Integrand size = 139, antiderivative size = 23 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=1+e^{\left (9-x+2 \left (1+e^3\right ) \left (e^x+x\right )\right )^2} \]
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Time = 1.39 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6, 6820, 12, 6838} \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{\left (\left (1+2 e^3\right ) x+2 \left (1+e^3\right ) e^x+9\right )^2} \]
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Rule 6
Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \exp \left (81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )\right ) \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+\left (2+8 e^6\right ) x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx \\ & = \int 2 e^{\left (9+2 e^x \left (1+e^3\right )+\left (1+2 e^3\right ) x\right )^2} \left (1+2 e^3+2 e^x \left (1+e^3\right )\right ) \left (9+2 e^x \left (1+e^3\right )+\left (1+2 e^3\right ) x\right ) \, dx \\ & = 2 \int e^{\left (9+2 e^x \left (1+e^3\right )+\left (1+2 e^3\right ) x\right )^2} \left (1+2 e^3+2 e^x \left (1+e^3\right )\right ) \left (9+2 e^x \left (1+e^3\right )+\left (1+2 e^3\right ) x\right ) \, dx \\ & = e^{\left (9+2 e^x \left (1+e^3\right )+\left (1+2 e^3\right ) x\right )^2} \\ \end{align*}
Time = 2.05 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{\left (9+2 e^x+2 e^{3+x}+x+2 e^3 x\right )^2} \]
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Timed out.
\[\int \left (\left (8 \,{\mathrm e}^{6}+16 \,{\mathrm e}^{3}+8\right ) {\mathrm e}^{2 x}+\left (\left (8 x +8\right ) {\mathrm e}^{6}+\left (12 x +48\right ) {\mathrm e}^{3}+4 x +40\right ) {\mathrm e}^{x}+8 x \,{\mathrm e}^{6}+\left (8 x +36\right ) {\mathrm e}^{3}+2 x +18\right ) {\mathrm e}^{\left (8 \,{\mathrm e}^{3}+4 \,{\mathrm e}^{6}+4\right ) {\mathrm e}^{2 x}+\left (8 x \,{\mathrm e}^{6}+\left (12 x +36\right ) {\mathrm e}^{3}+4 x +36\right ) {\mathrm e}^{x}+4 x^{2} {\mathrm e}^{6}+\left (4 x^{2}+36 x \right ) {\mathrm e}^{3}+x^{2}+18 x +81}d x\]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.61 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{\left (4 \, x^{2} e^{6} + x^{2} + 4 \, {\left (x^{2} + 9 \, x\right )} e^{3} + 4 \, {\left (e^{6} + 2 \, e^{3} + 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (2 \, x e^{6} + 3 \, {\left (x + 3\right )} e^{3} + x + 9\right )} e^{x} + 18 \, x + 81\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (20) = 40\).
Time = 0.23 (sec) , antiderivative size = 70, normalized size of antiderivative = 3.04 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{x^{2} + 4 x^{2} e^{6} + 18 x + \left (4 x^{2} + 36 x\right ) e^{3} + \left (4 x + 8 x e^{6} + \left (12 x + 36\right ) e^{3} + 36\right ) e^{x} + \left (4 + 8 e^{3} + 4 e^{6}\right ) e^{2 x} + 81} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (20) = 40\).
Time = 0.72 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{\left (4 \, x^{2} e^{6} + 4 \, x^{2} e^{3} + x^{2} + 36 \, x e^{3} + 8 \, x e^{\left (x + 6\right )} + 12 \, x e^{\left (x + 3\right )} + 4 \, x e^{x} + 18 \, x + 4 \, e^{\left (2 \, x\right )} + 4 \, e^{\left (2 \, x + 6\right )} + 8 \, e^{\left (2 \, x + 3\right )} + 36 \, e^{\left (x + 3\right )} + 36 \, e^{x} + 81\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (20) = 40\).
Time = 0.60 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx=e^{\left (4 \, x^{2} e^{6} + 4 \, x^{2} e^{3} + x^{2} + 36 \, x e^{3} + 8 \, x e^{\left (x + 6\right )} + 12 \, x e^{\left (x + 3\right )} + 4 \, x e^{x} + 18 \, x + 4 \, e^{\left (2 \, x\right )} + 4 \, e^{\left (2 \, x + 6\right )} + 8 \, e^{\left (2 \, x + 3\right )} + 36 \, e^{\left (x + 3\right )} + 36 \, e^{x} + 81\right )} \]
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Time = 11.65 (sec) , antiderivative size = 92, normalized size of antiderivative = 4.00 \[ \int e^{81+e^{2 x} \left (4+8 e^3+4 e^6\right )+18 x+x^2+4 e^6 x^2+e^3 \left (36 x+4 x^2\right )+e^x \left (36+4 x+8 e^6 x+e^3 (36+12 x)\right )} \left (18+e^{2 x} \left (8+16 e^3+8 e^6\right )+2 x+8 e^6 x+e^3 (36+8 x)+e^x \left (40+4 x+e^6 (8+8 x)+e^3 (48+12 x)\right )\right ) \, dx={\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{36\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{18\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{81}\,{\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6}\,{\mathrm {e}}^{8\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^3}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^{12\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{36\,{\mathrm {e}}^x}\,{\mathrm {e}}^{36\,x\,{\mathrm {e}}^3} \]
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