Integrand size = 76, antiderivative size = 31 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=-x+\frac {2 e^{5-e^{e^{\frac {e^{16} x}{3}}}-x}}{\log (5)} \]
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\[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=\int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx \]
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Rubi steps \begin{align*} \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 {\text {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 {\text {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 \text {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 \text {Subst}\left (\int e^{5-e^{e^{e^{16} x}}-3 x} \, dx,x,\frac {x}{3}\right )}{\log (5)} \\ & = -x-\frac {2 \text {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 \text {Subst}\left (\int e^{5-e^{e^{e^{16} x}}-3 x} \, dx,x,\frac {x}{3}\right )}{\log (5)} \\ \end{align*}
Time = 0.64 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.10 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=-\frac {-6 e^{5-e^{e^{\frac {e^{16} x}{3}}}-x}+x \log (125)}{\log (125)} \]
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84
method | result | size |
risch | \(\frac {2 \,{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}-x +5}}{\ln \left (5\right )}-x\) | \(26\) |
norman | \(\left (\frac {2}{\ln \left (5\right )}-x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}+x -5}\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}-x +5}\) | \(36\) |
parallelrisch | \(-\frac {\left (3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}+x -5} x \ln \left (5\right )-6\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{\frac {x \,{\mathrm e}^{16}}{3}}}-x +5}}{3 \ln \left (5\right )}\) | \(38\) |
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Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.81 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=-\frac {{\left (x e^{\left ({\left ({\left (x - 5\right )} e^{\left (\frac {1}{3} \, x e^{16} + 16\right )} + e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{16} - 16\right )}\right )} \log \left (5\right ) - 2\right )} e^{\left (-{\left ({\left (x - 5\right )} e^{\left (\frac {1}{3} \, x e^{16} + 16\right )} + e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{16} - 16\right )}\right )}}{\log \left (5\right )} \]
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Time = 0.21 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.65 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=- x + \frac {2 e^{- x - e^{e^{\frac {x e^{16}}{3}}} + 5}}{\log {\left (5 \right )}} \]
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none
Time = 0.27 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.90 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=-\frac {x \log \left (5\right ) - 2 \, e^{\left (-x - e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} + 5\right )}}{\log \left (5\right )} \]
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\[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=\int { -\frac {{\left (3 \, e^{\left (x + e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} - 5\right )} \log \left (5\right ) + 2 \, e^{\left (\frac {1}{3} \, x e^{16} + e^{\left (\frac {1}{3} \, x e^{16}\right )} + 16\right )} + 6\right )} e^{\left (-x - e^{\left (e^{\left (\frac {1}{3} \, x e^{16}\right )}\right )} + 5\right )}}{3 \, \log \left (5\right )} \,d x } \]
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {e^{5-e^{e^{\frac {e^{16} x}{3}}}-x} \left (-6-2 e^{16+e^{\frac {e^{16} x}{3}}+\frac {e^{16} x}{3}}-3 e^{-5+e^{e^{\frac {e^{16} x}{3}}}+x} \log (5)\right )}{3 \log (5)} \, dx=\frac {2\,{\mathrm {e}}^{-{\mathrm {e}}^{{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{16}}\right )}^{1/3}}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^5}{\ln \left (5\right )}-x \]
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