Optimal. Leaf size=27 \[ e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \]
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Rubi [F] time = 25.69, 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 (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\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 (-\frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^3}{\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}+\frac {3 \exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^2}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) \, dx\\ &=3 \int \frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^2}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx-\int \frac {\exp \left (e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}\right ) x^3}{\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 27, normalized size = 1.00 \begin {gather*} e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 179, normalized size = 6.63 \begin {gather*} \cosh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) - \sinh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [A] time = 0.47, size = 24, normalized size = 0.89
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{3}}{\ln \left (-\ln \left (23\right )+\ln \relax (3)-i \pi +3+x \right )}}}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}}\,{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}\,\left (\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )\,\left (9\,x^2-3\,x^2\,\left (\ln \left (\frac {23}{3}\right )+\Pi \,1{}\mathrm {i}\right )+3\,x^3\right )-x^3\right )}{{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}^2\,\left (\ln \left (\frac {23}{3}\right )-x-3+\Pi \,1{}\mathrm {i}\right )} \,d x \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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