Optimal. Leaf size=26 \[ \log \left (\frac {1}{50} \left (-1-e^{e^{-4-e^{x^4}+x}}+x\right )^2\right ) \]
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Rubi [F] time = 2.67, 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 {-2 x+e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x} \left (2 x-8 e^{x^4} x^4\right )}{x+e^{e^{-4-e^{x^4}+x}} x-x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 e^{-4-e^{x^4}} \left (e^{4+e^{x^4}}-e^{e^{-4-e^{x^4}+x}+x}\right )}{1+e^{e^{-4-e^{x^4}+x}}-x}-\frac {8 e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x+x^4} x^3}{1+e^{e^{-4-e^{x^4}+x}}-x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-4-e^{x^4}} \left (e^{4+e^{x^4}}-e^{e^{-4-e^{x^4}+x}+x}\right )}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\right )-8 \int \frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x+x^4} x^3}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\\ &=-\left (2 \int \frac {1-e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x}}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\right )-8 \int \frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x+x^4} x^3}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\\ &=-\left (2 \int \left (\frac {1}{1+e^{e^{-4-e^{x^4}+x}}-x}-\frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x}}{1+e^{e^{-4-e^{x^4}+x}}-x}\right ) \, dx\right )-8 \int \frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x+x^4} x^3}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\\ &=-\left (2 \int \frac {1}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\right )+2 \int \frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x}}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx-8 \int \frac {e^{-4-e^{x^4}+e^{-4-e^{x^4}+x}+x+x^4} x^3}{1+e^{e^{-4-e^{x^4}+x}}-x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 22, normalized size = 0.85 \begin {gather*} 2 \log \left (1+e^{e^{-4-e^{x^4}+x}}-x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 19, normalized size = 0.73 \begin {gather*} 2 \, \log \left (-x + e^{\left (e^{\left (x - e^{\left (x^{4}\right )} - 4\right )}\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.33, size = 54, normalized size = 2.08 \begin {gather*} -2 \, x + 2 \, e^{\left (x^{4}\right )} + 2 \, \log \left (-x e^{\left (x - e^{\left (x^{4}\right )}\right )} + e^{\left (x - e^{\left (x^{4}\right )} + e^{\left (x - e^{\left (x^{4}\right )} - 4\right )}\right )} + e^{\left (x - e^{\left (x^{4}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.77
method | result | size |
risch | \(2 \ln \left ({\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x^{4}}+x -4}}-x +1\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 19, normalized size = 0.73 \begin {gather*} 2 \, \log \left (-x + e^{\left (e^{\left (x - e^{\left (x^{4}\right )} - 4\right )}\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.26, size = 21, normalized size = 0.81 \begin {gather*} 2\,\ln \left ({\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^{x^4}}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}-x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 17, normalized size = 0.65 \begin {gather*} 2 \log {\left (- x + e^{e^{x - e^{x^{4}} - 4}} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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