3.67.26 \(\int \frac {e^{-x} (-819200000000-25600000000 x-30720000000000 x^2-1024000000000 x^3-537600000000000 x^4-19200000000000 x^5-5824000000000000 x^6-224000000000000 x^7-43680000000000000 x^8-1820000000000000 x^9-240240000000000000 x^{10}-10920000000000000 x^{11}-1001000000000000000 x^{12}-50050000000000000 x^{13}-3217500000000000000 x^{14}-178750000000000000 x^{15}-8043750000000000000 x^{16}-502734375000000000 x^{17}-15640625000000000000 x^{18}-1117187500000000000 x^{19}-23460937500000000000 x^{20}-1955078125000000000 x^{21}-26660156250000000000 x^{22}-2666015625000000000 x^{23}-22216796875000000000 x^{24}-2777099609375000000 x^{25}-12817382812500000000 x^{26}-2136230468750000000 x^{27}-4577636718750000000 x^{28}-1144409179687500000 x^{29}-762939453125000000 x^{30}-381469726562500000 x^{31}-59604644775390625 x^{33})}{x^{33}} \, dx\)

Optimal. Leaf size=16 \[ 390625 e^{-x} \left (5+\frac {2}{x^2}\right )^{16} \]

________________________________________________________________________________________

Rubi [B]  time = 10.66, antiderivative size = 168, normalized size of antiderivative = 10.50, number of steps used = 563, number of rules used = 4, integrand size = 169, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2199, 2194, 2177, 2178} \begin {gather*} \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} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-819200000000 - 25600000000*x - 30720000000000*x^2 - 1024000000000*x^3 - 537600000000000*x^4 - 1920000000
0000*x^5 - 5824000000000000*x^6 - 224000000000000*x^7 - 43680000000000000*x^8 - 1820000000000000*x^9 - 2402400
00000000000*x^10 - 10920000000000000*x^11 - 1001000000000000000*x^12 - 50050000000000000*x^13 - 32175000000000
00000*x^14 - 178750000000000000*x^15 - 8043750000000000000*x^16 - 502734375000000000*x^17 - 156406250000000000
00*x^18 - 1117187500000000000*x^19 - 23460937500000000000*x^20 - 1955078125000000000*x^21 - 266601562500000000
00*x^22 - 2666015625000000000*x^23 - 22216796875000000000*x^24 - 2777099609375000000*x^25 - 128173828125000000
00*x^26 - 2136230468750000000*x^27 - 4577636718750000000*x^28 - 1144409179687500000*x^29 - 762939453125000000*
x^30 - 381469726562500000*x^31 - 59604644775390625*x^33)/(E^x*x^33),x]

[Out]

59604644775390625/E^x + 25600000000/(E^x*x^32) + 1024000000000/(E^x*x^30) + 19200000000000/(E^x*x^28) + 224000
000000000/(E^x*x^26) + 1820000000000000/(E^x*x^24) + 10920000000000000/(E^x*x^22) + 50050000000000000/(E^x*x^2
0) + 178750000000000000/(E^x*x^18) + 502734375000000000/(E^x*x^16) + 1117187500000000000/(E^x*x^14) + 19550781
25000000000/(E^x*x^12) + 2666015625000000000/(E^x*x^10) + 2777099609375000000/(E^x*x^8) + 2136230468750000000/
(E^x*x^6) + 1144409179687500000/(E^x*x^4) + 381469726562500000/(E^x*x^2)

Rule 2177

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[((c + d*x)^(m
+ 1)*(b*F^(g*(e + f*x)))^n)/(d*(m + 1)), x] - Dist[(f*g*n*Log[F])/(d*(m + 1)), Int[(c + d*x)^(m + 1)*(b*F^(g*
(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] &&  !$UseGamma ===
True

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2199

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), w*NormalizePo
werOfLinear[u, x]^m, x], x] /; FreeQ[{F, c}, x] && PolynomialQ[w, x] && LinearQ[v, x] && PowerOfLinearQ[u, x]
&& IntegerQ[m] &&  !$UseGamma === True

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-59604644775390625 e^{-x}-\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}\right ) \, dx\\ &=-\left (25600000000 \int \frac {e^{-x}}{x^{32}} \, dx\right )-819200000000 \int \frac {e^{-x}}{x^{33}} \, dx-1024000000000 \int \frac {e^{-x}}{x^{30}} \, dx-19200000000000 \int \frac {e^{-x}}{x^{28}} \, dx-30720000000000 \int \frac {e^{-x}}{x^{31}} \, dx-224000000000000 \int \frac {e^{-x}}{x^{26}} \, dx-537600000000000 \int \frac {e^{-x}}{x^{29}} \, dx-1820000000000000 \int \frac {e^{-x}}{x^{24}} \, dx-5824000000000000 \int \frac {e^{-x}}{x^{27}} \, dx-10920000000000000 \int \frac {e^{-x}}{x^{22}} \, dx-43680000000000000 \int \frac {e^{-x}}{x^{25}} \, dx-50050000000000000 \int \frac {e^{-x}}{x^{20}} \, dx-59604644775390625 \int e^{-x} \, dx-178750000000000000 \int \frac {e^{-x}}{x^{18}} \, dx-240240000000000000 \int \frac {e^{-x}}{x^{23}} \, dx-381469726562500000 \int \frac {e^{-x}}{x^2} \, dx-502734375000000000 \int \frac {e^{-x}}{x^{16}} \, dx-762939453125000000 \int \frac {e^{-x}}{x^3} \, dx-1001000000000000000 \int \frac {e^{-x}}{x^{21}} \, dx-1117187500000000000 \int \frac {e^{-x}}{x^{14}} \, dx-1144409179687500000 \int \frac {e^{-x}}{x^4} \, dx-1955078125000000000 \int \frac {e^{-x}}{x^{12}} \, dx-2136230468750000000 \int \frac {e^{-x}}{x^6} \, dx-2666015625000000000 \int \frac {e^{-x}}{x^{10}} \, dx-2777099609375000000 \int \frac {e^{-x}}{x^8} \, dx-3217500000000000000 \int \frac {e^{-x}}{x^{19}} \, dx-4577636718750000000 \int \frac {e^{-x}}{x^5} \, dx-8043750000000000000 \int \frac {e^{-x}}{x^{17}} \, dx-12817382812500000000 \int \frac {e^{-x}}{x^7} \, dx-15640625000000000000 \int \frac {e^{-x}}{x^{15}} \, dx-22216796875000000000 \int \frac {e^{-x}}{x^9} \, dx-23460937500000000000 \int \frac {e^{-x}}{x^{13}} \, dx-26660156250000000000 \int \frac {e^{-x}}{x^{11}} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.04, size = 19, normalized size = 1.19 \begin {gather*} \frac {390625 e^{-x} \left (2+5 x^2\right )^{16}}{x^{32}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-819200000000 - 25600000000*x - 30720000000000*x^2 - 1024000000000*x^3 - 537600000000000*x^4 - 1920
0000000000*x^5 - 5824000000000000*x^6 - 224000000000000*x^7 - 43680000000000000*x^8 - 1820000000000000*x^9 - 2
40240000000000000*x^10 - 10920000000000000*x^11 - 1001000000000000000*x^12 - 50050000000000000*x^13 - 32175000
00000000000*x^14 - 178750000000000000*x^15 - 8043750000000000000*x^16 - 502734375000000000*x^17 - 156406250000
00000000*x^18 - 1117187500000000000*x^19 - 23460937500000000000*x^20 - 1955078125000000000*x^21 - 266601562500
00000000*x^22 - 2666015625000000000*x^23 - 22216796875000000000*x^24 - 2777099609375000000*x^25 - 128173828125
00000000*x^26 - 2136230468750000000*x^27 - 4577636718750000000*x^28 - 1144409179687500000*x^29 - 7629394531250
00000*x^30 - 381469726562500000*x^31 - 59604644775390625*x^33)/(E^x*x^33),x]

[Out]

(390625*(2 + 5*x^2)^16)/(E^x*x^32)

________________________________________________________________________________________

fricas [B]  time = 0.57, size = 91, normalized size = 5.69 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^30-1144409179687500000*x^29-45
77636718750000000*x^28-2136230468750000000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-22216796875
000000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125000000000*x^21-2346093750000000000
0*x^20-1117187500000000000*x^19-15640625000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-178
750000000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-1001000000000000000*x^12-1092000000000000
0*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)/x
^33/exp(x),x, algorithm="fricas")

[Out]

390625*(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 + 12812
8000000*x^12 + 27955200000*x^10 + 4659200000*x^8 + 573440000*x^6 + 49152000*x^4 + 2621440*x^2 + 65536)*e^(-x)/
x^32

________________________________________________________________________________________

giac [B]  time = 0.24, size = 156, normalized size = 9.75 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^30-1144409179687500000*x^29-45
77636718750000000*x^28-2136230468750000000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-22216796875
000000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125000000000*x^21-2346093750000000000
0*x^20-1117187500000000000*x^19-15640625000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-178
750000000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-1001000000000000000*x^12-1092000000000000
0*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)/x
^33/exp(x),x, algorithm="giac")

[Out]

390625*(152587890625*x^32*e^(-x) + 976562500000*x^30*e^(-x) + 2929687500000*x^28*e^(-x) + 5468750000000*x^26*e
^(-x) + 7109375000000*x^24*e^(-x) + 6825000000000*x^22*e^(-x) + 5005000000000*x^20*e^(-x) + 2860000000000*x^18
*e^(-x) + 1287000000000*x^16*e^(-x) + 457600000000*x^14*e^(-x) + 128128000000*x^12*e^(-x) + 27955200000*x^10*e
^(-x) + 4659200000*x^8*e^(-x) + 573440000*x^6*e^(-x) + 49152000*x^4*e^(-x) + 2621440*x^2*e^(-x) + 65536*e^(-x)
)/x^32

________________________________________________________________________________________

maple [B]  time = 0.67, size = 92, normalized size = 5.75

method	result	size
gosper	\(\frac {390625 \left (152587890625 x^{32}[phone] x^{30}[phone] x^{28}[phone] x^{26}[phone] x^{24}[phone] x^{22}[phone] x^{20}[phone] x^{18}[phone] x^{16}[phone] x^{14}[phone] x^{12}[phone] x^{10}[phone] x^{8}[phone] x^{6}[phone] x^{4}+2621440 x^{2}+65536\right ) {\mathrm e}^{-x}}{x^{32}}\)	\(92\)
risch	\(\frac {390625 \left (152587890625 x^{32}[phone] x^{30}[phone] x^{28}[phone] x^{26}[phone] x^{24}[phone] x^{22}[phone] x^{20}[phone] x^{18}[phone] x^{16}[phone] x^{14}[phone] x^{12}[phone] x^{10}[phone] x^{8}[phone] x^{6}[phone] x^{4}+2621440 x^{2}+65536\right ) {\mathrm e}^{-x}}{x^{32}}\)	\(92\)
default	\(59604644775390625 \,{\mathrm e}^{-x}+\frac {1024000000000 \,{\mathrm e}^{-x}}{x^{30}}+\frac {25600000000 \,{\mathrm e}^{-x}}{x^{32}}+\frac {2136230468750000000 \,{\mathrm e}^{-x}}{x^{6}}+\frac {2777099609375000000 \,{\mathrm e}^{-x}}{x^{8}}+\frac {2666015625000000000 \,{\mathrm e}^{-x}}{x^{10}}+\frac {1955078125000000000 \,{\mathrm e}^{-x}}{x^{12}}+\frac {1117187500000000000 \,{\mathrm e}^{-x}}{x^{14}}+\frac {502734375000000000 \,{\mathrm e}^{-x}}{x^{16}}+\frac {178750000000000000 \,{\mathrm e}^{-x}}{x^{18}}+\frac {50050000000000000 \,{\mathrm e}^{-x}}{x^{20}}+\frac {10920000000000000 \,{\mathrm e}^{-x}}{x^{22}}+\frac {1820000000000000 \,{\mathrm e}^{-x}}{x^{24}}+\frac {224000000000000 \,{\mathrm e}^{-x}}{x^{26}}+\frac {19200000000000 \,{\mathrm e}^{-x}}{x^{28}}+\frac {1144409179687500000 \,{\mathrm e}^{-x}}{x^{4}}+\frac {381469726562500000 \,{\mathrm e}^{-x}}{x^{2}}\)	\(152\)
meijerg	\(\text {Expression too large to display}\)	\(5737\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^30-1144409179687500000*x^29-45776367
18750000000*x^28-2136230468750000000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-22216796875000000
000*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^16-178750000
000000000*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^6-1
9200000000000*x^5-537600000000000*x^4-1024000000000*x^3-30720000000000*x^2-25600000000*x-819200000000)/x^33/ex
p(x),x,method=_RETURNVERBOSE)

[Out]

390625*(152587890625*x^32+976562500000*x^30+2929687500000*x^28+5468750000000*x^26+7109375000000*x^24+682500000
0000*x^22+5005000000000*x^20+2860000000000*x^18+1287000000000*x^16+457600000000*x^14+128128000000*x^12+2795520
0000*x^10+4659200000*x^8+573440000*x^6+49152000*x^4+2621440*x^2+65536)/exp(x)/x^32

________________________________________________________________________________________

maxima [C]  time = 0.50, size = 167, normalized size = 10.44 \begin {gather*} 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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-59604644775390625*x^33-381469726562500000*x^31-762939453125000000*x^30-1144409179687500000*x^29-45
77636718750000000*x^28-2136230468750000000*x^27-12817382812500000000*x^26-2777099609375000000*x^25-22216796875
000000000*x^24-2666015625000000000*x^23-26660156250000000000*x^22-1955078125000000000*x^21-2346093750000000000
0*x^20-1117187500000000000*x^19-15640625000000000000*x^18-502734375000000000*x^17-8043750000000000000*x^16-178
750000000000000*x^15-3217500000000000000*x^14-50050000000000000*x^13-1001000000000000000*x^12-1092000000000000
0*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)/x
^33/exp(x),x, algorithm="maxima")

[Out]

59604644775390625*e^(-x) + 381469726562500000*gamma(-1, x) + 762939453125000000*gamma(-2, x) + 114440917968750
0000*gamma(-3, x) + 4577636718750000000*gamma(-4, x) + 2136230468750000000*gamma(-5, x) + 12817382812500000000
*gamma(-6, x) + 2777099609375000000*gamma(-7, x) + 22216796875000000000*gamma(-8, x) + 2666015625000000000*gam
ma(-9, x) + 26660156250000000000*gamma(-10, x) + 1955078125000000000*gamma(-11, x) + 23460937500000000000*gamm
a(-12, 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) + 10920000000000000*gamma(-21, x) +
240240000000000000*gamma(-22, x) + 1820000000000000*gamma(-23, x) + 43680000000000000*gamma(-24, x) + 2240000
00000000*gamma(-25, x) + 5824000000000000*gamma(-26, x) + 19200000000000*gamma(-27, x) + 537600000000000*gamma
(-28, x) + 1024000000000*gamma(-29, x) + 30720000000000*gamma(-30, x) + 25600000000*gamma(-31, x) + 8192000000
00*gamma(-32, x)

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mupad [B]  time = 4.43, size = 90, normalized size = 5.62 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-x)*(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 + 2402400000000
00000*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^1
8 + 1117187500000000000*x^19 + 23460937500000000000*x^20 + 1955078125000000000*x^21 + 26660156250000000000*x^2
2 + 2666015625000000000*x^23 + 22216796875000000000*x^24 + 2777099609375000000*x^25 + 12817382812500000000*x^2
6 + 2136230468750000000*x^27 + 4577636718750000000*x^28 + 1144409179687500000*x^29 + 762939453125000000*x^30 +
381469726562500000*x^31 + 59604644775390625*x^33 + 819200000000))/x^33,x)

[Out]

(exp(-x)*(1024000000000*x^2 + 19200000000000*x^4 + 224000000000000*x^6 + 1820000000000000*x^8 + 10920000000000
000*x^10 + 50050000000000000*x^12 + 178750000000000000*x^14 + 502734375000000000*x^16 + 1117187500000000000*x^
18 + 1955078125000000000*x^20 + 2666015625000000000*x^22 + 2777099609375000000*x^24 + 2136230468750000000*x^26
+ 1144409179687500000*x^28 + 381469726562500000*x^30 + 59604644775390625*x^32 + 25600000000))/x^32

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sympy [B]  time = 0.30, size = 88, normalized size = 5.50 \begin {gather*} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-59604644775390625*x**33-381469726562500000*x**31-762939453125000000*x**30-1144409179687500000*x**2
9-4577636718750000000*x**28-2136230468750000000*x**27-12817382812500000000*x**26-2777099609375000000*x**25-222
16796875000000000*x**24-2666015625000000000*x**23-26660156250000000000*x**22-1955078125000000000*x**21-2346093
7500000000000*x**20-1117187500000000000*x**19-15640625000000000000*x**18-502734375000000000*x**17-804375000000
0000000*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**8-22400000000
0000*x**7-5824000000000000*x**6-19200000000000*x**5-537600000000000*x**4-1024000000000*x**3-30720000000000*x**
2-25600000000*x-819200000000)/x**33/exp(x),x)

[Out]

(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 + 18
20000000000000*x**8 + 224000000000000*x**6 + 19200000000000*x**4 + 1024000000000*x**2 + 25600000000)*exp(-x)/x
**32

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