Integrand size = 415, antiderivative size = 37 \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=\left (-e^{x+e^{4+\frac {x}{x+\frac {3}{-e^x+x}}} x^2}+x^2\right )^2 \]
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Timed out. \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Time = 1.87 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.95 \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=\left (e^{x \left (1+e^{5-\frac {3}{3-e^x x+x^2}} x\right )}-x^2\right )^2 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(78\) vs. \(2(34)=68\).
Time = 57.59 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.14
method | result | size |
risch | \(x^{4}-2 \,{\mathrm e}^{x \left (x \,{\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+1\right )} x^{2}+{\mathrm e}^{2 x \left (x \,{\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+1\right )}\) | \(79\) |
parallelrisch | \(x^{4}-2 \,{\mathrm e}^{x^{2} {\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+x} x^{2}+{\mathrm e}^{2 x^{2} {\mathrm e}^{\frac {5 \,{\mathrm e}^{x} x -5 x^{2}-12}{{\mathrm e}^{x} x -x^{2}-3}}+2 x}-27\) | \(81\) |
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Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (34) = 68\).
Time = 0.27 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.11 \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=x^{4} - 2 \, x^{2} e^{\left (x^{2} e^{\left (\frac {5 \, x^{2} - 5 \, x e^{x} + 12}{x^{2} - x e^{x} + 3}\right )} + x\right )} + e^{\left (2 \, x^{2} e^{\left (\frac {5 \, x^{2} - 5 \, x e^{x} + 12}{x^{2} - x e^{x} + 3}\right )} + 2 \, x\right )} \]
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Timed out. \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=\text {Timed out} \]
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none
Time = 0.32 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.62 \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=x^{4} - 2 \, x^{2} e^{\left (x^{2} e^{\left (-\frac {3}{x^{2} - x e^{x} + 3} + 5\right )} + x\right )} + e^{\left (2 \, x^{2} e^{\left (-\frac {3}{x^{2} - x e^{x} + 3} + 5\right )} + 2 \, x\right )} \]
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Exception generated. \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx=\text {Exception raised: RuntimeError} \]
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Time = 14.62 (sec) , antiderivative size = 129, normalized size of antiderivative = 3.49 \[ \int \frac {36 x^3+24 x^5+4 e^{2 x} x^5+4 x^7+e^x \left (-24 x^4-8 x^6\right )+e^{2 x+2 e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (18+12 x^2+2 e^{2 x} x^2+2 x^4+e^x \left (-12 x-4 x^3\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (36 x+36 x^3+4 e^{2 x} x^3+4 x^5+e^x \left (-30 x^2-6 x^3-8 x^4\right )\right )\right )+e^{x+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} x^2} \left (-36 x-18 x^2-24 x^3-12 x^4-4 x^5-2 x^6+e^{2 x} \left (-4 x^3-2 x^4\right )+e^x \left (24 x^2+12 x^3+8 x^4+4 x^5\right )+e^{\frac {-12+5 e^x x-5 x^2}{-3+e^x x-x^2}} \left (-36 x^3-36 x^5-4 e^{2 x} x^5-4 x^7+e^x \left (30 x^4+6 x^5+8 x^6\right )\right )\right )}{9+6 x^2+e^{2 x} x^2+x^4+e^x \left (-6 x-2 x^3\right )} \, dx={\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{\frac {12}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{-\frac {5\,x\,{\mathrm {e}}^x}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{\frac {5\,x^2}{x^2-x\,{\mathrm {e}}^x+3}}}+x^4-2\,x^2\,{\mathrm {e}}^x\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{\frac {12}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{-\frac {5\,x\,{\mathrm {e}}^x}{x^2-x\,{\mathrm {e}}^x+3}}\,{\mathrm {e}}^{\frac {5\,x^2}{x^2-x\,{\mathrm {e}}^x+3}}} \]
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