Optimal. Leaf size=31 \[ -x+\frac {2 e^{5-e^{e^{\frac {e^{16} x}{3}}}-x}}{\log (5)} \]
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Rubi [F] time = 1.09, 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^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right ) \, dx}{3 \log (5)}\\ &=\frac {\operatorname {Subst}\left (\int e^{5-e^{e^{e^{16} x}}-3 x} \left (-6-2 e^{16+e^{e^{16} x}+e^{16} x}-3 e^{-5+e^{e^{e^{16} x}}+3 x} \log (5)\right ) \, dx,x,\frac {x}{3}\right )}{\log (5)}\\ &=\frac {\operatorname {Subst}\left (\int \left (-6 e^{5-e^{e^{e^{16} x}}-3 x}-2 e^{21-e^{e^{e^{16} x}}+e^{e^{16} x}-3 x+e^{16} x}-3 \log (5)\right ) \, dx,x,\frac {x}{3}\right )}{\log (5)}\\ &=-x-\frac {2 \operatorname {Subst}\left (\int e^{21-e^{e^{e^{16} x}}+e^{e^{16} x}-3 x+e^{16} x} \, dx,x,\frac {x}{3}\right )}{\log (5)}-\frac {6 \operatorname {Subst}\left (\int e^{5-e^{e^{e^{16} x}}-3 x} \, dx,x,\frac {x}{3}\right )}{\log (5)}\\ &=-x-\frac {2 \operatorname {Subst}\left (\int e^{21-e^{e^{e^{16} x}}+e^{e^{16} x}-3 \left (1-\frac {e^{16}}{3}\right ) x} \, dx,x,\frac {x}{3}\right )}{\log (5)}-\frac {6 \operatorname {Subst}\left (\int e^{5-e^{e^{e^{16} x}}-3 x} \, dx,x,\frac {x}{3}\right )}{\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.59, size = 34, normalized size = 1.10 \begin {gather*} -\frac {-6 e^{5-e^{e^{\frac {e^{16} x}{3}}}-x}+x \log (125)}{\log (125)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.62, size = 87, normalized size = 2.81 \begin {gather*} -\frac {{\left (x e^{\left ({\left ({\left (x - 5\right )} e^{\left (\frac {1}{3} \, x e^{16} + 16\right )} + e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{16} - 16\right )}\right )} \log \relax (5) - 2\right )} e^{\left (-{\left ({\left (x - 5\right )} e^{\left (\frac {1}{3} \, x e^{16} + 16\right )} + e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{16} - 16\right )}\right )}}{\log \relax (5)} \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*} \int -\frac {{\left (3 \, e^{\left (x + e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} - 5\right )} \log \relax (5) + 2 \, e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )} + 6\right )} e^{\left (-x - e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} + 5\right )}}{3 \, \log \relax (5)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 26, normalized size = 0.84
method | result | size |
risch | \(\frac {2 \,{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}-x +5}}{\ln \relax (5)}-x\) | \(26\) |
norman | \(\left (\frac {2}{\ln \relax (5)}-x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}+x -5}\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}-x +5}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 28, normalized size = 0.90 \begin {gather*} -\frac {x \log \relax (5) - 2 \, e^{\left (-x - e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} + 5\right )}}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 27, normalized size = 0.87 \begin {gather*} \frac {2\,{\mathrm {e}}^{-{\mathrm {e}}^{{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{16}}\right )}^{1/3}}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^5}{\ln \relax (5)}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 20, normalized size = 0.65 \begin {gather*} - x + \frac {2 e^{- x - e^{e^{\frac {x e^{16}}{3}}} + 5}}{\log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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