Optimal. Leaf size=23 \[ e^{\frac {\left (e^x-x\right ) \left (i \pi +\log \left (\frac {13}{6}\right )\right )}{x^6}} \]
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Rubi [A]
time = 1.24, antiderivative size = 34, normalized size of antiderivative = 1.48, number of steps
used = 1, number of rules used = 1, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6838}
\begin {gather*} \exp \left (\frac {e^x \left (\log \left (\frac {13}{6}\right )+i \pi \right )-x \left (\log \left (\frac {13}{6}\right )+i \pi \right )}{x^6}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (\frac {e^x \left (i \pi +\log \left (\frac {13}{6}\right )\right )-x \left (i \pi +\log \left (\frac {13}{6}\right )\right )}{x^6}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Both result and optimal contain complex but leaf count is larger than twice
the leaf count of optimal. \(61\) vs. \(2(23)=46\).
time = 0.51, size = 61, normalized size = 2.65 \begin {gather*} -\frac {i \left (\frac {6}{13}\right )^{\frac {1}{x^5}} e^{-\frac {i \pi }{x^5}+\frac {e^x \left (i \pi +\log \left (\frac {13}{6}\right )\right )}{x^6}} \left (i \pi +\log \left (\frac {13}{6}\right )\right )}{\pi -i \log \left (\frac {13}{6}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.12, size = 27, normalized size = 1.17
method | result | size |
norman | \({\mathrm e}^{\frac {\left (\ln \left (\frac {13}{6}\right )+i \pi \right ) {\mathrm e}^{x}-x \left (\ln \left (\frac {13}{6}\right )+i \pi \right )}{x^{6}}}\) | \(27\) |
risch | \({\mathrm e}^{\frac {\left (i \pi -\ln \left (2\right )-\ln \left (3\right )+\ln \left (13\right )\right ) \left ({\mathrm e}^{x}-x \right )}{x^{6}}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.66, size = 61, normalized size = 2.65 \begin {gather*} e^{\left (-\frac {i \, \pi }{x^{5}} + \frac {i \, \pi e^{x}}{x^{6}} - \frac {\log \left (13\right )}{x^{5}} + \frac {e^{x} \log \left (13\right )}{x^{6}} + \frac {\log \left (3\right )}{x^{5}} - \frac {e^{x} \log \left (3\right )}{x^{6}} + \frac {\log \left (2\right )}{x^{5}} - \frac {e^{x} \log \left (2\right )}{x^{6}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 31, normalized size = 1.35 \begin {gather*} e^{\left (-\frac {i \, \pi }{x^{5}} + \frac {i \, \pi e^{x}}{x^{6}} - \frac {\log \left (\frac {13}{6}\right )}{x^{5}} + \frac {e^{x} \log \left (\frac {13}{6}\right )}{x^{6}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [A]
time = 0.42, size = 31, normalized size = 1.35 \begin {gather*} e^{\left (-\frac {i \, \pi }{x^{5}} + \frac {i \, \pi e^{x}}{x^{6}} - \frac {\log \left (\frac {13}{6}\right )}{x^{5}} + \frac {e^{x} \log \left (\frac {13}{6}\right )}{x^{6}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.99, size = 49, normalized size = 2.13 \begin {gather*} \frac {6^{\frac {1}{x^5}}\,{13}^{\frac {{\mathrm {e}}^x}{x^6}}\,{\mathrm {e}}^{\frac {\Pi \,{\mathrm {e}}^x\,1{}\mathrm {i}}{x^6}}\,{\mathrm {e}}^{-\frac {\Pi \,1{}\mathrm {i}}{x^5}}}{6^{\frac {{\mathrm {e}}^x}{x^6}}\,{13}^{\frac {1}{x^5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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