Integrand size = 163, antiderivative size = 27 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\left (e^{e^{5 e^x} x}+\frac {1}{3} \left (e+e^{3 x}\right )\right )^2} \]
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Time = 2.39 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {12, 6820, 6838} \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\frac {1}{9} \left (e^{3 x}+3 e^{e^{5 e^x} x}+e\right )^2} \]
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Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int \exp \left (\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )\right ) \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx \\ & = \frac {1}{3} \int 2 e^{\frac {1}{9} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right )^2} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right ) \left (e^{3 x}+e^{5 e^x+e^{5 e^x} x}+5 e^{5 e^x+x+e^{5 e^x} x} x\right ) \, dx \\ & = \frac {2}{3} \int e^{\frac {1}{9} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right )^2} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right ) \left (e^{3 x}+e^{5 e^x+e^{5 e^x} x}+5 e^{5 e^x+x+e^{5 e^x} x} x\right ) \, dx \\ & = e^{\frac {1}{9} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right )^2} \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\frac {1}{9} \left (e+e^{3 x}+3 e^{e^{5 e^x} x}\right )^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(22)=44\).
Time = 83.10 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{5 \,{\mathrm e}^{x}}}+\frac {2 \,{\mathrm e}^{x \left ({\mathrm e}^{5 \,{\mathrm e}^{x}}+3\right )}}{3}+\frac {2 \,{\mathrm e}^{x \,{\mathrm e}^{5 \,{\mathrm e}^{x}}+1}}{3}+\frac {{\mathrm e}^{6 x}}{9}+\frac {2 \,{\mathrm e}^{1+3 x}}{9}+\frac {{\mathrm e}^{2}}{9}}\) | \(54\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{5 \,{\mathrm e}^{x}}}+\frac {\left (6 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}\right ) {\mathrm e}^{x \,{\mathrm e}^{5 \,{\mathrm e}^{x}}}}{9}+\frac {{\mathrm e}^{6 x}}{9}+\frac {2 \,{\mathrm e} \,{\mathrm e}^{3 x}}{9}+\frac {{\mathrm e}^{2}}{9}}\) | \(56\) |
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\left (\frac {1}{9} \, {\left (6 \, {\left (e^{7} + e^{\left (3 \, x + 6\right )}\right )} e^{\left (x e^{\left (5 \, e^{x}\right )}\right )} + e^{8} + 9 \, e^{\left (2 \, x e^{\left (5 \, e^{x}\right )} + 6\right )} + e^{\left (6 \, x + 6\right )} + 2 \, e^{\left (3 \, x + 7\right )}\right )} e^{\left (-6\right )}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (24) = 48\).
Time = 5.04 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.26 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\left (\frac {2 e^{3 x}}{3} + \frac {2 e}{3}\right ) e^{x e^{5 e^{x}}} + \frac {e^{6 x}}{9} + \frac {2 e e^{3 x}}{9} + e^{2 x e^{5 e^{x}}} + \frac {e^{2}}{9}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (22) = 44\).
Time = 0.50 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.04 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=e^{\left (\frac {1}{9} \, e^{2} + e^{\left (2 \, x e^{\left (5 \, e^{x}\right )}\right )} + \frac {2}{3} \, e^{\left (x e^{\left (5 \, e^{x}\right )} + 3 \, x\right )} + \frac {2}{3} \, e^{\left (x e^{\left (5 \, e^{x}\right )} + 1\right )} + \frac {1}{9} \, e^{\left (6 \, x\right )} + \frac {2}{9} \, e^{\left (3 \, x + 1\right )}\right )} \]
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\[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx=\int { \frac {2}{3} \, {\left (3 \, {\left (5 \, x e^{x} + 1\right )} e^{\left (2 \, x e^{\left (5 \, e^{x}\right )} + 5 \, e^{x}\right )} + {\left ({\left ({\left (5 \, x e^{x} + 1\right )} e^{\left (3 \, x\right )} + 5 \, x e^{\left (x + 1\right )} + e\right )} e^{\left (5 \, e^{x}\right )} + 3 \, e^{\left (3 \, x\right )}\right )} e^{\left (x e^{\left (5 \, e^{x}\right )}\right )} + e^{\left (6 \, x\right )} + e^{\left (3 \, x + 1\right )}\right )} e^{\left (\frac {2}{3} \, {\left (e + e^{\left (3 \, x\right )}\right )} e^{\left (x e^{\left (5 \, e^{x}\right )}\right )} + \frac {1}{9} \, e^{2} + e^{\left (2 \, x e^{\left (5 \, e^{x}\right )}\right )} + \frac {1}{9} \, e^{\left (6 \, x\right )} + \frac {2}{9} \, e^{\left (3 \, x + 1\right )}\right )} \,d x } \]
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Time = 13.46 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.22 \[ \int \frac {1}{3} e^{\frac {1}{9} \left (e^2+e^{6 x}+9 e^{2 e^{5 e^x} x}+2 e^{1+3 x}+e^{e^{5 e^x} x} \left (6 e+6 e^{3 x}\right )\right )} \left (2 e^{6 x}+2 e^{1+3 x}+e^{5 e^x+2 e^{5 e^x} x} \left (6+30 e^x x\right )+e^{e^{5 e^x} x} \left (6 e^{3 x}+e^{5 e^x} \left (2 e+10 e^{1+x} x+e^{3 x} \left (2+10 e^x x\right )\right )\right )\right ) \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{6\,x}}{9}}\,{\mathrm {e}}^{\frac {2\,\mathrm {e}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{5\,{\mathrm {e}}^x}}}{3}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^2}{9}}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{5\,{\mathrm {e}}^x}}}\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{3\,x}\,\mathrm {e}}{9}}\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{5\,{\mathrm {e}}^x}}}{3}} \]
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