Integrand size = 332, antiderivative size = 31 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=-2+e^{e^{e^{\left (9+\left (\frac {25}{x^2}-x\right )^2+\frac {2}{e^4 x}\right )^2}}} \] Output:
exp(exp(exp((9+(25/x^2-x)^2+2/exp(4)/x)^2)))-2
Time = 0.47 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.29 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=e^{e^{e^{\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}}}} \] Input:
Integrate[(E^(-8 + E^E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100 *x^9 + 18*x^10 + x^12))/(E^8*x^8)) + E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^ 7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8)) + (4*x^6 + E^4*(2500*x^ 3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750 *x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8))*(-8*x^6 + E^4*(-12500*x^3 + 400*x^6 - 36*x^7 + 4*x^9) + E^8*(-3125000 + 312500*x^3 - 45000*x^4 - 7500*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12)))/x^9,x]
Output:
E^E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (-8 x^6+e^4 \left (4 x^9-36 x^7+400 x^6-12500 x^3\right )+e^8 \left (4 x^{12}+36 x^{10}-100 x^9+900 x^7-7500 x^6-45000 x^4+312500 x^3-3125000\right )\right ) \exp \left (\exp \left (\exp \left (\frac {4 x^6+e^4 \left (4 x^9+36 x^7-200 x^6+2500 x^3\right )+e^8 \left (x^{12}+18 x^{10}-100 x^9+81 x^8-900 x^7+3750 x^6+11250 x^4-62500 x^3+390625\right )}{e^8 x^8}\right )\right )+\exp \left (\frac {4 x^6+e^4 \left (4 x^9+36 x^7-200 x^6+2500 x^3\right )+e^8 \left (x^{12}+18 x^{10}-100 x^9+81 x^8-900 x^7+3750 x^6+11250 x^4-62500 x^3+390625\right )}{e^8 x^8}\right )+\frac {4 x^6+e^4 \left (4 x^9+36 x^7-200 x^6+2500 x^3\right )+e^8 \left (x^{12}+18 x^{10}-100 x^9+81 x^8-900 x^7+3750 x^6+11250 x^4-62500 x^3+390625\right )}{e^8 x^8}-8\right )}{x^9} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-8 x^6+e^4 \left (4 x^9-36 x^7+400 x^6-12500 x^3\right )+e^8 \left (4 x^{12}+36 x^{10}-100 x^9+900 x^7-7500 x^6-45000 x^4+312500 x^3-3125000\right )\right ) \exp \left (\frac {x^8 \exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+8\right )+x^8 \exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8\right )+e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (75 e^4-4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (4 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+8} x^3+36 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+8} x+4 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+4} \left (1-25 e^4\right )+\frac {36 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+4} \left (-1+25 e^4\right )}{x^2}-\frac {4 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}-\frac {45000 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+8}}{x^5}+\frac {12500 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+4} \left (-1+25 e^4\right )}{x^6}-\frac {3125000 e^{\frac {e^8 x^{12}+18 e^8 x^{10}+4 e^4 \left (1-25 e^4\right ) x^9+e^{8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}} x^8+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}+8} x^8+73 e^8 x^8+36 e^4 \left (1-25 e^4\right ) x^7+4 \left (1+\frac {25}{2} e^4 \left (-4+75 e^4\right )\right ) x^6+11250 e^8 x^4+2500 e^4 \left (1-25 e^4\right ) x^3+390625 e^8}{e^8 x^8}+8}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (-2 x^6+e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3+e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right ) \exp \left (\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+\frac {390625}{x^8}-\frac {62500}{x^5}+x^4+\frac {11250}{x^4}+18 x^2+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-100 x-\frac {900}{x}+73\right )}{x^9}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {\exp \left (x^4+18 x^2-100 x+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6+e^4 \left (-x^6+9 x^4-100 x^3+3125\right ) x^3+e^8 \left (-x^{12}-9 x^{10}+25 x^9-225 x^7+1875 x^6+11250 x^4-78125 x^3+781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2-100 x+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6+e^4 \left (-x^6+9 x^4-100 x^3+3125\right ) x^3+e^8 \left (-x^{12}-9 x^{10}+25 x^9-225 x^7+1875 x^6+11250 x^4-78125 x^3+781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2-100 x+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81-\frac {900}{x}+\frac {2 \left (1875+\frac {2}{e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4-50 x^3+625\right )}{e^4 x^5}-\frac {62500}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {\exp \left (x^4+18 x^2+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}\right )+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}\right ) \left (2 x^6-e^4 \left (x^6-9 x^4+100 x^3-3125\right ) x^3-e^8 \left (x^{12}+9 x^{10}-25 x^9+225 x^7-1875 x^6-11250 x^4+78125 x^3-781250\right )\right )}{x^9}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x^3-9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} x+e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )+\frac {9 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (1-25 e^4\right )}{x^2}+\frac {e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+73+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (2-100 e^4+1875 e^8\right )}{x^3}+\frac {11250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^5}-\frac {3125 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+77+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}} \left (-1+25 e^4\right )}{x^6}+\frac {781250 e^{x^4+18 x^2+e^{e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}}+e^{\frac {\left (2 x^3+e^4 \left (x^6+9 x^4-50 x^3+625\right )\right )^2}{e^8 x^8}}+81+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}+\frac {11250}{x^4}+\frac {4 \left (x^6+9 x^4+625\right )}{e^4 x^5}-\frac {100 \left (x^6+9 x^4+\frac {2 x^3}{e^4}+625\right )}{x^5}+\frac {390625}{x^8}}}{x^9}\right )dx\) |
Input:
Int[(E^(-8 + E^E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8 *(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8)) + E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^ 7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81 *x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8)) + (4*x^6 + E^4*(2500*x^3 - 20 0*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8))*(-8*x^6 + E^4*(- 12500*x^3 + 400*x^6 - 36*x^7 + 4*x^9) + E^8*(-3125000 + 312500*x^3 - 45000 *x^4 - 7500*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12)))/x^9,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(29)=58\).
Time = 111.26 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32
\[{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {\left ({\mathrm e}^{8} x^{12}+18 \,{\mathrm e}^{8} x^{10}+4 x^{9} {\mathrm e}^{4}-100 \,{\mathrm e}^{8} x^{9}+81 \,{\mathrm e}^{8} x^{8}+36 x^{7} {\mathrm e}^{4}-900 \,{\mathrm e}^{8} x^{7}-200 x^{6} {\mathrm e}^{4}+3750 \,{\mathrm e}^{8} x^{6}+4 x^{6}+11250 x^{4} {\mathrm e}^{8}+2500 x^{3} {\mathrm e}^{4}-62500 x^{3} {\mathrm e}^{8}+390625 \,{\mathrm e}^{8}\right ) {\mathrm e}^{-8}}{x^{8}}}}}\]
Input:
int(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000 )*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^ 10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4 *x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+1 8*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^ 2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(exp(exp (((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625 )*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x ^9/exp(4)^2,x)
Output:
exp(exp(exp((exp(8)*x^12+18*exp(8)*x^10+4*x^9*exp(4)-100*exp(8)*x^9+81*exp (8)*x^8+36*x^7*exp(4)-900*exp(8)*x^7-200*x^6*exp(4)+3750*exp(8)*x^6+4*x^6+ 11250*x^4*exp(8)+2500*x^3*exp(4)-62500*x^3*exp(8)+390625*exp(8))*exp(-8)/x ^8)))
Leaf count of result is larger than twice the leaf count of optimal. 412 vs. \(2 (25) = 50\).
Time = 0.09 (sec) , antiderivative size = 412, normalized size of antiderivative = 13.29 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=e^{\left (\frac {{\left (x^{8} e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} + 8\right )} + x^{8} e^{\left (e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + 8\right )} + 4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 73 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} - \frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} - e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + 8\right )} \] Input:
integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3 125000)*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12 +18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4 )^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp((( x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*e xp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(e xp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+ 390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^ 2)))/x^9/exp(4)^2,x, algorithm="fricas")
Output:
e^((x^8*e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^ 6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^ 3)*e^4)*e^(-8)/x^8 + 8) + x^8*e^(e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 8 1*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8) + 8) + 4*x^6 + (x^12 + 18*x^1 0 - 100*x^9 + 73*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625 )*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8 - (4*x^6 + (x^1 2 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^ 3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8 - e^( (4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x ^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^( -8)/x^8) + 8)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).
Time = 3.50 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.68 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=e^{e^{e^{\frac {4 x^{6} + \left (4 x^{9} + 36 x^{7} - 200 x^{6} + 2500 x^{3}\right ) e^{4} + \left (x^{12} + 18 x^{10} - 100 x^{9} + 81 x^{8} - 900 x^{7} + 3750 x^{6} + 11250 x^{4} - 62500 x^{3} + 390625\right ) e^{8}}{x^{8} e^{8}}}}} \] Input:
integrate(((4*x**12+36*x**10-100*x**9+900*x**7-7500*x**6-45000*x**4+312500 *x**3-3125000)*exp(4)**2+(4*x**9-36*x**7+400*x**6-12500*x**3)*exp(4)-8*x** 6)*exp(((x**12+18*x**10-100*x**9+81*x**8-900*x**7+3750*x**6+11250*x**4-625 00*x**3+390625)*exp(4)**2+(4*x**9+36*x**7-200*x**6+2500*x**3)*exp(4)+4*x** 6)/x**8/exp(4)**2)*exp(exp(((x**12+18*x**10-100*x**9+81*x**8-900*x**7+3750 *x**6+11250*x**4-62500*x**3+390625)*exp(4)**2+(4*x**9+36*x**7-200*x**6+250 0*x**3)*exp(4)+4*x**6)/x**8/exp(4)**2))*exp(exp(exp(((x**12+18*x**10-100*x **9+81*x**8-900*x**7+3750*x**6+11250*x**4-62500*x**3+390625)*exp(4)**2+(4* x**9+36*x**7-200*x**6+2500*x**3)*exp(4)+4*x**6)/x**8/exp(4)**2)))/x**9/exp (4)**2,x)
Output:
exp(exp(exp((4*x**6 + (4*x**9 + 36*x**7 - 200*x**6 + 2500*x**3)*exp(4) + ( x**12 + 18*x**10 - 100*x**9 + 81*x**8 - 900*x**7 + 3750*x**6 + 11250*x**4 - 62500*x**3 + 390625)*exp(8))*exp(-8)/x**8)))
Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (25) = 50\).
Time = 2.11 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.39 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=e^{\left (e^{\left (e^{\left (x^{4} + 18 \, x^{2} + 4 \, x e^{\left (-4\right )} - 100 \, x + \frac {36 \, e^{\left (-4\right )}}{x} - \frac {900}{x} - \frac {200 \, e^{\left (-4\right )}}{x^{2}} + \frac {4 \, e^{\left (-8\right )}}{x^{2}} + \frac {3750}{x^{2}} + \frac {11250}{x^{4}} + \frac {2500 \, e^{\left (-4\right )}}{x^{5}} - \frac {62500}{x^{5}} + \frac {390625}{x^{8}} + 81\right )}\right )}\right )} \] Input:
integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3 125000)*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12 +18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4 )^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp((( x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*e xp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(e xp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+ 390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^ 2)))/x^9/exp(4)^2,x, algorithm="maxima")
Output:
e^(e^(e^(x^4 + 18*x^2 + 4*x*e^(-4) - 100*x + 36*e^(-4)/x - 900/x - 200*e^( -4)/x^2 + 4*e^(-8)/x^2 + 3750/x^2 + 11250/x^4 + 2500*e^(-4)/x^5 - 62500/x^ 5 + 390625/x^8 + 81)))
\[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=\int { -\frac {4 \, {\left (2 \, x^{6} - {\left (x^{12} + 9 \, x^{10} - 25 \, x^{9} + 225 \, x^{7} - 1875 \, x^{6} - 11250 \, x^{4} + 78125 \, x^{3} - 781250\right )} e^{8} - {\left (x^{9} - 9 \, x^{7} + 100 \, x^{6} - 3125 \, x^{3}\right )} e^{4}\right )} e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} + e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + e^{\left (e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )}\right )} - 8\right )}}{x^{9}} \,d x } \] Input:
integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3 125000)*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12 +18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4 )^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp((( x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*e xp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(e xp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+ 390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^ 2)))/x^9/exp(4)^2,x, algorithm="giac")
Output:
integrate(-4*(2*x^6 - (x^12 + 9*x^10 - 25*x^9 + 225*x^7 - 1875*x^6 - 11250 *x^4 + 78125*x^3 - 781250)*e^8 - (x^9 - 9*x^7 + 100*x^6 - 3125*x^3)*e^4)*e ^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250 *x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e ^(-8)/x^8 + e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 375 0*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 62 5*x^3)*e^4)*e^(-8)/x^8) + e^(e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^ 8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9* x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8)) - 8)/x^9, x)
Time = 3.50 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.81 \[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx={\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{-8}}{x^2}}\,{\mathrm {e}}^{\frac {36\,{\mathrm {e}}^{-4}}{x}}\,{\mathrm {e}}^{-\frac {200\,{\mathrm {e}}^{-4}}{x^2}}\,{\mathrm {e}}^{\frac {2500\,{\mathrm {e}}^{-4}}{x^5}}\,{\mathrm {e}}^{-100\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{81}\,{\mathrm {e}}^{18\,x^2}\,{\mathrm {e}}^{-\frac {900}{x}}\,{\mathrm {e}}^{\frac {3750}{x^2}}\,{\mathrm {e}}^{\frac {11250}{x^4}}\,{\mathrm {e}}^{-\frac {62500}{x^5}}\,{\mathrm {e}}^{\frac {390625}{x^8}}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{-4}}}} \] Input:
int(-(exp((exp(-8)*(exp(8)*(11250*x^4 - 62500*x^3 + 3750*x^6 - 900*x^7 + 8 1*x^8 - 100*x^9 + 18*x^10 + x^12 + 390625) + 4*x^6 + exp(4)*(2500*x^3 - 20 0*x^6 + 36*x^7 + 4*x^9)))/x^8)*exp(-8)*exp(exp((exp(-8)*(exp(8)*(11250*x^4 - 62500*x^3 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12 + 39 0625) + 4*x^6 + exp(4)*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9)))/x^8))*exp(e xp(exp((exp(-8)*(exp(8)*(11250*x^4 - 62500*x^3 + 3750*x^6 - 900*x^7 + 81*x ^8 - 100*x^9 + 18*x^10 + x^12 + 390625) + 4*x^6 + exp(4)*(2500*x^3 - 200*x ^6 + 36*x^7 + 4*x^9)))/x^8)))*(8*x^6 - exp(8)*(312500*x^3 - 45000*x^4 - 75 00*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12 - 3125000) + exp(4)*(12500*x ^3 - 400*x^6 + 36*x^7 - 4*x^9)))/x^9,x)
Output:
exp(exp(exp((4*exp(-8))/x^2)*exp((36*exp(-4))/x)*exp(-(200*exp(-4))/x^2)*e xp((2500*exp(-4))/x^5)*exp(-100*x)*exp(x^4)*exp(81)*exp(18*x^2)*exp(-900/x )*exp(3750/x^2)*exp(11250/x^4)*exp(-62500/x^5)*exp(390625/x^8)*exp(4*x*exp (-4))))
\[ \int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}}+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}} \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx=\int \frac {\left (\left (4 x^{12}+36 x^{10}-100 x^{9}+900 x^{7}-7500 x^{6}-45000 x^{4}+312500 x^{3}-3125000\right ) \left ({\mathrm e}^{4}\right )^{2}+\left (4 x^{9}-36 x^{7}+400 x^{6}-12500 x^{3}\right ) {\mathrm e}^{4}-8 x^{6}\right ) {\mathrm e}^{\frac {\left (x^{12}+18 x^{10}-100 x^{9}+81 x^{8}-900 x^{7}+3750 x^{6}+11250 x^{4}-62500 x^{3}+390625\right ) \left ({\mathrm e}^{4}\right )^{2}+\left (4 x^{9}+36 x^{7}-200 x^{6}+2500 x^{3}\right ) {\mathrm e}^{4}+4 x^{6}}{x^{8} \left ({\mathrm e}^{4}\right )^{2}}} {\mathrm e}^{{\mathrm e}^{\frac {\left (x^{12}+18 x^{10}-100 x^{9}+81 x^{8}-900 x^{7}+3750 x^{6}+11250 x^{4}-62500 x^{3}+390625\right ) \left ({\mathrm e}^{4}\right )^{2}+\left (4 x^{9}+36 x^{7}-200 x^{6}+2500 x^{3}\right ) {\mathrm e}^{4}+4 x^{6}}{x^{8} \left ({\mathrm e}^{4}\right )^{2}}}} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {\left (x^{12}+18 x^{10}-100 x^{9}+81 x^{8}-900 x^{7}+3750 x^{6}+11250 x^{4}-62500 x^{3}+390625\right ) \left ({\mathrm e}^{4}\right )^{2}+\left (4 x^{9}+36 x^{7}-200 x^{6}+2500 x^{3}\right ) {\mathrm e}^{4}+4 x^{6}}{x^{8} \left ({\mathrm e}^{4}\right )^{2}}}}}}{x^{9} \left ({\mathrm e}^{4}\right )^{2}}d x \] Input:
int(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000 )*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^ 10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4 *x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+1 8*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^ 2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(exp(exp (((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625 )*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x ^9/exp(4)^2,x)
Output:
int(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000 )*exp(4)^2+(4*x^9-36*x^7+400*x^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^ 10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4 *x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+1 8*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^ 2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(exp(exp (((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625 )*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x ^9/exp(4)^2,x)