Optimal. Leaf size=28 \[ e^{\frac {36}{x^2}-\frac {x \left (x+\log \left (e^e-x\right )\right )}{-1+e x}} \]
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Rubi [F] time = 72.05, 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 (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}\right ) \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^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 \frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{\left (e^e-x\right ) x^3 (1-e x)^2} \, dx\\ &=\int \left (\frac {72 \exp \left (2+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right )}{\left (e^e-x\right ) (-1+e x)^2}+\frac {72 \exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right )}{\left (e^e-x\right ) x^2 (-1+e x)^2}-\frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) x}{\left (e^e-x\right ) (-1+e x)^2}-\frac {2 \exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) x^2}{\left (e^e-x\right ) (-1+e x)^2}+\frac {\exp \left (1+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \left (-144+x^3+x^4\right )}{\left (e^e-x\right ) x (-1+e x)^2}-\frac {\exp \left (e+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \left (72-144 e x+72 e^2 x^2-2 x^4+e x^5\right )}{\left (e^e-x\right ) x^3 (-1+e x)^2}+\frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \log \left (e^e-x\right )}{(-1+e x)^2}\right ) \, dx\\ &=-\left (2 \int \frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) x^2}{\left (e^e-x\right ) (-1+e x)^2} \, dx\right )+72 \int \frac {\exp \left (2+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right )}{\left (e^e-x\right ) (-1+e x)^2} \, dx+72 \int \frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right )}{\left (e^e-x\right ) x^2 (-1+e x)^2} \, dx-\int \frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) x}{\left (e^e-x\right ) (-1+e x)^2} \, dx+\int \frac {\exp \left (1+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \left (-144+x^3+x^4\right )}{\left (e^e-x\right ) x (-1+e x)^2} \, dx-\int \frac {\exp \left (e+\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \left (72-144 e x+72 e^2 x^2-2 x^4+e x^5\right )}{\left (e^e-x\right ) x^3 (-1+e x)^2} \, dx+\int \frac {\exp \left (\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{x^2 (-1+e x)}\right ) \log \left (e^e-x\right )}{(-1+e x)^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.37, size = 43, normalized size = 1.54 \begin {gather*} e^{\frac {36-36 e x+x^4}{x^2-e x^3}} \left (e^e-x\right )^{\frac {x}{1-e x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 39, normalized size = 1.39 \begin {gather*} e^{\left (-\frac {x^{4} + x^{3} \log \left (-x + e^{e}\right ) - 36 \, x e + 36}{x^{3} e - x^{2}}\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 {{\left (2 \, x^{5} + x^{4} - 72 \, x^{3} e^{2} - {\left (x^{6} + x^{5} - 144 \, x^{2}\right )} e - {\left (2 \, x^{4} - 72 \, x^{2} e^{2} - {\left (x^{5} - 144 \, x\right )} e - 72\right )} e^{e} + {\left (x^{4} - x^{3} e^{e}\right )} \log \left (-x + e^{e}\right ) - 72 \, x\right )} e^{\left (-\frac {x^{4} + x^{3} \log \left (-x + e^{e}\right ) - 36 \, x e + 36}{x^{3} e - x^{2}}\right )}}{x^{6} e^{2} - 2 \, x^{5} e + x^{4} - {\left (x^{5} e^{2} - 2 \, x^{4} e + x^{3}\right )} e^{e}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 39, normalized size = 1.39
method | result | size |
risch | \({\mathrm e}^{\frac {-x^{3} \ln \left ({\mathrm e}^{{\mathrm e}}-x \right )+36 x \,{\mathrm e}-x^{4}-36}{x^{2} \left (x \,{\mathrm e}-1\right )}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.56, size = 62, normalized size = 2.21 \begin {gather*} e^{\left (-x e^{\left (-1\right )} - e^{\left (-1\right )} \log \left (-x + e^{e}\right ) - \frac {\log \left (-x + e^{e}\right )}{x e^{2} - e} - \frac {1}{x e^{3} - e^{2}} + \frac {36}{x^{2}} - e^{\left (-2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.37, size = 68, normalized size = 2.43 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {36}{x^3\,\mathrm {e}-x^2}}\,{\mathrm {e}}^{-\frac {x^2}{x\,\mathrm {e}-1}}\,{\mathrm {e}}^{-\frac {36\,\mathrm {e}}{x-x^2\,\mathrm {e}}}}{{\left ({\mathrm {e}}^{\mathrm {e}}-x\right )}^{\frac {x}{x\,\mathrm {e}-1}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 10.99, size = 34, normalized size = 1.21 \begin {gather*} e^{\frac {- x^{4} - x^{3} \log {\left (- x + e^{e} \right )} + 36 e x - 36}{e x^{3} - x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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