3.32.70 \(\int \frac {e^{\frac {8589934592-38654705664 x+81604378624 x^2-107374182400 x^3+98650030080 x^4-67175972864 x^5+35114713088 x^6-14394851328 x^7+4685824000 x^8-1218314240 x^9+253034496 x^{10}-41746432 x^{11}+5404672 x^{12}-537600 x^{13}+39680 x^{14}-2048 x^{15}+66 x^{16}-x^{17}-x^{34}}{4294967296-17179869184 x+32212254720 x^2-37580963840 x^3+30534533120 x^4-18320719872 x^5+8396996608 x^6-2998927360 x^7+843448320 x^8-187432960 x^9+32800768 x^{10}-4472832 x^{11}+465920 x^{12}-35840 x^{13}+1920 x^{14}-64 x^{15}+x^{16}}} (51539607552-219043332096 x+438086664192 x^2-547608330240 x^3+479157288960 x^4-311452237824 x^5+155726118912 x^6-61178118144 x^7+19118161920 x^8-4779540480 x^9+955908096 x^{10}-152076288 x^{11}+19009536 x^{12}-1827840 x^{13}+130560 x^{14}-6528 x^{15}+204 x^{16}-3 x^{17}+408 x^{33}-54 x^{34})}{-17179869184+73014444032 x-146028888064 x^2+182536110080 x^3-159719096320 x^4+103817412608 x^5-51908706304 x^6+20392706048 x^7-6372720640 x^8+1593180160 x^9-318636032 x^{10}+50692096 x^{11}-6336512 x^{12}+609280 x^{13}-43520 x^{14}+2176 x^{15}-68 x^{16}+x^{17}} \, dx\)
Optimal. Leaf size=19 \[ 3 e^{2-x-\frac {x^{34}}{(-4+x)^{16}}} \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^((8589934592 - 38654705664*x + 81604378624*x^2 - 107374182400*x^3 + 98650030080*x^4 - 67175972864*x^5 +
35114713088*x^6 - 14394851328*x^7 + 4685824000*x^8 - 1218314240*x^9 + 253034496*x^10 - 41746432*x^11 + 540467
2*x^12 - 537600*x^13 + 39680*x^14 - 2048*x^15 + 66*x^16 - x^17 - x^34)/(4294967296 - 17179869184*x + 322122547
20*x^2 - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8
- 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16))*(515
39607552 - 219043332096*x + 438086664192*x^2 - 547608330240*x^3 + 479157288960*x^4 - 311452237824*x^5 + 155726
118912*x^6 - 61178118144*x^7 + 19118161920*x^8 - 4779540480*x^9 + 955908096*x^10 - 152076288*x^11 + 19009536*x
^12 - 1827840*x^13 + 130560*x^14 - 6528*x^15 + 204*x^16 - 3*x^17 + 408*x^33 - 54*x^34))/(-17179869184 + 730144
44032*x - 146028888064*x^2 + 182536110080*x^3 - 159719096320*x^4 + 103817412608*x^5 - 51908706304*x^6 + 203927
06048*x^7 - 6372720640*x^8 + 1593180160*x^9 - 318636032*x^10 + 50692096*x^11 - 6336512*x^12 + 609280*x^13 - 43
520*x^14 + 2176*x^15 - 68*x^16 + x^17),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [B] time = 0.36, size = 97, normalized size = 5.11 \begin {gather*} 3 e^{-\frac {-8589934592+38654705664 x-81604378624 x^2+107374182400 x^3-98650030080 x^4+67175972864 x^5-35114713088 x^6+14394851328 x^7-4685824000 x^8+1218314240 x^9-253034496 x^{10}+41746432 x^{11}-5404672 x^{12}+537600 x^{13}-39680 x^{14}+2048 x^{15}-66 x^{16}+x^{17}+x^{34}}{(-4+x)^{16}}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((8589934592 - 38654705664*x + 81604378624*x^2 - 107374182400*x^3 + 98650030080*x^4 - 67175972864
*x^5 + 35114713088*x^6 - 14394851328*x^7 + 4685824000*x^8 - 1218314240*x^9 + 253034496*x^10 - 41746432*x^11 +
5404672*x^12 - 537600*x^13 + 39680*x^14 - 2048*x^15 + 66*x^16 - x^17 - x^34)/(4294967296 - 17179869184*x + 322
12254720*x^2 - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 8434483
20*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16)
)*(51539607552 - 219043332096*x + 438086664192*x^2 - 547608330240*x^3 + 479157288960*x^4 - 311452237824*x^5 +
155726118912*x^6 - 61178118144*x^7 + 19118161920*x^8 - 4779540480*x^9 + 955908096*x^10 - 152076288*x^11 + 1900
9536*x^12 - 1827840*x^13 + 130560*x^14 - 6528*x^15 + 204*x^16 - 3*x^17 + 408*x^33 - 54*x^34))/(-17179869184 +
73014444032*x - 146028888064*x^2 + 182536110080*x^3 - 159719096320*x^4 + 103817412608*x^5 - 51908706304*x^6 +
20392706048*x^7 - 6372720640*x^8 + 1593180160*x^9 - 318636032*x^10 + 50692096*x^11 - 6336512*x^12 + 609280*x^1
3 - 43520*x^14 + 2176*x^15 - 68*x^16 + x^17),x]
[Out]
3/E^((-8589934592 + 38654705664*x - 81604378624*x^2 + 107374182400*x^3 - 98650030080*x^4 + 67175972864*x^5 - 3
5114713088*x^6 + 14394851328*x^7 - 4685824000*x^8 + 1218314240*x^9 - 253034496*x^10 + 41746432*x^11 - 5404672*
x^12 + 537600*x^13 - 39680*x^14 + 2048*x^15 - 66*x^16 + x^17 + x^34)/(-4 + x)^16)
________________________________________________________________________________________
fricas [B] time = 0.56, size = 171, normalized size = 9.00 \begin {gather*} 3 \, e^{\left (-\frac {x^{34} + x^{17} - 66 \, x^{16} + 2048 \, x^{15} - 39680 \, x^{14} + 537600 \, x^{13} - 5404672 \, x^{12} + 41746432 \, x^{11} - 253034496 \, x^{10} + 1218314240 \, x^{9} - 4685824000 \, x^{8} + 14394851328 \, x^{7} - 35114713088 \, x^{6} + 67175972864 \, x^{5} - 98650030080 \, x^{4} + 107374182400 \, x^{3} - 81604378624 \, x^{2} + 38654705664 \, x - 8589934592}{x^{16} - 64 \, x^{15} + 1920 \, x^{14} - 35840 \, x^{13} + 465920 \, x^{12} - 4472832 \, x^{11} + 32800768 \, x^{10} - 187432960 \, x^{9} + 843448320 \, x^{8} - 2998927360 \, x^{7} + 8396996608 \, x^{6} - 18320719872 \, x^{5} + 30534533120 \, x^{4} - 37580963840 \, x^{3} + 32212254720 \, x^{2} - 17179869184 \, x + 4294967296}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-54*x^34+408*x^33-3*x^17+204*x^16-6528*x^15+130560*x^14-1827840*x^13+19009536*x^12-152076288*x^11+9
55908096*x^10-4779540480*x^9+19118161920*x^8-61178118144*x^7+155726118912*x^6-311452237824*x^5+479157288960*x^
4-547608330240*x^3+438086664192*x^2-219043332096*x+51539607552)*exp((-x^34-x^17+66*x^16-2048*x^15+39680*x^14-5
37600*x^13+5404672*x^12-41746432*x^11+253034496*x^10-1218314240*x^9+4685824000*x^8-14394851328*x^7+35114713088
*x^6-67175972864*x^5+98650030080*x^4-107374182400*x^3+81604378624*x^2-38654705664*x+8589934592)/(x^16-64*x^15+
1920*x^14-35840*x^13+465920*x^12-4472832*x^11+32800768*x^10-187432960*x^9+843448320*x^8-2998927360*x^7+8396996
608*x^6-18320719872*x^5+30534533120*x^4-37580963840*x^3+32212254720*x^2-17179869184*x+4294967296))/(x^17-68*x^
16+2176*x^15-43520*x^14+609280*x^13-6336512*x^12+50692096*x^11-318636032*x^10+1593180160*x^9-6372720640*x^8+20
392706048*x^7-51908706304*x^6+103817412608*x^5-159719096320*x^4+182536110080*x^3-146028888064*x^2+73014444032*
x-17179869184),x, algorithm="fricas")
[Out]
3*e^(-(x^34 + x^17 - 66*x^16 + 2048*x^15 - 39680*x^14 + 537600*x^13 - 5404672*x^12 + 41746432*x^11 - 253034496
*x^10 + 1218314240*x^9 - 4685824000*x^8 + 14394851328*x^7 - 35114713088*x^6 + 67175972864*x^5 - 98650030080*x^
4 + 107374182400*x^3 - 81604378624*x^2 + 38654705664*x - 8589934592)/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13
+ 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6
- 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296))
________________________________________________________________________________________
giac [B] time = 0.82, size = 1614, normalized size = 84.95 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-54*x^34+408*x^33-3*x^17+204*x^16-6528*x^15+130560*x^14-1827840*x^13+19009536*x^12-152076288*x^11+9
55908096*x^10-4779540480*x^9+19118161920*x^8-61178118144*x^7+155726118912*x^6-311452237824*x^5+479157288960*x^
4-547608330240*x^3+438086664192*x^2-219043332096*x+51539607552)*exp((-x^34-x^17+66*x^16-2048*x^15+39680*x^14-5
37600*x^13+5404672*x^12-41746432*x^11+253034496*x^10-1218314240*x^9+4685824000*x^8-14394851328*x^7+35114713088
*x^6-67175972864*x^5+98650030080*x^4-107374182400*x^3+81604378624*x^2-38654705664*x+8589934592)/(x^16-64*x^15+
1920*x^14-35840*x^13+465920*x^12-4472832*x^11+32800768*x^10-187432960*x^9+843448320*x^8-2998927360*x^7+8396996
608*x^6-18320719872*x^5+30534533120*x^4-37580963840*x^3+32212254720*x^2-17179869184*x+4294967296))/(x^17-68*x^
16+2176*x^15-43520*x^14+609280*x^13-6336512*x^12+50692096*x^11-318636032*x^10+1593180160*x^9-6372720640*x^8+20
392706048*x^7-51908706304*x^6+103817412608*x^5-159719096320*x^4+182536110080*x^3-146028888064*x^2+73014444032*
x-17179869184),x, algorithm="giac")
[Out]
3*e^(-x^34/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x
^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 3
2212254720*x^2 - 17179869184*x + 4294967296) - x^17/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4
472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^
5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) + 66*x^16/(x^16 - 64*x^1
5 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998
927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869
184*x + 4294967296) - 2048*x^15/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 328007
68*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4
- 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) + 39680*x^14/(x^16 - 64*x^15 + 1920*x^14 - 3
5840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396
996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 429496729
6) - 537600*x^13/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 18743
2960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x
^3 + 32212254720*x^2 - 17179869184*x + 4294967296) + 5404672*x^12/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 4
65920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 -
18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 41746432
*x^11/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 +
843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 322122
54720*x^2 - 17179869184*x + 4294967296) + 253034496*x^10/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^1
2 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 183207198
72*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 1218314240*x^9/(x
^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 84344832
0*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^
2 - 17179869184*x + 4294967296) + 4685824000*x^8/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472
832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 +
30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 14394851328*x^7/(x^16 - 6
4*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 -
2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 171
79869184*x + 4294967296) + 35114713088*x^6/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^
11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534
533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 67175972864*x^5/(x^16 - 64*x^15
+ 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 29989
27360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 171798691
84*x + 4294967296) + 98650030080*x^4/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 3
2800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120
*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 107374182400*x^3/(x^16 - 64*x^15 + 19
20*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360
*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x
+ 4294967296) + 81604378624*x^2/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 328007
68*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4
- 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 38654705664*x/(x^16 - 64*x^15 + 1920*x^14
- 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8
396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840*x^3 + 32212254720*x^2 - 17179869184*x + 429496
7296) + 8589934592/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x^10 - 187
432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37580963840
*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296))
________________________________________________________________________________________
maple [F(-1)] time = 180.00, size = 0, normalized size = 0.00 hanged
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-54*x^34+408*x^33-3*x^17+204*x^16-6528*x^15+130560*x^14-1827840*x^13+19009536*x^12-152076288*x^11+9559080
96*x^10-4779540480*x^9+19118161920*x^8-61178118144*x^7+155726118912*x^6-311452237824*x^5+479157288960*x^4-5476
08330240*x^3+438086664192*x^2-219043332096*x+51539607552)*exp((-x^34-x^17+66*x^16-2048*x^15+39680*x^14-537600*
x^13+5404672*x^12-41746432*x^11+253034496*x^10-1218314240*x^9+4685824000*x^8-14394851328*x^7+35114713088*x^6-6
7175972864*x^5+98650030080*x^4-107374182400*x^3+81604378624*x^2-38654705664*x+8589934592)/(x^16-64*x^15+1920*x
^14-35840*x^13+465920*x^12-4472832*x^11+32800768*x^10-187432960*x^9+843448320*x^8-2998927360*x^7+8396996608*x^
6-18320719872*x^5+30534533120*x^4-37580963840*x^3+32212254720*x^2-17179869184*x+4294967296))/(x^17-68*x^16+217
6*x^15-43520*x^14+609280*x^13-6336512*x^12+50692096*x^11-318636032*x^10+1593180160*x^9-6372720640*x^8+20392706
048*x^7-51908706304*x^6+103817412608*x^5-159719096320*x^4+182536110080*x^3-146028888064*x^2+73014444032*x-1717
9869184),x,method=_RETURNVERBOSE)
[Out]
int((-54*x^34+408*x^33-3*x^17+204*x^16-6528*x^15+130560*x^14-1827840*x^13+19009536*x^12-152076288*x^11+9559080
96*x^10-4779540480*x^9+19118161920*x^8-61178118144*x^7+155726118912*x^6-311452237824*x^5+479157288960*x^4-5476
08330240*x^3+438086664192*x^2-219043332096*x+51539607552)*exp((-x^34-x^17+66*x^16-2048*x^15+39680*x^14-537600*
x^13+5404672*x^12-41746432*x^11+253034496*x^10-1218314240*x^9+4685824000*x^8-14394851328*x^7+35114713088*x^6-6
7175972864*x^5+98650030080*x^4-107374182400*x^3+81604378624*x^2-38654705664*x+8589934592)/(x^16-64*x^15+1920*x
^14-35840*x^13+465920*x^12-4472832*x^11+32800768*x^10-187432960*x^9+843448320*x^8-2998927360*x^7+8396996608*x^
6-18320719872*x^5+30534533120*x^4-37580963840*x^3+32212254720*x^2-17179869184*x+4294967296))/(x^17-68*x^16+217
6*x^15-43520*x^14+609280*x^13-6336512*x^12+50692096*x^11-318636032*x^10+1593180160*x^9-6372720640*x^8+20392706
048*x^7-51908706304*x^6+103817412608*x^5-159719096320*x^4+182536110080*x^3-146028888064*x^2+73014444032*x-1717
9869184),x,method=_RETURNVERBOSE)
________________________________________________________________________________________
maxima [B] time = 26.58, size = 805, normalized size = 42.37 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-54*x^34+408*x^33-3*x^17+204*x^16-6528*x^15+130560*x^14-1827840*x^13+19009536*x^12-152076288*x^11+9
55908096*x^10-4779540480*x^9+19118161920*x^8-61178118144*x^7+155726118912*x^6-311452237824*x^5+479157288960*x^
4-547608330240*x^3+438086664192*x^2-219043332096*x+51539607552)*exp((-x^34-x^17+66*x^16-2048*x^15+39680*x^14-5
37600*x^13+5404672*x^12-41746432*x^11+253034496*x^10-1218314240*x^9+4685824000*x^8-14394851328*x^7+35114713088
*x^6-67175972864*x^5+98650030080*x^4-107374182400*x^3+81604378624*x^2-38654705664*x+8589934592)/(x^16-64*x^15+
1920*x^14-35840*x^13+465920*x^12-4472832*x^11+32800768*x^10-187432960*x^9+843448320*x^8-2998927360*x^7+8396996
608*x^6-18320719872*x^5+30534533120*x^4-37580963840*x^3+32212254720*x^2-17179869184*x+4294967296))/(x^17-68*x^
16+2176*x^15-43520*x^14+609280*x^13-6336512*x^12+50692096*x^11-318636032*x^10+1593180160*x^9-6372720640*x^8+20
392706048*x^7-51908706304*x^6+103817412608*x^5-159719096320*x^4+182536110080*x^3-146028888064*x^2+73014444032*
x-17179869184),x, algorithm="maxima")
[Out]
3*e^(-x^18 - 64*x^17 - 2176*x^16 - 52224*x^15 - 992256*x^14 - 15876096*x^13 - 222265344*x^12 - 2794192896*x^11
- 32133218304*x^10 - 342754328576*x^9 - 3427543285760*x^8 - 32405863792640*x^7 - 291652774133760*x^6 - 251270
0823306240*x^5 - 20819521107394560*x^4 - 166556168859156480*x^3 - 1290810308658462720*x^2 - 971904232401666048
1*x - 295147905179352825856/(x^16 - 64*x^15 + 1920*x^14 - 35840*x^13 + 465920*x^12 - 4472832*x^11 + 32800768*x
^10 - 187432960*x^9 + 843448320*x^8 - 2998927360*x^7 + 8396996608*x^6 - 18320719872*x^5 + 30534533120*x^4 - 37
580963840*x^3 + 32212254720*x^2 - 17179869184*x + 4294967296) - 2508757194024499019776/(x^15 - 60*x^14 + 1680*
x^13 - 29120*x^12 + 349440*x^11 - 3075072*x^10 + 20500480*x^9 - 105431040*x^8 + 421724160*x^7 - 1312030720*x^6
+ 3148873728*x^5 - 5725224960*x^4 + 7633633280*x^3 - 7046430720*x^2 + 4026531840*x - 1073741824) - 1034862342
5351058456576/(x^14 - 56*x^13 + 1456*x^12 - 23296*x^11 + 256256*x^10 - 2050048*x^9 + 12300288*x^8 - 56229888*x
^7 + 196804608*x^6 - 524812288*x^5 + 1049624576*x^4 - 1526726656*x^3 + 1526726656*x^2 - 939524096*x + 26843545
6) - 27596329134269489217536/(x^13 - 52*x^12 + 1248*x^11 - 18304*x^10 + 183040*x^9 - 1317888*x^8 + 7028736*x^7
- 28114944*x^6 + 84344832*x^5 - 187432960*x^4 + 299892736*x^3 - 327155712*x^2 + 218103808*x - 67108864) - 534
67887697647135358976/(x^12 - 48*x^11 + 1056*x^10 - 14080*x^9 + 126720*x^8 - 811008*x^7 + 3784704*x^6 - 1297612
8*x^5 + 32440320*x^4 - 57671680*x^3 + 69206016*x^2 - 50331648*x + 16777216) - 80201831546470703038464/(x^11 -
44*x^10 + 880*x^9 - 10560*x^8 + 84480*x^7 - 473088*x^6 + 1892352*x^5 - 5406720*x^4 + 10813440*x^3 - 14417920*x
^2 + 11534336*x - 4194304) - 96910546451985432838144/(x^10 - 40*x^9 + 720*x^8 - 7680*x^7 + 53760*x^6 - 258048*
x^5 + 860160*x^4 - 1966080*x^3 + 2949120*x^2 - 2621440*x + 1048576) - 96910546451985432838144/(x^9 - 36*x^8 +
576*x^7 - 5376*x^6 + 32256*x^5 - 129024*x^4 + 344064*x^3 - 589824*x^2 + 589824*x - 262144) - 81768273568862708
957184/(x^8 - 32*x^7 + 448*x^6 - 3584*x^5 + 17920*x^4 - 57344*x^3 + 114688*x^2 - 131072*x + 65536) - 590548642
44178623135744/(x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384) - 3690929015261163
9459840/(x^6 - 24*x^5 + 240*x^4 - 1280*x^3 + 3840*x^2 - 6144*x + 4096) - 20132340083242712432640/(x^5 - 20*x^4
+ 160*x^3 - 640*x^2 + 1280*x - 1024) - 9646746289887133040640/(x^4 - 16*x^3 + 96*x^2 - 256*x + 256) - 4081315
738029171671040/(x^3 - 12*x^2 + 48*x - 64) - 1530493401760939376640/(x^2 - 8*x + 16) - 510164467253646458880/(
x - 4) - 71272977042788843518)
________________________________________________________________________________________
mupad [B] time = 2.35, size = 1631, normalized size = 85.84 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(-(38654705664*x - 81604378624*x^2 + 107374182400*x^3 - 98650030080*x^4 + 67175972864*x^5 - 351147130
88*x^6 + 14394851328*x^7 - 4685824000*x^8 + 1218314240*x^9 - 253034496*x^10 + 41746432*x^11 - 5404672*x^12 + 5
37600*x^13 - 39680*x^14 + 2048*x^15 - 66*x^16 + x^17 + x^34 - 8589934592)/(32212254720*x^2 - 17179869184*x - 3
7580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 1874329
60*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*(
219043332096*x - 438086664192*x^2 + 547608330240*x^3 - 479157288960*x^4 + 311452237824*x^5 - 155726118912*x^6
+ 61178118144*x^7 - 19118161920*x^8 + 4779540480*x^9 - 955908096*x^10 + 152076288*x^11 - 19009536*x^12 + 18278
40*x^13 - 130560*x^14 + 6528*x^15 - 204*x^16 + 3*x^17 - 408*x^33 + 54*x^34 - 51539607552))/(73014444032*x - 14
6028888064*x^2 + 182536110080*x^3 - 159719096320*x^4 + 103817412608*x^5 - 51908706304*x^6 + 20392706048*x^7 -
6372720640*x^8 + 1593180160*x^9 - 318636032*x^10 + 50692096*x^11 - 6336512*x^12 + 609280*x^13 - 43520*x^14 + 2
176*x^15 - 68*x^16 + x^17 - 17179869184),x)
[Out]
3*exp(-(38654705664*x)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5
+ 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12
- 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-(67175972864*x^5)/(32212254720*x^2 - 1717986918
4*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 -
187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967
296))*exp((98650030080*x^4)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872
*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920
*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp((81604378624*x^2)/(32212254720*x^2 - 171798
69184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^
8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 429
4967296))*exp(-(107374182400*x^3)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320
719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 +
465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-x^17/(32212254720*x^2 - 17179869184*
x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 18
7432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 429496729
6))*exp(-x^34/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996
608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*
x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp((66*x^16)/(32212254720*x^2 - 17179869184*x - 37580963840*
x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32
800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-(2048*x
^15)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 -
2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 19
20*x^14 - 64*x^15 + x^16 + 4294967296))*exp((39680*x^14)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 +
30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768
*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-(537600*x^13)
/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 299
8927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x
^14 - 64*x^15 + x^16 + 4294967296))*exp((5404672*x^12)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30
534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x
^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-(41746432*x^11)
/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 299
8927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x
^14 - 64*x^15 + x^16 + 4294967296))*exp((253034496*x^10)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 +
30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768
*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp((4685824000*x^
8)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2
998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920
*x^14 - 64*x^15 + x^16 + 4294967296))*exp(8589934592/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 3053
4533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^1
0 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp((35114713088*x^6)/
(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998
927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^
14 - 64*x^15 + x^16 + 4294967296))*exp(-(1218314240*x^9)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 +
30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 - 2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768
*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 1920*x^14 - 64*x^15 + x^16 + 4294967296))*exp(-(14394851328*
x^7)/(32212254720*x^2 - 17179869184*x - 37580963840*x^3 + 30534533120*x^4 - 18320719872*x^5 + 8396996608*x^6 -
2998927360*x^7 + 843448320*x^8 - 187432960*x^9 + 32800768*x^10 - 4472832*x^11 + 465920*x^12 - 35840*x^13 + 19
20*x^14 - 64*x^15 + x^16 + 4294967296))
________________________________________________________________________________________
sympy [B] time = 3.83, size = 170, normalized size = 8.95 \begin {gather*} 3 e^{\frac {- x^{34} - x^{17} + 66 x^{16} - 2048 x^{15} + 39680 x^{14} - 537600 x^{13} + 5404672 x^{12} - 41746432 x^{11} + 253034496 x^{10} - 1218314240 x^{9} + 4685824000 x^{8} - 14394851328 x^{7} + 35114713088 x^{6} - 67175972864 x^{5} + 98650030080 x^{4} - 107374182400 x^{3} + 81604378624 x^{2} - 38654705664 x + 8589934592}{x^{16} - 64 x^{15} + 1920 x^{14} - 35840 x^{13} + 465920 x^{12} - 4472832 x^{11} + 32800768 x^{10} - 187432960 x^{9} + 843448320 x^{8} - 2998927360 x^{7} + 8396996608 x^{6} - 18320719872 x^{5} + 30534533120 x^{4} - 37580963840 x^{3} + 32212254720 x^{2} - 17179869184 x + 4294967296}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-54*x**34+408*x**33-3*x**17+204*x**16-6528*x**15+130560*x**14-1827840*x**13+19009536*x**12-15207628
8*x**11+955908096*x**10-4779540480*x**9+19118161920*x**8-61178118144*x**7+155726118912*x**6-311452237824*x**5+
479157288960*x**4-547608330240*x**3+438086664192*x**2-219043332096*x+51539607552)*exp((-x**34-x**17+66*x**16-2
048*x**15+39680*x**14-537600*x**13+5404672*x**12-41746432*x**11+253034496*x**10-1218314240*x**9+4685824000*x**
8-14394851328*x**7+35114713088*x**6-67175972864*x**5+98650030080*x**4-107374182400*x**3+81604378624*x**2-38654
705664*x+8589934592)/(x**16-64*x**15+1920*x**14-35840*x**13+465920*x**12-4472832*x**11+32800768*x**10-18743296
0*x**9+843448320*x**8-2998927360*x**7+8396996608*x**6-18320719872*x**5+30534533120*x**4-37580963840*x**3+32212
254720*x**2-17179869184*x+4294967296))/(x**17-68*x**16+2176*x**15-43520*x**14+609280*x**13-6336512*x**12+50692
096*x**11-318636032*x**10+1593180160*x**9-6372720640*x**8+20392706048*x**7-51908706304*x**6+103817412608*x**5-
159719096320*x**4+182536110080*x**3-146028888064*x**2+73014444032*x-17179869184),x)
[Out]
3*exp((-x**34 - x**17 + 66*x**16 - 2048*x**15 + 39680*x**14 - 537600*x**13 + 5404672*x**12 - 41746432*x**11 +
253034496*x**10 - 1218314240*x**9 + 4685824000*x**8 - 14394851328*x**7 + 35114713088*x**6 - 67175972864*x**5 +
98650030080*x**4 - 107374182400*x**3 + 81604378624*x**2 - 38654705664*x + 8589934592)/(x**16 - 64*x**15 + 192
0*x**14 - 35840*x**13 + 465920*x**12 - 4472832*x**11 + 32800768*x**10 - 187432960*x**9 + 843448320*x**8 - 2998
927360*x**7 + 8396996608*x**6 - 18320719872*x**5 + 30534533120*x**4 - 37580963840*x**3 + 32212254720*x**2 - 17
179869184*x + 4294967296))
________________________________________________________________________________________