Optimal. Leaf size=19 \[ e^{e^{\frac {8}{5} x^5 (i \pi +\log (4))}} \]
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Rubi [A]
time = 0.26, antiderivative size = 24, normalized size of antiderivative = 1.26, number of steps
used = 4, number of rules used = 4, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 6847, 2320,
2225} \begin {gather*} e^{2^{\frac {16 x^5}{5}} e^{\frac {8}{5} i \pi x^5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rule 2320
Rule 6847
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=(8 (i \pi +\log (4))) \int \exp \left (e^{\frac {8}{5} x^5 (i \pi +\log (4))}+\frac {8}{5} x^5 (i \pi +\log (4))\right ) x^4 \, dx\\ &=\frac {1}{5} (8 (i \pi +\log (4))) \text {Subst}\left (\int \exp \left (e^{\frac {8}{5} x (i \pi +\log (4))}+\frac {8}{5} x (i \pi +\log (4))\right ) \, dx,x,x^5\right )\\ &=\text {Subst}\left (\int e^x \, dx,x,e^{\frac {8}{5} x^5 (i \pi +\log (4))}\right )\\ &=e^{e^{\frac {8}{5} x^5 (i \pi +\log (4))}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 19, normalized size = 1.00 \begin {gather*} e^{e^{\frac {8}{5} x^5 (i \pi +\log (4))}} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Both result and optimal contain complex but leaf count of result is larger than twice
the leaf count of optimal. 38 vs. \(2 (16 ) = 32\).
time = 0.92, size = 39, normalized size = 2.05
method | result | size |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{\frac {8 x^{5} \left (2 \ln \left (2\right )+i \pi \right )}{5}}}\) | \(17\) |
norman | \({\mathrm e}^{{\mathrm e}^{\frac {8 x^{5} \left (2 \ln \left (2\right )+i \pi \right )}{5}}}\) | \(17\) |
default | \({\mathrm e}^{{\mathrm e}^{\frac {8 x^{5} \left (2 \ln \left (2\right )+i \pi \right )}{5}}}\) | \(39\) |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{\frac {8 x^{5} \left (2 \ln \left (2\right )+i \pi \right )}{5}}} \pi }{\pi -2 i \ln \left (2\right )}-\frac {2 i {\mathrm e}^{{\mathrm e}^{\frac {8 x^{5} \left (2 \ln \left (2\right )+i \pi \right )}{5}}} \ln \left (2\right )}{\pi -2 i \ln \left (2\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 39, normalized size = 2.05 \begin {gather*} \cosh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) - \sinh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 39, normalized size = 2.05 \begin {gather*} \cosh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) - \sinh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 115.87, size = 17, normalized size = 0.89 \begin {gather*} e^{e^{\frac {8 x^{5} \cdot \left (2 \log {\left (2 \right )} + i \pi \right )}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 39, normalized size = 2.05 \begin {gather*} \cosh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) - \sinh \left (-e^{\left (\frac {8}{5} i \, \pi x^{5} + \frac {16}{5} \, x^{5} \log \left (2\right )\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.60, size = 17, normalized size = 0.89 \begin {gather*} {\mathrm {e}}^{2^{\frac {16\,x^5}{5}}\,{\mathrm {e}}^{\frac {\Pi \,x^5\,8{}\mathrm {i}}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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