Optimal. Leaf size=24 \[ e^{e^{e^{-1+x}}} \left (4-4 e^{-x}\right )+\log \left (x^4\right ) \]
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Rubi [F] time = 0.68, 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 {e^{-x} \left (4 e^x+e^{e^{e^{-1+x}}} \left (4 x+e^{e^{-1+x}} \left (-4 e^{-1+x} x+4 e^{-1+2 x} x\right )\right )\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4 e^{e^{e^{-1+x}}-x}+4 e^{-1+e^{e^{-1+x}}+e^{-1+x}+x}+\frac {4 \left (e-e^{e^{e^{-1+x}}+e^{-1+x}} x\right )}{e x}\right ) \, dx\\ &=4 \int e^{e^{e^{-1+x}}-x} \, dx+4 \int e^{-1+e^{e^{-1+x}}+e^{-1+x}+x} \, dx+\frac {4 \int \frac {e-e^{e^{e^{-1+x}}+e^{-1+x}} x}{x} \, dx}{e}\\ &=4 \operatorname {Subst}\left (\int e^{-1+e^{\frac {x}{e}}+\frac {x}{e}} \, dx,x,e^x\right )+4 \operatorname {Subst}\left (\int \frac {e^{e^{\frac {x}{e}}}}{x^2} \, dx,x,e^x\right )+\frac {4 \int \left (-e^{e^{e^{-1+x}}+e^{-1+x}}+\frac {e}{x}\right ) \, dx}{e}\\ &=4 \log (x)+4 \operatorname {Subst}\left (\int \frac {e^{e^{\frac {x}{e}}}}{x^2} \, dx,x,e^x\right )-\frac {4 \int e^{e^{e^{-1+x}}+e^{-1+x}} \, dx}{e}+(4 e) \operatorname {Subst}\left (\int e^{-1+x} \, dx,x,e^{e^{-1+x}}\right )\\ &=4 e^{e^{e^{-1+x}}}+4 \log (x)+4 \operatorname {Subst}\left (\int \frac {e^{e^{\frac {x}{e}}}}{x^2} \, dx,x,e^x\right )-\frac {4 \operatorname {Subst}\left (\int \frac {e^{e^x+x}}{x} \, dx,x,e^{-1+x}\right )}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 24, normalized size = 1.00 \begin {gather*} 4 \left (e^{e^{e^{-1+x}}-x} \left (-1+e^x\right )+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.29, size = 23, normalized size = 0.96 \begin {gather*} 4 \, {\left ({\left (e^{x} - 1\right )} e^{\left (e^{\left (e^{\left (x - 1\right )}\right )}\right )} + e^{x} \log \relax (x)\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.37, size = 44, normalized size = 1.83 \begin {gather*} 4 \, {\left (e^{\left (x + e^{\left (x - 1\right )} + e^{\left (e^{\left (x - 1\right )}\right )}\right )} - e^{\left (e^{\left (x - 1\right )} + e^{\left (e^{\left (x - 1\right )}\right )}\right )}\right )} e^{\left (-x - e^{\left (x - 1\right )}\right )} + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 22, normalized size = 0.92
method | result | size |
risch | \(4 \ln \relax (x )+4 \left ({\mathrm e}^{x}-1\right ) {\mathrm e}^{-x +{\mathrm e}^{{\mathrm e}^{x -1}}}\) | \(22\) |
norman | \(\left (4 \,{\mathrm e}^{-1} {\mathrm e} \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} {\mathrm e}^{-1}}}-4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} {\mathrm e}^{-1}}}\right ) {\mathrm e}^{-x}+4 \ln \relax (x )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 21, normalized size = 0.88 \begin {gather*} 4 \, {\left (e^{x} - 1\right )} e^{\left (-x + e^{\left (e^{\left (x - 1\right )}\right )}\right )} + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.16, size = 23, normalized size = 0.96 \begin {gather*} 4\,\ln \relax (x)+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-1}\,{\mathrm {e}}^x}-x}\,\left (4\,{\mathrm {e}}^x-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 81.61, size = 20, normalized size = 0.83 \begin {gather*} \left (4 - 4 e^{- x}\right ) e^{e^{\frac {e^{x}}{e}}} + 4 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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