Optimal. Leaf size=34 \[ e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}} x+(5+x-\log (3)) (-1+x-\log (x)) \]
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Rubi [F] time = 2.93, 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^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}} \left (8 e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}} x+x \log ^3\left (\frac {x}{4}\right )+e^{e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}} \left (\left (-5+3 x+2 x^2+(1-x) \log (3)\right ) \log ^3\left (\frac {x}{4}\right )-x \log ^3\left (\frac {x}{4}\right ) \log (x)\right )\right )}{x \log ^3\left (\frac {x}{4}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3+e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}-\frac {5}{x}+2 x-\log (3)+\frac {\log (3)}{x}+\frac {8 e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}+\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}{\log ^3\left (\frac {x}{4}\right )}-\log (x)\right ) \, dx\\ &=\int \left (3+e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}+2 x+\frac {-5+\log (3)}{x}-\log (3)+\frac {8 e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}+\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}{\log ^3\left (\frac {x}{4}\right )}-\log (x)\right ) \, dx\\ &=x^2+x (3-\log (3))-(5-\log (3)) \log (x)+8 \int \frac {e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}+\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}{\log ^3\left (\frac {x}{4}\right )} \, dx+\int e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}} \, dx-\int \log (x) \, dx\\ &=x+x^2+x (3-\log (3))-x \log (x)-(5-\log (3)) \log (x)+4 \operatorname {Subst}\left (\int e^{-e^{\frac {4}{\log ^2(x)}}} \, dx,x,\frac {x}{4}\right )+32 \operatorname {Subst}\left (\int \frac {e^{-e^{\frac {4}{\log ^2(x)}}+\frac {4}{\log ^2(x)}}}{\log ^3(x)} \, dx,x,\frac {x}{4}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.35, size = 36, normalized size = 1.06 \begin {gather*} x \left (4+e^{-e^{\frac {4}{\log ^2\left (\frac {x}{4}\right )}}}+x-\log (3)\right )+(-5-x+\log (3)) \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 56, normalized size = 1.65 \begin {gather*} {\left ({\left (x^{2} - x \log \relax (3) - 2 \, x \log \relax (2) - {\left (x - \log \relax (3) + 5\right )} \log \left (\frac {1}{4} \, x\right ) + 4 \, x\right )} e^{\left (e^{\left (\frac {4}{\log \left (\frac {1}{4} \, x\right )^{2}}\right )}\right )} + x\right )} e^{\left (-e^{\left (\frac {4}{\log \left (\frac {1}{4} \, x\right )^{2}}\right )}\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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 46, normalized size = 1.35
method | result | size |
risch | \(-x \ln \relax (x )+\ln \relax (3) \ln \relax (x )-x \ln \relax (3)+x^{2}-5 \ln \relax (x )+4 x +x \,{\mathrm e}^{-{\mathrm e}^{\frac {4}{\left (2 \ln \relax (2)-\ln \relax (x )\right )^{2}}}}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 53, normalized size = 1.56 \begin {gather*} x^{2} + x e^{\left (-e^{\left (\frac {4}{4 \, \log \relax (2)^{2} - 4 \, \log \relax (2) \log \relax (x) + \log \relax (x)^{2}}\right )}\right )} - x \log \relax (3) - x \log \relax (x) + \log \relax (3) \log \relax (x) + 4 \, x - 5 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.42, size = 50, normalized size = 1.47 \begin {gather*} \ln \relax (x)\,\left (\ln \relax (3)-5\right )+x\,{\mathrm {e}}^{-{\mathrm {e}}^{\frac {4}{{\ln \relax (x)}^2-4\,\ln \relax (2)\,\ln \relax (x)+4\,{\ln \relax (2)}^2}}}-x\,\left (\ln \relax (3)-4\right )-x\,\ln \relax (x)+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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