Integrand size = 218, antiderivative size = 35 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=4 \left (3-5 e^{-e^x}\right ) \left (x+\frac {3 x}{x+\left (x+\frac {x^2}{4}\right )^2}\right )^2 \] Output:
4*(3-5/exp(exp(x)))*(3/((1/4*x^2+x)^2+x)*x+x)^2
Time = 0.08 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=\frac {4 e^{-e^x} \left (-5+3 e^{e^x}\right ) \left (48+16 x+16 x^2+8 x^3+x^4\right )^2}{\left (16+16 x+8 x^2+x^3\right )^2} \] Input:
Integrate[(983040 + 819200*x - 215040*x^2 - 460800*x^3 - 501760*x^4 - 3840 00*x^5 - 180480*x^6 - 53120*x^7 - 9600*x^8 - 960*x^9 - 40*x^10 + E^E^x*(-5 89824 - 491520*x + 129024*x^2 + 276480*x^3 + 301056*x^4 + 230400*x^5 + 108 288*x^6 + 31872*x^7 + 5760*x^8 + 576*x^9 + 24*x^10) + E^x*(737280 + 122880 0*x + 1433600*x^2 + 1274880*x^3 + 921600*x^4 + 527360*x^5 + 245760*x^6 + 9 4080*x^7 + 26560*x^8 + 4800*x^9 + 480*x^10 + 20*x^11))/(E^E^x*(4096 + 1228 8*x + 18432*x^2 + 17152*x^3 + 10752*x^4 + 4608*x^5 + 1328*x^6 + 240*x^7 + 24*x^8 + x^9)),x]
Output:
(4*(-5 + 3*E^E^x)*(48 + 16*x + 16*x^2 + 8*x^3 + x^4)^2)/(E^E^x*(16 + 16*x + 8*x^2 + x^3)^2)
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.
| \(\displaystyle \int \frac {e^{-e^x} \left (-40 x^{10}-960 x^9-9600 x^8-53120 x^7-180480 x^6-384000 x^5-501760 x^4-460800 x^3-215040 x^2+e^{e^x} \left (24 x^{10}+576 x^9+5760 x^8+31872 x^7+108288 x^6+230400 x^5+301056 x^4+276480 x^3+129024 x^2-491520 x-589824\right )+819200 x+e^x \left (20 x^{11}+480 x^{10}+4800 x^9+26560 x^8+94080 x^7+245760 x^6+527360 x^5+921600 x^4+1274880 x^3+1433600 x^2+1228800 x+737280\right )+983040\right )}{x^9+24 x^8+240 x^7+1328 x^6+4608 x^5+10752 x^4+17152 x^3+18432 x^2+12288 x+4096} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {e^{-e^x} \left (-40 x^{10}-960 x^9-9600 x^8-53120 x^7-180480 x^6-384000 x^5-501760 x^4-460800 x^3-215040 x^2+e^{e^x} \left (24 x^{10}+576 x^9+5760 x^8+31872 x^7+108288 x^6+230400 x^5+301056 x^4+276480 x^3+129024 x^2-491520 x-589824\right )+819200 x+e^x \left (20 x^{11}+480 x^{10}+4800 x^9+26560 x^8+94080 x^7+245760 x^6+527360 x^5+921600 x^4+1274880 x^3+1433600 x^2+1228800 x+737280\right )+983040\right )}{\left (x^3+8 x^2+16 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {460800 e^{-e^x} x^3}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {215040 e^{-e^x} x^2}{\left (x^3+8 x^2+16 x+16\right )^3}+\frac {819200 e^{-e^x} x}{\left (x^3+8 x^2+16 x+16\right )^3}+\frac {983040 e^{-e^x}}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {40 e^{-e^x} x^{10}}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {960 e^{-e^x} x^9}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {9600 e^{-e^x} x^8}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {53120 e^{-e^x} x^7}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {180480 e^{-e^x} x^6}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {384000 e^{-e^x} x^5}{\left (x^3+8 x^2+16 x+16\right )^3}-\frac {501760 e^{-e^x} x^4}{\left (x^3+8 x^2+16 x+16\right )^3}+\frac {20 e^{x-e^x} \left (x^4+8 x^3+16 x^2+16 x+48\right )^2}{\left (x^3+8 x^2+16 x+16\right )^2}+\frac {24 \left (x^4+8 x^3+16 x^2+16 x+48\right ) \left (x^6+16 x^5+96 x^4+288 x^3+368 x^2-256 x-512\right )}{\left (x^3+8 x^2+16 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 e^{-e^x} \left (x^4+8 x^3+16 x^2+16 x+48\right ) \left (6 e^{e^x} \left (x^6+16 x^5+96 x^4+288 x^3+368 x^2-256 x-512\right )-10 \left (x^6+16 x^5+96 x^4+288 x^3+368 x^2-256 x-512\right )+5 e^x \left (x^7+16 x^6+96 x^5+288 x^4+560 x^3+896 x^2+1024 x+768\right )\right )}{\left (x^3+8 x^2+16 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {e^{-e^x} \left (x^4+8 x^3+16 x^2+16 x+48\right ) \left (-6 e^{e^x} \left (-x^6-16 x^5-96 x^4-288 x^3-368 x^2+256 x+512\right )+10 \left (-x^6-16 x^5-96 x^4-288 x^3-368 x^2+256 x+512\right )+5 e^x \left (x^7+16 x^6+96 x^5+288 x^4+560 x^3+896 x^2+1024 x+768\right )\right )}{\left (x^3+8 x^2+16 x+16\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {5 e^{x-e^x} \left (x^4+8 x^3+16 x^2+16 x+48\right )^2}{\left (x^3+8 x^2+16 x+16\right )^2}-\frac {10 e^{-e^x} \left (x^6+16 x^5+96 x^4+288 x^3+368 x^2-256 x-512\right ) \left (x^4+8 x^3+16 x^2+16 x+48\right )}{\left (x^3+8 x^2+16 x+16\right )^3}+\frac {6 \left (x^6+16 x^5+96 x^4+288 x^3+368 x^2-256 x-512\right ) \left (x^4+8 x^3+16 x^2+16 x+48\right )}{\left (x^3+8 x^2+16 x+16\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \left (5 \int e^{x-e^x} x^2dx+368640 \int \frac {e^{-e^x}}{\left (x^3+8 x^2+16 x+16\right )^3}dx+368640 \int \frac {e^{-e^x} x}{\left (x^3+8 x^2+16 x+16\right )^3}dx+69120 \int \frac {e^{-e^x} x^2}{\left (x^3+8 x^2+16 x+16\right )^3}dx-23040 \int \frac {e^{-e^x}}{\left (x^3+8 x^2+16 x+16\right )^2}dx+11520 \int \frac {e^{x-e^x}}{\left (x^3+8 x^2+16 x+16\right )^2}dx-15360 \int \frac {e^{-e^x} x}{\left (x^3+8 x^2+16 x+16\right )^2}dx-3840 \int \frac {e^{-e^x} x^2}{\left (x^3+8 x^2+16 x+16\right )^2}dx+960 \int \frac {e^{-e^x}}{x^3+8 x^2+16 x+16}dx+480 \int \frac {e^{x-e^x} x}{x^3+8 x^2+16 x+16}dx-10 \int e^{-e^x} xdx+\frac {3 \left (x^4+8 x^3+16 x^2+16 x+48\right )^2}{\left (x^3+8 x^2+16 x+16\right )^2}\right )\) |
Input:
Int[(983040 + 819200*x - 215040*x^2 - 460800*x^3 - 501760*x^4 - 384000*x^5 - 180480*x^6 - 53120*x^7 - 9600*x^8 - 960*x^9 - 40*x^10 + E^E^x*(-589824 - 491520*x + 129024*x^2 + 276480*x^3 + 301056*x^4 + 230400*x^5 + 108288*x^ 6 + 31872*x^7 + 5760*x^8 + 576*x^9 + 24*x^10) + E^x*(737280 + 1228800*x + 1433600*x^2 + 1274880*x^3 + 921600*x^4 + 527360*x^5 + 245760*x^6 + 94080*x ^7 + 26560*x^8 + 4800*x^9 + 480*x^10 + 20*x^11))/(E^E^x*(4096 + 12288*x + 18432*x^2 + 17152*x^3 + 10752*x^4 + 4608*x^5 + 1328*x^6 + 240*x^7 + 24*x^8 + x^9)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(132\) vs. \(2(31)=62\).
Time = 2.63 (sec) , antiderivative size = 133, normalized size of antiderivative = 3.80
| method | result | size |
| risch | \(12 x^{2}+\frac {1152 x^{4}+9216 x^{3}+18432 x^{2}+18432 x +27648}{x^{6}+16 x^{5}+96 x^{4}+288 x^{3}+512 x^{2}+512 x +256}-\frac {20 \left (x^{8}+16 x^{7}+96 x^{6}+288 x^{5}+608 x^{4}+1280 x^{3}+1792 x^{2}+1536 x +2304\right ) {\mathrm e}^{-{\mathrm e}^{x}}}{x^{6}+16 x^{5}+96 x^{4}+288 x^{3}+512 x^{2}+512 x +256}\) | \(133\) |
| parallelrisch | \(\frac {\left (-4423680-2949120 x +1152 \,{\mathrm e}^{{\mathrm e}^{x}} x^{8}-1671168 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}-1966080 x \,{\mathrm e}^{{\mathrm e}^{x}}-626688 x^{3} {\mathrm e}^{{\mathrm e}^{x}}+215040 x^{5} {\mathrm e}^{{\mathrm e}^{x}}+18432 \,{\mathrm e}^{{\mathrm e}^{x}} x^{7}+103296 \,{\mathrm e}^{{\mathrm e}^{x}} x^{6}+786432 \,{\mathrm e}^{{\mathrm e}^{x}}-30720 x^{7}-1920 x^{8}-1167360 x^{4}-2457600 x^{3}-3440640 x^{2}-184320 x^{6}-552960 x^{5}\right ) {\mathrm e}^{-{\mathrm e}^{x}}}{96 x^{6}+1536 x^{5}+9216 x^{4}+27648 x^{3}+49152 x^{2}+49152 x +24576}\) | \(137\) |
Input:
int(((24*x^10+576*x^9+5760*x^8+31872*x^7+108288*x^6+230400*x^5+301056*x^4+ 276480*x^3+129024*x^2-491520*x-589824)*exp(exp(x))+(20*x^11+480*x^10+4800* x^9+26560*x^8+94080*x^7+245760*x^6+527360*x^5+921600*x^4+1274880*x^3+14336 00*x^2+1228800*x+737280)*exp(x)-40*x^10-960*x^9-9600*x^8-53120*x^7-180480* x^6-384000*x^5-501760*x^4-460800*x^3-215040*x^2+819200*x+983040)/(x^9+24*x ^8+240*x^7+1328*x^6+4608*x^5+10752*x^4+17152*x^3+18432*x^2+12288*x+4096)/e xp(exp(x)),x,method=_RETURNVERBOSE)
Output:
12*x^2+(1152*x^4+9216*x^3+18432*x^2+18432*x+27648)/(x^6+16*x^5+96*x^4+288* x^3+512*x^2+512*x+256)-20*(x^8+16*x^7+96*x^6+288*x^5+608*x^4+1280*x^3+1792 *x^2+1536*x+2304)/(x^6+16*x^5+96*x^4+288*x^3+512*x^2+512*x+256)*exp(-exp(x ))
Leaf count of result is larger than twice the leaf count of optimal. 120 vs. \(2 (33) = 66\).
Time = 0.07 (sec) , antiderivative size = 120, normalized size of antiderivative = 3.43 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=-\frac {4 \, {\left (5 \, x^{8} + 80 \, x^{7} + 480 \, x^{6} + 1440 \, x^{5} + 3040 \, x^{4} + 6400 \, x^{3} + 8960 \, x^{2} - 3 \, {\left (x^{8} + 16 \, x^{7} + 96 \, x^{6} + 288 \, x^{5} + 608 \, x^{4} + 1280 \, x^{3} + 1792 \, x^{2} + 1536 \, x + 2304\right )} e^{\left (e^{x}\right )} + 7680 \, x + 11520\right )} e^{\left (-e^{x}\right )}}{x^{6} + 16 \, x^{5} + 96 \, x^{4} + 288 \, x^{3} + 512 \, x^{2} + 512 \, x + 256} \] Input:
integrate(((24*x^10+576*x^9+5760*x^8+31872*x^7+108288*x^6+230400*x^5+30105 6*x^4+276480*x^3+129024*x^2-491520*x-589824)*exp(exp(x))+(20*x^11+480*x^10 +4800*x^9+26560*x^8+94080*x^7+245760*x^6+527360*x^5+921600*x^4+1274880*x^3 +1433600*x^2+1228800*x+737280)*exp(x)-40*x^10-960*x^9-9600*x^8-53120*x^7-1 80480*x^6-384000*x^5-501760*x^4-460800*x^3-215040*x^2+819200*x+983040)/(x^ 9+24*x^8+240*x^7+1328*x^6+4608*x^5+10752*x^4+17152*x^3+18432*x^2+12288*x+4 096)/exp(exp(x)),x, algorithm="fricas")
Output:
-4*(5*x^8 + 80*x^7 + 480*x^6 + 1440*x^5 + 3040*x^4 + 6400*x^3 + 8960*x^2 - 3*(x^8 + 16*x^7 + 96*x^6 + 288*x^5 + 608*x^4 + 1280*x^3 + 1792*x^2 + 1536 *x + 2304)*e^(e^x) + 7680*x + 11520)*e^(-e^x)/(x^6 + 16*x^5 + 96*x^4 + 288 *x^3 + 512*x^2 + 512*x + 256)
Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 129, normalized size of antiderivative = 3.69 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=12 x^{2} + \frac {1152 x^{4} + 9216 x^{3} + 18432 x^{2} + 18432 x + 27648}{x^{6} + 16 x^{5} + 96 x^{4} + 288 x^{3} + 512 x^{2} + 512 x + 256} + \frac {\left (- 20 x^{8} - 320 x^{7} - 1920 x^{6} - 5760 x^{5} - 12160 x^{4} - 25600 x^{3} - 35840 x^{2} - 30720 x - 46080\right ) e^{- e^{x}}}{x^{6} + 16 x^{5} + 96 x^{4} + 288 x^{3} + 512 x^{2} + 512 x + 256} \] Input:
integrate(((24*x**10+576*x**9+5760*x**8+31872*x**7+108288*x**6+230400*x**5 +301056*x**4+276480*x**3+129024*x**2-491520*x-589824)*exp(exp(x))+(20*x**1 1+480*x**10+4800*x**9+26560*x**8+94080*x**7+245760*x**6+527360*x**5+921600 *x**4+1274880*x**3+1433600*x**2+1228800*x+737280)*exp(x)-40*x**10-960*x**9 -9600*x**8-53120*x**7-180480*x**6-384000*x**5-501760*x**4-460800*x**3-2150 40*x**2+819200*x+983040)/(x**9+24*x**8+240*x**7+1328*x**6+4608*x**5+10752* x**4+17152*x**3+18432*x**2+12288*x+4096)/exp(exp(x)),x)
Output:
12*x**2 + (1152*x**4 + 9216*x**3 + 18432*x**2 + 18432*x + 27648)/(x**6 + 1 6*x**5 + 96*x**4 + 288*x**3 + 512*x**2 + 512*x + 256) + (-20*x**8 - 320*x* *7 - 1920*x**6 - 5760*x**5 - 12160*x**4 - 25600*x**3 - 35840*x**2 - 30720* x - 46080)*exp(-exp(x))/(x**6 + 16*x**5 + 96*x**4 + 288*x**3 + 512*x**2 + 512*x + 256)
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (33) = 66\).
Time = 0.22 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.34 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=\frac {4 \, {\left (3 \, x^{8} + 48 \, x^{7} + 288 \, x^{6} + 864 \, x^{5} + 1824 \, x^{4} + 3840 \, x^{3} + 5376 \, x^{2} - 5 \, {\left (x^{8} + 16 \, x^{7} + 96 \, x^{6} + 288 \, x^{5} + 608 \, x^{4} + 1280 \, x^{3} + 1792 \, x^{2} + 1536 \, x + 2304\right )} e^{\left (-e^{x}\right )} + 4608 \, x + 6912\right )}}{x^{6} + 16 \, x^{5} + 96 \, x^{4} + 288 \, x^{3} + 512 \, x^{2} + 512 \, x + 256} \] Input:
integrate(((24*x^10+576*x^9+5760*x^8+31872*x^7+108288*x^6+230400*x^5+30105 6*x^4+276480*x^3+129024*x^2-491520*x-589824)*exp(exp(x))+(20*x^11+480*x^10 +4800*x^9+26560*x^8+94080*x^7+245760*x^6+527360*x^5+921600*x^4+1274880*x^3 +1433600*x^2+1228800*x+737280)*exp(x)-40*x^10-960*x^9-9600*x^8-53120*x^7-1 80480*x^6-384000*x^5-501760*x^4-460800*x^3-215040*x^2+819200*x+983040)/(x^ 9+24*x^8+240*x^7+1328*x^6+4608*x^5+10752*x^4+17152*x^3+18432*x^2+12288*x+4 096)/exp(exp(x)),x, algorithm="maxima")
Output:
4*(3*x^8 + 48*x^7 + 288*x^6 + 864*x^5 + 1824*x^4 + 3840*x^3 + 5376*x^2 - 5 *(x^8 + 16*x^7 + 96*x^6 + 288*x^5 + 608*x^4 + 1280*x^3 + 1792*x^2 + 1536*x + 2304)*e^(-e^x) + 4608*x + 6912)/(x^6 + 16*x^5 + 96*x^4 + 288*x^3 + 512* x^2 + 512*x + 256)
\[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=\int { -\frac {4 \, {\left (10 \, x^{10} + 240 \, x^{9} + 2400 \, x^{8} + 13280 \, x^{7} + 45120 \, x^{6} + 96000 \, x^{5} + 125440 \, x^{4} + 115200 \, x^{3} + 53760 \, x^{2} - 5 \, {\left (x^{11} + 24 \, x^{10} + 240 \, x^{9} + 1328 \, x^{8} + 4704 \, x^{7} + 12288 \, x^{6} + 26368 \, x^{5} + 46080 \, x^{4} + 63744 \, x^{3} + 71680 \, x^{2} + 61440 \, x + 36864\right )} e^{x} - 6 \, {\left (x^{10} + 24 \, x^{9} + 240 \, x^{8} + 1328 \, x^{7} + 4512 \, x^{6} + 9600 \, x^{5} + 12544 \, x^{4} + 11520 \, x^{3} + 5376 \, x^{2} - 20480 \, x - 24576\right )} e^{\left (e^{x}\right )} - 204800 \, x - 245760\right )} e^{\left (-e^{x}\right )}}{x^{9} + 24 \, x^{8} + 240 \, x^{7} + 1328 \, x^{6} + 4608 \, x^{5} + 10752 \, x^{4} + 17152 \, x^{3} + 18432 \, x^{2} + 12288 \, x + 4096} \,d x } \] Input:
integrate(((24*x^10+576*x^9+5760*x^8+31872*x^7+108288*x^6+230400*x^5+30105 6*x^4+276480*x^3+129024*x^2-491520*x-589824)*exp(exp(x))+(20*x^11+480*x^10 +4800*x^9+26560*x^8+94080*x^7+245760*x^6+527360*x^5+921600*x^4+1274880*x^3 +1433600*x^2+1228800*x+737280)*exp(x)-40*x^10-960*x^9-9600*x^8-53120*x^7-1 80480*x^6-384000*x^5-501760*x^4-460800*x^3-215040*x^2+819200*x+983040)/(x^ 9+24*x^8+240*x^7+1328*x^6+4608*x^5+10752*x^4+17152*x^3+18432*x^2+12288*x+4 096)/exp(exp(x)),x, algorithm="giac")
Output:
integrate(-4*(10*x^10 + 240*x^9 + 2400*x^8 + 13280*x^7 + 45120*x^6 + 96000 *x^5 + 125440*x^4 + 115200*x^3 + 53760*x^2 - 5*(x^11 + 24*x^10 + 240*x^9 + 1328*x^8 + 4704*x^7 + 12288*x^6 + 26368*x^5 + 46080*x^4 + 63744*x^3 + 716 80*x^2 + 61440*x + 36864)*e^x - 6*(x^10 + 24*x^9 + 240*x^8 + 1328*x^7 + 45 12*x^6 + 9600*x^5 + 12544*x^4 + 11520*x^3 + 5376*x^2 - 20480*x - 24576)*e^ (e^x) - 204800*x - 245760)*e^(-e^x)/(x^9 + 24*x^8 + 240*x^7 + 1328*x^6 + 4 608*x^5 + 10752*x^4 + 17152*x^3 + 18432*x^2 + 12288*x + 4096), x)
Time = 2.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=\frac {4\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,\left (3\,{\mathrm {e}}^{{\mathrm {e}}^x}-5\right )\,{\left (x^4+8\,x^3+16\,x^2+16\,x+48\right )}^2}{{\left (x^3+8\,x^2+16\,x+16\right )}^2} \] Input:
int(-(exp(-exp(x))*(215040*x^2 - exp(x)*(1228800*x + 1433600*x^2 + 1274880 *x^3 + 921600*x^4 + 527360*x^5 + 245760*x^6 + 94080*x^7 + 26560*x^8 + 4800 *x^9 + 480*x^10 + 20*x^11 + 737280) - exp(exp(x))*(129024*x^2 - 491520*x + 276480*x^3 + 301056*x^4 + 230400*x^5 + 108288*x^6 + 31872*x^7 + 5760*x^8 + 576*x^9 + 24*x^10 - 589824) - 819200*x + 460800*x^3 + 501760*x^4 + 38400 0*x^5 + 180480*x^6 + 53120*x^7 + 9600*x^8 + 960*x^9 + 40*x^10 - 983040))/( 12288*x + 18432*x^2 + 17152*x^3 + 10752*x^4 + 4608*x^5 + 1328*x^6 + 240*x^ 7 + 24*x^8 + x^9 + 4096),x)
Output:
(4*exp(-exp(x))*(3*exp(exp(x)) - 5)*(16*x + 16*x^2 + 8*x^3 + x^4 + 48)^2)/ (16*x + 8*x^2 + x^3 + 16)^2
Time = 0.23 (sec) , antiderivative size = 154, normalized size of antiderivative = 4.40 \[ \int \frac {e^{-e^x} \left (983040+819200 x-215040 x^2-460800 x^3-501760 x^4-384000 x^5-180480 x^6-53120 x^7-9600 x^8-960 x^9-40 x^{10}+e^{e^x} \left (-589824-491520 x+129024 x^2+276480 x^3+301056 x^4+230400 x^5+108288 x^6+31872 x^7+5760 x^8+576 x^9+24 x^{10}\right )+e^x \left (737280+1228800 x+1433600 x^2+1274880 x^3+921600 x^4+527360 x^5+245760 x^6+94080 x^7+26560 x^8+4800 x^9+480 x^{10}+20 x^{11}\right )\right )}{4096+12288 x+18432 x^2+17152 x^3+10752 x^4+4608 x^5+1328 x^6+240 x^7+24 x^8+x^9} \, dx=\frac {12 e^{e^{x}} x^{8}+192 e^{e^{x}} x^{7}+936 e^{e^{x}} x^{6}-13440 e^{e^{x}} x^{4}-46848 e^{e^{x}} x^{3}-89088 e^{e^{x}} x^{2}-92160 e^{e^{x}} x -27648 e^{e^{x}}-20 x^{8}-320 x^{7}-1920 x^{6}-5760 x^{5}-12160 x^{4}-25600 x^{3}-35840 x^{2}-30720 x -46080}{e^{e^{x}} \left (x^{6}+16 x^{5}+96 x^{4}+288 x^{3}+512 x^{2}+512 x +256\right )} \] Input:
int(((24*x^10+576*x^9+5760*x^8+31872*x^7+108288*x^6+230400*x^5+301056*x^4+ 276480*x^3+129024*x^2-491520*x-589824)*exp(exp(x))+(20*x^11+480*x^10+4800* x^9+26560*x^8+94080*x^7+245760*x^6+527360*x^5+921600*x^4+1274880*x^3+14336 00*x^2+1228800*x+737280)*exp(x)-40*x^10-960*x^9-9600*x^8-53120*x^7-180480* x^6-384000*x^5-501760*x^4-460800*x^3-215040*x^2+819200*x+983040)/(x^9+24*x ^8+240*x^7+1328*x^6+4608*x^5+10752*x^4+17152*x^3+18432*x^2+12288*x+4096)/e xp(exp(x)),x)
Output:
(4*(3*e**(e**x)*x**8 + 48*e**(e**x)*x**7 + 234*e**(e**x)*x**6 - 3360*e**(e **x)*x**4 - 11712*e**(e**x)*x**3 - 22272*e**(e**x)*x**2 - 23040*e**(e**x)* x - 6912*e**(e**x) - 5*x**8 - 80*x**7 - 480*x**6 - 1440*x**5 - 3040*x**4 - 6400*x**3 - 8960*x**2 - 7680*x - 11520))/(e**(e**x)*(x**6 + 16*x**5 + 96* x**4 + 288*x**3 + 512*x**2 + 512*x + 256))