Optimal. Leaf size=35 \[ \frac {1}{4} e^{e^{4 e^{-x-\frac {2}{x-x^2}} x^2}} \left (1+e^5\right ) \]
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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 [A] time = 0.30, size = 36, normalized size = 1.03 \begin {gather*} \frac {1}{4} e^{e^{4 e^{\frac {2}{-1+x}-\frac {2}{x}-x} x^2}} \left (1+e^5\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 206, normalized size = 5.89 \begin {gather*} \frac {1}{4} \, {\left (e^{5} + 1\right )} e^{\left (-x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )}\right )} - {\left (x^{3} - x^{2}\right )} e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x} + \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\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 (x^{4} - 4 \, x^{3} + 5 \, x^{2} + {\left (x^{4} - 4 \, x^{3} + 5 \, x^{2} + 2 \, x - 2\right )} e^{5} + 2 \, x - 2\right )} e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x} + e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )}\right )}\right )}}{4 \, {\left (x^{3} - 2 \, x^{2} + x\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 86, normalized size = 2.46
method | result | size |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{\frac {x^{2} \ln \left (4 x \right )-x^{3}-x \ln \left (4 x \right )+x^{2}+2}{x \left (x -1\right )}}}} {\mathrm e}^{5}}{4}+\frac {{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{\frac {x^{2} \ln \left (4 x \right )-x^{3}-x \ln \left (4 x \right )+x^{2}+2}{x \left (x -1\right )}}}}}{4}\) | \(86\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 30, normalized size = 0.86 \begin {gather*} \frac {1}{4} \, {\left (e^{5} + 1\right )} e^{\left (e^{\left (4 \, x^{2} e^{\left (-x + \frac {2}{x - 1} - \frac {2}{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.47, size = 83, normalized size = 2.37 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,x\,x^{\frac {x}{x-x^2}}\,{\mathrm {e}}^{\frac {x^3}{x-x^2}}\,{\mathrm {e}}^{-\frac {x^2}{x-x^2}}\,{\mathrm {e}}^{-\frac {2}{x-x^2}}}{x^{\frac {x^2}{x-x^2}}}}}\,\left (\frac {{\mathrm {e}}^5}{4}+\frac {1}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.89, size = 36, normalized size = 1.03 \begin {gather*} \frac {\left (1 + e^{5}\right ) e^{e^{x e^{\frac {- x^{3} + x^{2} + \left (x^{2} - x\right ) \log {\left (4 x \right )} + 2}{x^{2} - x}}}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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