result | size |
risch | \(\frac {x^{4 \,{\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{x}}+3}} {\mathrm e}^{\ln \relax (x )^{2}+400+4 \,{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{x}}+6}-80 \,{\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{x}}+3}}}{x^{40}}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.64, size = 44, normalized size = 2.00 \begin {gather*} \frac {e^{\left (4 \, e^{\left (x e^{\left (e^{x}\right )} + 3\right )} \log \relax (x) + \log \relax (x)^{2} + 4 \, e^{\left (2 \, x e^{\left (e^{x}\right )} + 6\right )} - 80 \, e^{\left (x e^{\left (e^{x}\right )} + 3\right )} + 400\right )}}{x^{40}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.37, size = 46, normalized size = 2.09 \begin {gather*} \frac {x^{4\,{\mathrm {e}}^3\,{\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^x}}}\,{\mathrm {e}}^{400}\,{\mathrm {e}}^{{\ln \relax (x)}^2}\,{\mathrm {e}}^{4\,{\mathrm {e}}^6\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{{\mathrm {e}}^x}}}\,{\mathrm {e}}^{-80\,{\mathrm {e}}^3\,{\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^x}}}}{x^{40}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 25.63, size = 41, normalized size = 1.86 \begin {gather*} \frac {e^{\left (4 \log {\relax (x )} - 80\right ) e^{x e^{e^{x}} + 3} + 4 e^{2 x e^{e^{x}} + 6} + \log {\relax (x )}^{2} + 400}}{x^{40}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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