Integrand size = 169, antiderivative size = 16 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=390625 e^{-x} \left (5+\frac {2}{x^2}\right )^{16} \] Output:
390625*(5+2/x^2)^16/exp(x)
Time = 0.58 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.19 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {390625 e^{-x} \left (2+5 x^2\right )^{16}}{x^{32}} \] Input:
Integrate[(-819200000000 - 25600000000*x - 30720000000000*x^2 - 1024000000 000*x^3 - 537600000000000*x^4 - 19200000000000*x^5 - 5824000000000000*x^6 - 224000000000000*x^7 - 43680000000000000*x^8 - 1820000000000000*x^9 - 240 240000000000000*x^10 - 10920000000000000*x^11 - 1001000000000000000*x^12 - 50050000000000000*x^13 - 3217500000000000000*x^14 - 178750000000000000*x^ 15 - 8043750000000000000*x^16 - 502734375000000000*x^17 - 1564062500000000 0000*x^18 - 1117187500000000000*x^19 - 23460937500000000000*x^20 - 1955078 125000000000*x^21 - 26660156250000000000*x^22 - 2666015625000000000*x^23 - 22216796875000000000*x^24 - 2777099609375000000*x^25 - 128173828125000000 00*x^26 - 2136230468750000000*x^27 - 4577636718750000000*x^28 - 1144409179 687500000*x^29 - 762939453125000000*x^30 - 381469726562500000*x^31 - 59604 644775390625*x^33)/(E^x*x^33),x]
Output:
(390625*(2 + 5*x^2)^16)/(E^x*x^32)
Leaf count is larger than twice the leaf count of optimal. \(168\) vs. \(2(16)=32\).
Time = 8.18 (sec) , antiderivative size = 168, normalized size of antiderivative = 10.50, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2629, 2009}
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.
| \(\displaystyle \int \frac {e^{-x} \left (-59604644775390625 x^{33}-381469726562500000 x^{31}-762939453125000000 x^{30}-1144409179687500000 x^{29}-4577636718750000000 x^{28}-2136230468750000000 x^{27}-12817382812500000000 x^{26}-2777099609375000000 x^{25}-22216796875000000000 x^{24}-2666015625000000000 x^{23}-26660156250000000000 x^{22}-1955078125000000000 x^{21}-23460937500000000000 x^{20}-1117187500000000000 x^{19}-15640625000000000000 x^{18}-502734375000000000 x^{17}-8043750000000000000 x^{16}-178750000000000000 x^{15}-3217500000000000000 x^{14}-50050000000000000 x^{13}-1001000000000000000 x^{12}-10920000000000000 x^{11}-240240000000000000 x^{10}-1820000000000000 x^9-43680000000000000 x^8-224000000000000 x^7-5824000000000000 x^6-19200000000000 x^5-537600000000000 x^4-1024000000000 x^3-30720000000000 x^2-25600000000 x-819200000000\right )}{x^{33}} \, dx\) |
| \(\Big \downarrow \) 2629 |
| \(\displaystyle \int \left (-\frac {819200000000 e^{-x}}{x^{33}}-\frac {25600000000 e^{-x}}{x^{32}}-\frac {30720000000000 e^{-x}}{x^{31}}-\frac {1024000000000 e^{-x}}{x^{30}}-\frac {537600000000000 e^{-x}}{x^{29}}-\frac {19200000000000 e^{-x}}{x^{28}}-\frac {5824000000000000 e^{-x}}{x^{27}}-\frac {224000000000000 e^{-x}}{x^{26}}-\frac {43680000000000000 e^{-x}}{x^{25}}-\frac {1820000000000000 e^{-x}}{x^{24}}-\frac {240240000000000000 e^{-x}}{x^{23}}-\frac {10920000000000000 e^{-x}}{x^{22}}-\frac {1001000000000000000 e^{-x}}{x^{21}}-\frac {50050000000000000 e^{-x}}{x^{20}}-\frac {3217500000000000000 e^{-x}}{x^{19}}-\frac {178750000000000000 e^{-x}}{x^{18}}-\frac {8043750000000000000 e^{-x}}{x^{17}}-\frac {502734375000000000 e^{-x}}{x^{16}}-\frac {15640625000000000000 e^{-x}}{x^{15}}-\frac {1117187500000000000 e^{-x}}{x^{14}}-\frac {23460937500000000000 e^{-x}}{x^{13}}-\frac {1955078125000000000 e^{-x}}{x^{12}}-\frac {26660156250000000000 e^{-x}}{x^{11}}-\frac {2666015625000000000 e^{-x}}{x^{10}}-\frac {22216796875000000000 e^{-x}}{x^9}-\frac {2777099609375000000 e^{-x}}{x^8}-\frac {12817382812500000000 e^{-x}}{x^7}-\frac {2136230468750000000 e^{-x}}{x^6}-\frac {4577636718750000000 e^{-x}}{x^5}-\frac {1144409179687500000 e^{-x}}{x^4}-\frac {762939453125000000 e^{-x}}{x^3}-\frac {381469726562500000 e^{-x}}{x^2}-59604644775390625 e^{-x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {25600000000 e^{-x}}{x^{32}}+\frac {1024000000000 e^{-x}}{x^{30}}+\frac {19200000000000 e^{-x}}{x^{28}}+\frac {224000000000000 e^{-x}}{x^{26}}+\frac {1820000000000000 e^{-x}}{x^{24}}+\frac {10920000000000000 e^{-x}}{x^{22}}+\frac {50050000000000000 e^{-x}}{x^{20}}+\frac {178750000000000000 e^{-x}}{x^{18}}+\frac {502734375000000000 e^{-x}}{x^{16}}+\frac {1117187500000000000 e^{-x}}{x^{14}}+\frac {1955078125000000000 e^{-x}}{x^{12}}+\frac {2666015625000000000 e^{-x}}{x^{10}}+\frac {2777099609375000000 e^{-x}}{x^8}+\frac {2136230468750000000 e^{-x}}{x^6}+\frac {1144409179687500000 e^{-x}}{x^4}+\frac {381469726562500000 e^{-x}}{x^2}+59604644775390625 e^{-x}\) |
Input:
Int[(-819200000000 - 25600000000*x - 30720000000000*x^2 - 1024000000000*x^ 3 - 537600000000000*x^4 - 19200000000000*x^5 - 5824000000000000*x^6 - 2240 00000000000*x^7 - 43680000000000000*x^8 - 1820000000000000*x^9 - 240240000 000000000*x^10 - 10920000000000000*x^11 - 1001000000000000000*x^12 - 50050 000000000000*x^13 - 3217500000000000000*x^14 - 178750000000000000*x^15 - 8 043750000000000000*x^16 - 502734375000000000*x^17 - 15640625000000000000*x ^18 - 1117187500000000000*x^19 - 23460937500000000000*x^20 - 1955078125000 000000*x^21 - 26660156250000000000*x^22 - 2666015625000000000*x^23 - 22216 796875000000000*x^24 - 2777099609375000000*x^25 - 12817382812500000000*x^2 6 - 2136230468750000000*x^27 - 4577636718750000000*x^28 - 1144409179687500 000*x^29 - 762939453125000000*x^30 - 381469726562500000*x^31 - 59604644775 390625*x^33)/(E^x*x^33),x]
Output:
59604644775390625/E^x + 25600000000/(E^x*x^32) + 1024000000000/(E^x*x^30) + 19200000000000/(E^x*x^28) + 224000000000000/(E^x*x^26) + 182000000000000 0/(E^x*x^24) + 10920000000000000/(E^x*x^22) + 50050000000000000/(E^x*x^20) + 178750000000000000/(E^x*x^18) + 502734375000000000/(E^x*x^16) + 1117187 500000000000/(E^x*x^14) + 1955078125000000000/(E^x*x^12) + 266601562500000 0000/(E^x*x^10) + 2777099609375000000/(E^x*x^8) + 2136230468750000000/(E^x *x^6) + 1144409179687500000/(E^x*x^4) + 381469726562500000/(E^x*x^2)
Int[(F_)^(v_)*(Px_)*((d_.) + (e_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandInte grand[F^v, Px*(d + e*x)^m, x], x] /; FreeQ[{F, d, e, m}, x] && PolynomialQ[ Px, x] && LinearQ[v, x] && !TrueQ[$UseGamma]
Leaf count of result is larger than twice the leaf count of optimal. \(91\) vs. \(2(15)=30\).
Time = 1.15 (sec) , antiderivative size = 92, normalized size of antiderivative = 5.75
| method | result | size |
| gosper | \(\frac {390625 \left (152587890625 x^{32}+976562500000 x^{30}+2929687500000 x^{28}+5468750000000 x^{26}+7109375000000 x^{24}+6825000000000 x^{22}+5005000000000 x^{20}+2860000000000 x^{18}+1287000000000 x^{16}+457600000000 x^{14}+128128000000 x^{12}+27955200000 x^{10}+4659200000 x^{8}+573440000 x^{6}+49152000 x^{4}+2621440 x^{2}+65536\right ) {\mathrm e}^{-x}}{x^{32}}\) | \(92\) |
| risch | \(\frac {390625 \left (152587890625 x^{32}+976562500000 x^{30}+2929687500000 x^{28}+5468750000000 x^{26}+7109375000000 x^{24}+6825000000000 x^{22}+5005000000000 x^{20}+2860000000000 x^{18}+1287000000000 x^{16}+457600000000 x^{14}+128128000000 x^{12}+27955200000 x^{10}+4659200000 x^{8}+573440000 x^{6}+49152000 x^{4}+2621440 x^{2}+65536\right ) {\mathrm e}^{-x}}{x^{32}}\) | \(92\) |
| parallelrisch | \(-\frac {\left (-59604644775390625 x^{32}-381469726562500000 x^{30}-1144409179687500000 x^{28}-2136230468750000000 x^{26}-2777099609375000000 x^{24}-2666015625000000000 x^{22}-1955078125000000000 x^{20}-1117187500000000000 x^{18}-502734375000000000 x^{16}-178750000000000000 x^{14}-50050000000000000 x^{12}-10920000000000000 x^{10}-1820000000000000 x^{8}-224000000000000 x^{6}-19200000000000 x^{4}-1024000000000 x^{2}-25600000000\right ) {\mathrm e}^{-x}}{x^{32}}\) | \(92\) |
| default | \(59604644775390625 \,{\mathrm e}^{-x}+\frac {2136230468750000000 \,{\mathrm e}^{-x}}{x^{6}}+\frac {2777099609375000000 \,{\mathrm e}^{-x}}{x^{8}}+\frac {2666015625000000000 \,{\mathrm e}^{-x}}{x^{10}}+\frac {1955078125000000000 \,{\mathrm e}^{-x}}{x^{12}}+\frac {1117187500000000000 \,{\mathrm e}^{-x}}{x^{14}}+\frac {502734375000000000 \,{\mathrm e}^{-x}}{x^{16}}+\frac {178750000000000000 \,{\mathrm e}^{-x}}{x^{18}}+\frac {50050000000000000 \,{\mathrm e}^{-x}}{x^{20}}+\frac {10920000000000000 \,{\mathrm e}^{-x}}{x^{22}}+\frac {1820000000000000 \,{\mathrm e}^{-x}}{x^{24}}+\frac {224000000000000 \,{\mathrm e}^{-x}}{x^{26}}+\frac {19200000000000 \,{\mathrm e}^{-x}}{x^{28}}+\frac {1024000000000 \,{\mathrm e}^{-x}}{x^{30}}+\frac {25600000000 \,{\mathrm e}^{-x}}{x^{32}}+\frac {1144409179687500000 \,{\mathrm e}^{-x}}{x^{4}}+\frac {381469726562500000 \,{\mathrm e}^{-x}}{x^{2}}\) | \(152\) |
| orering | \(-\frac {\left (5 x^{2}+2\right ) \left (-59604644775390625 x^{33}-381469726562500000 x^{31}-762939453125000000 x^{30}-1144409179687500000 x^{29}-4577636718750000000 x^{28}-2136230468750000000 x^{27}-12817382812500000000 x^{26}-2777099609375000000 x^{25}-22216796875000000000 x^{24}-2666015625000000000 x^{23}-26660156250000000000 x^{22}-1955078125000000000 x^{21}-23460937500000000000 x^{20}-1117187500000000000 x^{19}-15640625000000000000 x^{18}-502734375000000000 x^{17}-8043750000000000000 x^{16}-178750000000000000 x^{15}-3217500000000000000 x^{14}-50050000000000000 x^{13}-1001000000000000000 x^{12}-10920000000000000 x^{11}-240240000000000000 x^{10}-1820000000000000 x^{9}-43680000000000000 x^{8}-224000000000000 x^{7}-5824000000000000 x^{6}-19200000000000 x^{5}-537600000000000 x^{4}-1024000000000 x^{3}-30720000000000 x^{2}-25600000000 x -819200000000\right ) {\mathrm e}^{-x}}{x^{32} \left (5 x^{3}+2 x +64\right )}\) | \(189\) |
| meijerg | \(\text {Expression too large to display}\) | \(5737\) |
Input:
int((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^ 30-1144409179687500000*x^29-4577636718750000000*x^28-2136230468750000000*x ^27-12817382812500000000*x^26-2777099609375000000*x^25-2221679687500000000 0*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125000000 000*x^21-23460937500000000000*x^20-1117187500000000000*x^19-15640625000000 000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-1787500000000 00000*x^15-3217500000000000000*x^14-50050000000000000*x^13-100100000000000 0000*x^12-10920000000000000*x^11-240240000000000000*x^10-1820000000000000* x^9-43680000000000000*x^8-224000000000000*x^7-5824000000000000*x^6-1920000 0000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2-25600 000000*x-819200000000)/x^33/exp(x),x,method=_RETURNVERBOSE)
Output:
390625*(152587890625*x^32+976562500000*x^30+2929687500000*x^28+54687500000 00*x^26+7109375000000*x^24+6825000000000*x^22+5005000000000*x^20+286000000 0000*x^18+1287000000000*x^16+457600000000*x^14+128128000000*x^12+279552000 00*x^10+4659200000*x^8+573440000*x^6+49152000*x^4+2621440*x^2+65536)/exp(x )/x^32
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (15) = 30\).
Time = 0.09 (sec) , antiderivative size = 91, normalized size of antiderivative = 5.69 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {390625 \, {\left (152587890625 \, x^{32} + 976562500000 \, x^{30} + 2929687500000 \, x^{28} + 5468750000000 \, x^{26} + 7109375000000 \, x^{24} + 6825000000000 \, x^{22} + 5005000000000 \, x^{20} + 2860000000000 \, x^{18} + 1287000000000 \, x^{16} + 457600000000 \, x^{14} + 128128000000 \, x^{12} + 27955200000 \, x^{10} + 4659200000 \, x^{8} + 573440000 \, x^{6} + 49152000 \, x^{4} + 2621440 \, x^{2} + 65536\right )} e^{\left (-x\right )}}{x^{32}} \] Input:
integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000 000*x^30-1144409179687500000*x^29-4577636718750000000*x^28-213623046875000 0000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-2221679687500 0000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125 000000000*x^21-23460937500000000000*x^20-1117187500000000000*x^19-15640625 000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-1787500 00000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-100100000 0000000000*x^12-10920000000000000*x^11-240240000000000000*x^10-18200000000 00000*x^9-43680000000000000*x^8-224000000000000*x^7-5824000000000000*x^6-1 9200000000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2 -25600000000*x-819200000000)/x^33/exp(x),x, algorithm="fricas")
Output:
390625*(152587890625*x^32 + 976562500000*x^30 + 2929687500000*x^28 + 54687 50000000*x^26 + 7109375000000*x^24 + 6825000000000*x^22 + 5005000000000*x^ 20 + 2860000000000*x^18 + 1287000000000*x^16 + 457600000000*x^14 + 1281280 00000*x^12 + 27955200000*x^10 + 4659200000*x^8 + 573440000*x^6 + 49152000* x^4 + 2621440*x^2 + 65536)*e^(-x)/x^32
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (12) = 24\).
Time = 0.15 (sec) , antiderivative size = 88, normalized size of antiderivative = 5.50 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {\left (59604644775390625 x^{32} + 381469726562500000 x^{30} + 1144409179687500000 x^{28} + 2136230468750000000 x^{26} + 2777099609375000000 x^{24} + 2666015625000000000 x^{22} + 1955078125000000000 x^{20} + 1117187500000000000 x^{18} + 502734375000000000 x^{16} + 178750000000000000 x^{14} + 50050000000000000 x^{12} + 10920000000000000 x^{10} + 1820000000000000 x^{8} + 224000000000000 x^{6} + 19200000000000 x^{4} + 1024000000000 x^{2} + 25600000000\right ) e^{- x}}{x^{32}} \] Input:
integrate((-59604644775390625*x**33-381469726562500000*x**31-7629394531250 00000*x**30-1144409179687500000*x**29-4577636718750000000*x**28-2136230468 750000000*x**27-12817382812500000000*x**26-2777099609375000000*x**25-22216 796875000000000*x**24-2666015625000000000*x**23-26660156250000000000*x**22 -1955078125000000000*x**21-23460937500000000000*x**20-1117187500000000000* x**19-15640625000000000000*x**18-502734375000000000*x**17-8043750000000000 000*x**16-178750000000000000*x**15-3217500000000000000*x**14-5005000000000 0000*x**13-1001000000000000000*x**12-10920000000000000*x**11-2402400000000 00000*x**10-1820000000000000*x**9-43680000000000000*x**8-224000000000000*x **7-5824000000000000*x**6-19200000000000*x**5-537600000000000*x**4-1024000 000000*x**3-30720000000000*x**2-25600000000*x-819200000000)/x**33/exp(x),x )
Output:
(59604644775390625*x**32 + 381469726562500000*x**30 + 1144409179687500000* x**28 + 2136230468750000000*x**26 + 2777099609375000000*x**24 + 2666015625 000000000*x**22 + 1955078125000000000*x**20 + 1117187500000000000*x**18 + 502734375000000000*x**16 + 178750000000000000*x**14 + 50050000000000000*x* *12 + 10920000000000000*x**10 + 1820000000000000*x**8 + 224000000000000*x* *6 + 19200000000000*x**4 + 1024000000000*x**2 + 25600000000)*exp(-x)/x**32
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.14 (sec) , antiderivative size = 167, normalized size of antiderivative = 10.44 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=59604644775390625 \, e^{\left (-x\right )} + 381469726562500000 \, \Gamma \left (-1, x\right ) + 762939453125000000 \, \Gamma \left (-2, x\right ) + 1144409179687500000 \, \Gamma \left (-3, x\right ) + 4577636718750000000 \, \Gamma \left (-4, x\right ) + 2136230468750000000 \, \Gamma \left (-5, x\right ) + 12817382812500000000 \, \Gamma \left (-6, x\right ) + 2777099609375000000 \, \Gamma \left (-7, x\right ) + 22216796875000000000 \, \Gamma \left (-8, x\right ) + 2666015625000000000 \, \Gamma \left (-9, x\right ) + 26660156250000000000 \, \Gamma \left (-10, x\right ) + 1955078125000000000 \, \Gamma \left (-11, x\right ) + 23460937500000000000 \, \Gamma \left (-12, x\right ) + 1117187500000000000 \, \Gamma \left (-13, x\right ) + 15640625000000000000 \, \Gamma \left (-14, x\right ) + 502734375000000000 \, \Gamma \left (-15, x\right ) + 8043750000000000000 \, \Gamma \left (-16, x\right ) + 178750000000000000 \, \Gamma \left (-17, x\right ) + 3217500000000000000 \, \Gamma \left (-18, x\right ) + 50050000000000000 \, \Gamma \left (-19, x\right ) + 1001000000000000000 \, \Gamma \left (-20, x\right ) + 10920000000000000 \, \Gamma \left (-21, x\right ) + 240240000000000000 \, \Gamma \left (-22, x\right ) + 1820000000000000 \, \Gamma \left (-23, x\right ) + 43680000000000000 \, \Gamma \left (-24, x\right ) + 224000000000000 \, \Gamma \left (-25, x\right ) + 5824000000000000 \, \Gamma \left (-26, x\right ) + 19200000000000 \, \Gamma \left (-27, x\right ) + 537600000000000 \, \Gamma \left (-28, x\right ) + 1024000000000 \, \Gamma \left (-29, x\right ) + 30720000000000 \, \Gamma \left (-30, x\right ) + 25600000000 \, \Gamma \left (-31, x\right ) + 819200000000 \, \Gamma \left (-32, x\right ) \] Input:
integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000 000*x^30-1144409179687500000*x^29-4577636718750000000*x^28-213623046875000 0000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-2221679687500 0000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125 000000000*x^21-23460937500000000000*x^20-1117187500000000000*x^19-15640625 000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-1787500 00000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-100100000 0000000000*x^12-10920000000000000*x^11-240240000000000000*x^10-18200000000 00000*x^9-43680000000000000*x^8-224000000000000*x^7-5824000000000000*x^6-1 9200000000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2 -25600000000*x-819200000000)/x^33/exp(x),x, algorithm="maxima")
Output:
59604644775390625*e^(-x) + 381469726562500000*gamma(-1, x) + 7629394531250 00000*gamma(-2, x) + 1144409179687500000*gamma(-3, x) + 457763671875000000 0*gamma(-4, x) + 2136230468750000000*gamma(-5, x) + 12817382812500000000*g amma(-6, x) + 2777099609375000000*gamma(-7, x) + 22216796875000000000*gamm a(-8, x) + 2666015625000000000*gamma(-9, x) + 26660156250000000000*gamma(- 10, x) + 1955078125000000000*gamma(-11, x) + 23460937500000000000*gamma(-1 2, x) + 1117187500000000000*gamma(-13, x) + 15640625000000000000*gamma(-14 , x) + 502734375000000000*gamma(-15, x) + 8043750000000000000*gamma(-16, x ) + 178750000000000000*gamma(-17, x) + 3217500000000000000*gamma(-18, x) + 50050000000000000*gamma(-19, x) + 1001000000000000000*gamma(-20, x) + 109 20000000000000*gamma(-21, x) + 240240000000000000*gamma(-22, x) + 18200000 00000000*gamma(-23, x) + 43680000000000000*gamma(-24, x) + 224000000000000 *gamma(-25, x) + 5824000000000000*gamma(-26, x) + 19200000000000*gamma(-27 , x) + 537600000000000*gamma(-28, x) + 1024000000000*gamma(-29, x) + 30720 000000000*gamma(-30, x) + 25600000000*gamma(-31, x) + 819200000000*gamma(- 32, x)
Leaf count of result is larger than twice the leaf count of optimal. 156 vs. \(2 (15) = 30\).
Time = 0.12 (sec) , antiderivative size = 156, normalized size of antiderivative = 9.75 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {390625 \, {\left (152587890625 \, x^{32} e^{\left (-x\right )} + 976562500000 \, x^{30} e^{\left (-x\right )} + 2929687500000 \, x^{28} e^{\left (-x\right )} + 5468750000000 \, x^{26} e^{\left (-x\right )} + 7109375000000 \, x^{24} e^{\left (-x\right )} + 6825000000000 \, x^{22} e^{\left (-x\right )} + 5005000000000 \, x^{20} e^{\left (-x\right )} + 2860000000000 \, x^{18} e^{\left (-x\right )} + 1287000000000 \, x^{16} e^{\left (-x\right )} + 457600000000 \, x^{14} e^{\left (-x\right )} + 128128000000 \, x^{12} e^{\left (-x\right )} + 27955200000 \, x^{10} e^{\left (-x\right )} + 4659200000 \, x^{8} e^{\left (-x\right )} + 573440000 \, x^{6} e^{\left (-x\right )} + 49152000 \, x^{4} e^{\left (-x\right )} + 2621440 \, x^{2} e^{\left (-x\right )} + 65536 \, e^{\left (-x\right )}\right )}}{x^{32}} \] Input:
integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000 000*x^30-1144409179687500000*x^29-4577636718750000000*x^28-213623046875000 0000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-2221679687500 0000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125 000000000*x^21-23460937500000000000*x^20-1117187500000000000*x^19-15640625 000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-1787500 00000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-100100000 0000000000*x^12-10920000000000000*x^11-240240000000000000*x^10-18200000000 00000*x^9-43680000000000000*x^8-224000000000000*x^7-5824000000000000*x^6-1 9200000000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2 -25600000000*x-819200000000)/x^33/exp(x),x, algorithm="giac")
Output:
390625*(152587890625*x^32*e^(-x) + 976562500000*x^30*e^(-x) + 292968750000 0*x^28*e^(-x) + 5468750000000*x^26*e^(-x) + 7109375000000*x^24*e^(-x) + 68 25000000000*x^22*e^(-x) + 5005000000000*x^20*e^(-x) + 2860000000000*x^18*e ^(-x) + 1287000000000*x^16*e^(-x) + 457600000000*x^14*e^(-x) + 12812800000 0*x^12*e^(-x) + 27955200000*x^10*e^(-x) + 4659200000*x^8*e^(-x) + 57344000 0*x^6*e^(-x) + 49152000*x^4*e^(-x) + 2621440*x^2*e^(-x) + 65536*e^(-x))/x^ 32
Time = 2.85 (sec) , antiderivative size = 90, normalized size of antiderivative = 5.62 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {{\mathrm {e}}^{-x}\,\left (59604644775390625\,x^{32}+381469726562500000\,x^{30}+1144409179687500000\,x^{28}+2136230468750000000\,x^{26}+2777099609375000000\,x^{24}+2666015625000000000\,x^{22}+1955078125000000000\,x^{20}+1117187500000000000\,x^{18}+502734375000000000\,x^{16}+178750000000000000\,x^{14}+50050000000000000\,x^{12}+10920000000000000\,x^{10}+1820000000000000\,x^8+224000000000000\,x^6+19200000000000\,x^4+1024000000000\,x^2+25600000000\right )}{x^{32}} \] Input:
int(-(exp(-x)*(25600000000*x + 30720000000000*x^2 + 1024000000000*x^3 + 53 7600000000000*x^4 + 19200000000000*x^5 + 5824000000000000*x^6 + 2240000000 00000*x^7 + 43680000000000000*x^8 + 1820000000000000*x^9 + 240240000000000 000*x^10 + 10920000000000000*x^11 + 1001000000000000000*x^12 + 50050000000 000000*x^13 + 3217500000000000000*x^14 + 178750000000000000*x^15 + 8043750 000000000000*x^16 + 502734375000000000*x^17 + 15640625000000000000*x^18 + 1117187500000000000*x^19 + 23460937500000000000*x^20 + 1955078125000000000 *x^21 + 26660156250000000000*x^22 + 2666015625000000000*x^23 + 22216796875 000000000*x^24 + 2777099609375000000*x^25 + 12817382812500000000*x^26 + 21 36230468750000000*x^27 + 4577636718750000000*x^28 + 1144409179687500000*x^ 29 + 762939453125000000*x^30 + 381469726562500000*x^31 + 59604644775390625 *x^33 + 819200000000))/x^33,x)
Output:
(exp(-x)*(1024000000000*x^2 + 19200000000000*x^4 + 224000000000000*x^6 + 1 820000000000000*x^8 + 10920000000000000*x^10 + 50050000000000000*x^12 + 17 8750000000000000*x^14 + 502734375000000000*x^16 + 1117187500000000000*x^18 + 1955078125000000000*x^20 + 2666015625000000000*x^22 + 27770996093750000 00*x^24 + 2136230468750000000*x^26 + 1144409179687500000*x^28 + 3814697265 62500000*x^30 + 59604644775390625*x^32 + 25600000000))/x^32
Time = 0.20 (sec) , antiderivative size = 92, normalized size of antiderivative = 5.75 \[ \int \frac {e^{-x} \left (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33}\right )}{x^{33}} \, dx=\frac {59604644775390625 x^{32}+381469726562500000 x^{30}+1144409179687500000 x^{28}+2136230468750000000 x^{26}+2777099609375000000 x^{24}+2666015625000000000 x^{22}+1955078125000000000 x^{20}+1117187500000000000 x^{18}+502734375000000000 x^{16}+178750000000000000 x^{14}+50050000000000000 x^{12}+10920000000000000 x^{10}+1820000000000000 x^{8}+224000000000000 x^{6}+19200000000000 x^{4}+1024000000000 x^{2}+25600000000}{e^{x} x^{32}} \] Input:
int((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^ 30-1144409179687500000*x^29-4577636718750000000*x^28-2136230468750000000*x ^27-12817382812500000000*x^26-2777099609375000000*x^25-2221679687500000000 0*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125000000 000*x^21-23460937500000000000*x^20-1117187500000000000*x^19-15640625000000 000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-1787500000000 00000*x^15-3217500000000000000*x^14-50050000000000000*x^13-100100000000000 0000*x^12-10920000000000000*x^11-240240000000000000*x^10-1820000000000000* x^9-43680000000000000*x^8-224000000000000*x^7-5824000000000000*x^6-1920000 0000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2-25600 000000*x-819200000000)/x^33/exp(x),x)
Output:
(390625*(152587890625*x**32 + 976562500000*x**30 + 2929687500000*x**28 + 5 468750000000*x**26 + 7109375000000*x**24 + 6825000000000*x**22 + 500500000 0000*x**20 + 2860000000000*x**18 + 1287000000000*x**16 + 457600000000*x**1 4 + 128128000000*x**12 + 27955200000*x**10 + 4659200000*x**8 + 573440000*x **6 + 49152000*x**4 + 2621440*x**2 + 65536))/(e**x*x**32)