Integrand size = 269, antiderivative size = 36 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{-\frac {x^2}{9}+\frac {16 \left (-x+x^2-\log (x)\right )^2}{\left (e^{2 x^2}+x\right )^2}} \]
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Timed out. \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(36)=72\).
Time = 0.68 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.14 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\frac {x^2 \left (144-e^{4 x^2}-288 x-2 e^{2 x^2} x+143 x^2\right )+144 \log ^2(x)}{9 \left (e^{2 x^2}+x\right )^2}} x^{-\frac {32 (-1+x) x}{\left (e^{2 x^2}+x\right )^2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(32)=64\).
Time = 0.07 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.25
\[{\mathrm e}^{\frac {-2 \,{\mathrm e}^{2 x^{2}} x^{3}+143 x^{4}-x^{2} {\mathrm e}^{4 x^{2}}-288 x^{2} \ln \left (x \right )-288 x^{3}+144 \ln \left (x \right )^{2}+288 x \ln \left (x \right )+144 x^{2}}{9 \,{\mathrm e}^{4 x^{2}}+18 x \,{\mathrm e}^{2 x^{2}}+9 x^{2}}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (32) = 64\).
Time = 0.27 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.19 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \left (x\right ) + 144 \, \log \left (x\right )^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (27) = 54\).
Time = 1.19 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.22 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\frac {143 x^{4} - 2 x^{3} e^{2 x^{2}} - 288 x^{3} - x^{2} e^{4 x^{2}} + 144 x^{2} + \left (- 288 x^{2} + 288 x\right ) \log {\left (x \right )} + 144 \log {\left (x \right )}^{2}}{9 x^{2} + 18 x e^{2 x^{2}} + 9 e^{4 x^{2}}}} \]
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\[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\int { \frac {2 \, {\left (143 \, x^{5} - 144 \, x^{4} - 3 \, x^{3} e^{\left (4 \, x^{2}\right )} - 144 \, x^{3} - x^{2} e^{\left (6 \, x^{2}\right )} - 144 \, {\left (4 \, x^{2} e^{\left (2 \, x^{2}\right )} + x\right )} \log \left (x\right )^{2} + 144 \, x^{2} - 3 \, {\left (192 \, x^{6} - 384 \, x^{5} + 97 \, x^{4} + 144 \, x^{3} - 48 \, x\right )} e^{\left (2 \, x^{2}\right )} - 144 \, {\left (x^{2} - {\left (8 \, x^{4} - 8 \, x^{3} - 2 \, x^{2} + x + 1\right )} e^{\left (2 \, x^{2}\right )} - x\right )} \log \left (x\right )\right )} e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \left (x\right ) + 144 \, \log \left (x\right )^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )}}{9 \, {\left (x^{4} + 3 \, x^{3} e^{\left (2 \, x^{2}\right )} + 3 \, x^{2} e^{\left (4 \, x^{2}\right )} + x e^{\left (6 \, x^{2}\right )}\right )}} \,d x } \]
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Exception generated. \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\text {Exception raised: TypeError} \]
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Time = 12.19 (sec) , antiderivative size = 232, normalized size of antiderivative = 6.44 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=x^{\frac {32\,\left (x-x^2\right )}{{\mathrm {e}}^{4\,x^2}+2\,x\,{\mathrm {e}}^{2\,x^2}+x^2}}\,{\mathrm {e}}^{\frac {144\,x^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {143\,x^4}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {288\,x^3}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {144\,{\ln \left (x\right )}^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {x^2\,{\mathrm {e}}^{4\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{2\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}} \]
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