3.81.18 \(\int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}+327641456 x^{13}-168042748 x^{15}+67334568 x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}+327641456 x^{12}-168042748 x^{14}+67334568 x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}+23178449018625 x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}+16738275785880 x^{16}-1920 x^{17}-10743242067610 x^{18}+5789669721888 x^{20}-2633985825000 x^{22}+1014667266639 x^{24}-331262302464 x^{26}+91550677392 x^{28}-21348937708 x^{30}+4177029780 x^{32}-679887504 x^{34}+90941519 x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48})}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}+23178449018625 x^{12}-21715716703800 x^{14}+16738275785880 x^{16}-10743242067610 x^{18}+5789669721888 x^{20}-2633985825000 x^{22}+1014667266639 x^{24}-331262302464 x^{26}+91550677392 x^{28}-21348937708 x^{30}+4177029780 x^{32}-679887504 x^{34}+90941519 x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx\)
Optimal. Leaf size=38 \[ e^{x+\frac {4 x^2}{\left (5-\frac {1}{4} \left (x^2+\left (1-\left (3-x^2\right )^2\right )^2\right )^2\right )^2}} \]
________________________________________________________________________________________
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^((16613776*x + 64*x^2 - 99128320*x^3 + 275697112*x^5 - 474425152*x^7 + 565203905*x^9 - 494075008*x^11 +
327641456*x^13 - 168042748*x^15 + 67334568*x^17 - 21141456*x^19 + 5182726*x^21 - 981456*x^23 + 140752*x^25 -
14780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(16613776 - 99128320*x^2 + 275697112*x^4 - 474425152*x^6 + 565203905*
x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456
*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32))*(67717750976 + 521728*x - 606070548480*x^2 + 1
556480*x^3 + 2589662421168*x^4 - 6021504*x^5 - 7030327854208*x^6 + 7306240*x^7 + 13612565902404*x^8 - 4580352*
x^9 - 20004182838240*x^10 + 1656576*x^11 + 23178449018625*x^12 - 349184*x^13 - 21715716703800*x^14 + 39936*x^1
5 + 16738275785880*x^16 - 1920*x^17 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 10146672
66639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887504*x^34 + 9094
1519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48))/(67717750976 - 606070548480
*x^2 + 2589662421168*x^4 - 7030327854208*x^6 + 13612565902404*x^8 - 20004182838240*x^10 + 23178449018625*x^12
- 21715716703800*x^14 + 16738275785880*x^16 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 +
1014667266639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887504*x^3
4 + 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 0.20, size = 51, normalized size = 1.34 \begin {gather*} e^{x+\frac {64 x^2}{\left (4076-12160 x^2+15681 x^4-11416 x^6+5112 x^8-1438 x^{10}+248 x^{12}-24 x^{14}+x^{16}\right )^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((16613776*x + 64*x^2 - 99128320*x^3 + 275697112*x^5 - 474425152*x^7 + 565203905*x^9 - 494075008*
x^11 + 327641456*x^13 - 168042748*x^15 + 67334568*x^17 - 21141456*x^19 + 5182726*x^21 - 981456*x^23 + 140752*x
^25 - 14780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(16613776 - 99128320*x^2 + 275697112*x^4 - 474425152*x^6 + 5652
03905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 -
981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32))*(67717750976 + 521728*x - 606070548480*x
^2 + 1556480*x^3 + 2589662421168*x^4 - 6021504*x^5 - 7030327854208*x^6 + 7306240*x^7 + 13612565902404*x^8 - 45
80352*x^9 - 20004182838240*x^10 + 1656576*x^11 + 23178449018625*x^12 - 349184*x^13 - 21715716703800*x^14 + 399
36*x^15 + 16738275785880*x^16 - 1920*x^17 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 10
14667266639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887504*x^34
+ 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48))/(67717750976 - 606070
548480*x^2 + 2589662421168*x^4 - 7030327854208*x^6 + 13612565902404*x^8 - 20004182838240*x^10 + 23178449018625
*x^12 - 21715716703800*x^14 + 16738275785880*x^16 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x
^22 + 1014667266639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 6798875
04*x^34 + 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48),x]
[Out]
E^(x + (64*x^2)/(4076 - 12160*x^2 + 15681*x^4 - 11416*x^6 + 5112*x^8 - 1438*x^10 + 248*x^12 - 24*x^14 + x^16)^
2)
________________________________________________________________________________________
fricas [B] time = 0.90, size = 171, normalized size = 4.50 \begin {gather*} e^{\left (\frac {x^{33} - 48 \, x^{31} + 1072 \, x^{29} - 14780 \, x^{27} + 140752 \, x^{25} - 981456 \, x^{23} + 5182726 \, x^{21} - 21141456 \, x^{19} + 67334568 \, x^{17} - 168042748 \, x^{15} + 327641456 \, x^{13} - 494075008 \, x^{11} + 565203905 \, x^{9} - 474425152 \, x^{7} + 275697112 \, x^{5} - 99128320 \, x^{3} + 64 \, x^{2} + 16613776 \, x}{x^{32} - 48 \, x^{30} + 1072 \, x^{28} - 14780 \, x^{26} + 140752 \, x^{24} - 981456 \, x^{22} + 5182726 \, x^{20} - 21141456 \, x^{18} + 67334568 \, x^{16} - 168042748 \, x^{14} + 327641456 \, x^{12} - 494075008 \, x^{10} + 565203905 \, x^{8} - 474425152 \, x^{6} + 275697112 \, x^{4} - 99128320 \, x^{2} + 16613776}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*
x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x
^20-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703800*x^14-349184*x^13+2317844901862
5*x^12+1656576*x^11-20004182838240*x^10-4580352*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x
^5+2589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x+67717750976)*exp((x^33-48*x^31+1072*x^29-14780*x^27
+140752*x^25-981456*x^23+5182726*x^21-21141456*x^19+67334568*x^17-168042748*x^15+327641456*x^13-494075008*x^11
+565203905*x^9-474425152*x^7+275697112*x^5-99128320*x^3+64*x^2+16613776*x)/(x^32-48*x^30+1072*x^28-14780*x^26+
140752*x^24-981456*x^22+5182726*x^20-21141456*x^18+67334568*x^16-168042748*x^14+327641456*x^12-494075008*x^10+
565203905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+16613776))/(x^48-72*x^46+2472*x^44-53850*x^42+835464*x^
40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^
26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+16738275785880*x^16-2171571670
3800*x^14+23178449018625*x^12-20004182838240*x^10+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-60607
0548480*x^2+67717750976),x, algorithm="fricas")
[Out]
e^((x^33 - 48*x^31 + 1072*x^29 - 14780*x^27 + 140752*x^25 - 981456*x^23 + 5182726*x^21 - 21141456*x^19 + 67334
568*x^17 - 168042748*x^15 + 327641456*x^13 - 494075008*x^11 + 565203905*x^9 - 474425152*x^7 + 275697112*x^5 -
99128320*x^3 + 64*x^2 + 16613776*x)/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 518
2726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 -
474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776))
________________________________________________________________________________________
giac [B] time = 0.90, size = 1565, normalized size = 41.18 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*
x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x
^20-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703800*x^14-349184*x^13+2317844901862
5*x^12+1656576*x^11-20004182838240*x^10-4580352*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x
^5+2589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x+67717750976)*exp((x^33-48*x^31+1072*x^29-14780*x^27
+140752*x^25-981456*x^23+5182726*x^21-21141456*x^19+67334568*x^17-168042748*x^15+327641456*x^13-494075008*x^11
+565203905*x^9-474425152*x^7+275697112*x^5-99128320*x^3+64*x^2+16613776*x)/(x^32-48*x^30+1072*x^28-14780*x^26+
140752*x^24-981456*x^22+5182726*x^20-21141456*x^18+67334568*x^16-168042748*x^14+327641456*x^12-494075008*x^10+
565203905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+16613776))/(x^48-72*x^46+2472*x^44-53850*x^42+835464*x^
40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^
26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+16738275785880*x^16-2171571670
3800*x^14+23178449018625*x^12-20004182838240*x^10+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-60607
0548480*x^2+67717750976),x, algorithm="giac")
[Out]
e^(x^33/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 +
67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x
^4 - 99128320*x^2 + 16613776) - 48*x^31/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 +
5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x
^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 1072*x^29/(x^32 - 48*x^30 + 1072*x^28 - 14780*
x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x
^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) - 14780*x^27/(
x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*
x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 9912
8320*x^2 + 16613776) + 140752*x^25/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182
726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 -
474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) - 981456*x^23/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^2
6 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12
- 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 5182726*x^21/(x
^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x
^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128
320*x^2 + 16613776) - 21141456*x^19/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 518
2726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 -
474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 67334568*x^17/(x^32 - 48*x^30 + 1072*x^28 - 14780*
x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x
^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) - 168042748*x^
15/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334
568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 -
99128320*x^2 + 16613776) + 327641456*x^13/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22
+ 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905
*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) - 494075008*x^11/(x^32 - 48*x^30 + 1072*x^28 -
14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 3276
41456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 56520
3905*x^9/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 +
67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*
x^4 - 99128320*x^2 + 16613776) - 474425152*x^7/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456
*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 5652
03905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 275697112*x^5/(x^32 - 48*x^30 + 1072*x^
28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 +
327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) - 9
9128320*x^3/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^1
8 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 2756971
12*x^4 - 99128320*x^2 + 16613776) + 64*x^2/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^2
2 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 56520390
5*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 16613776*x/(x^32 - 48*x^30 + 1072*x^28 - 14
780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 168042748*x^14 + 3276414
56*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776))
________________________________________________________________________________________
maple [B] time = 1.06, size = 129, normalized size = 3.39
|
|
|
| method |
result |
size |
|
|
|
| risch |
\({\mathrm e}^{\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}+67334568 x^{16}-168042748 x^{14}+327641456 x^{12}-494075008 x^{10}+565203905 x^{8}-474425152 x^{6}+275697112 x^{4}-99128320 x^{2}+64 x +16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^{8}-11416 x^{6}+15681 x^{4}-12160 x^{2}+4076\right )^{2}}}\) |
\(129\) |
| gosper |
\({\mathrm e}^{\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}+67334568 x^{16}-168042748 x^{14}+327641456 x^{12}-494075008 x^{10}+565203905 x^{8}-474425152 x^{6}+275697112 x^{4}-99128320 x^{2}+64 x +16613776\right )}{x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}+67334568 x^{16}-168042748 x^{14}+327641456 x^{12}-494075008 x^{10}+565203905 x^{8}-474425152 x^{6}+275697112 x^{4}-99128320 x^{2}+16613776}}\) |
\(169\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*x^32-2
1348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-10
743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703800*x^14-349184*x^13+23178449018625*x^12
+1656576*x^11-20004182838240*x^10-4580352*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x^5+258
9662421168*x^4+1556480*x^3-606070548480*x^2+521728*x+67717750976)*exp((x^33-48*x^31+1072*x^29-14780*x^27+14075
2*x^25-981456*x^23+5182726*x^21-21141456*x^19+67334568*x^17-168042748*x^15+327641456*x^13-494075008*x^11+56520
3905*x^9-474425152*x^7+275697112*x^5-99128320*x^3+64*x^2+16613776*x)/(x^32-48*x^30+1072*x^28-14780*x^26+140752
*x^24-981456*x^22+5182726*x^20-21141456*x^18+67334568*x^16-168042748*x^14+327641456*x^12-494075008*x^10+565203
905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+16613776))/(x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-982
3272*x^38+90941519*x^36-679887504*x^34+4177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+101
4667266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+16738275785880*x^16-21715716703800*x
^14+23178449018625*x^12-20004182838240*x^10+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-60607054848
0*x^2+67717750976),x,method=_RETURNVERBOSE)
[Out]
exp(x*(x^32-48*x^30+1072*x^28-14780*x^26+140752*x^24-981456*x^22+5182726*x^20-21141456*x^18+67334568*x^16-1680
42748*x^14+327641456*x^12-494075008*x^10+565203905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+64*x+16613776)
/(x^16-24*x^14+248*x^12-1438*x^10+5112*x^8-11416*x^6+15681*x^4-12160*x^2+4076)^2)
________________________________________________________________________________________
maxima [B] time = 5.92, size = 90, normalized size = 2.37 \begin {gather*} e^{\left (x + \frac {64 \, x^{2}}{x^{32} - 48 \, x^{30} + 1072 \, x^{28} - 14780 \, x^{26} + 140752 \, x^{24} - 981456 \, x^{22} + 5182726 \, x^{20} - 21141456 \, x^{18} + 67334568 \, x^{16} - 168042748 \, x^{14} + 327641456 \, x^{12} - 494075008 \, x^{10} + 565203905 \, x^{8} - 474425152 \, x^{6} + 275697112 \, x^{4} - 99128320 \, x^{2} + 16613776}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*
x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x
^20-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703800*x^14-349184*x^13+2317844901862
5*x^12+1656576*x^11-20004182838240*x^10-4580352*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x
^5+2589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x+67717750976)*exp((x^33-48*x^31+1072*x^29-14780*x^27
+140752*x^25-981456*x^23+5182726*x^21-21141456*x^19+67334568*x^17-168042748*x^15+327641456*x^13-494075008*x^11
+565203905*x^9-474425152*x^7+275697112*x^5-99128320*x^3+64*x^2+16613776*x)/(x^32-48*x^30+1072*x^28-14780*x^26+
140752*x^24-981456*x^22+5182726*x^20-21141456*x^18+67334568*x^16-168042748*x^14+327641456*x^12-494075008*x^10+
565203905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+16613776))/(x^48-72*x^46+2472*x^44-53850*x^42+835464*x^
40-9823272*x^38+90941519*x^36-679887504*x^34+4177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^
26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+16738275785880*x^16-2171571670
3800*x^14+23178449018625*x^12-20004182838240*x^10+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-60607
0548480*x^2+67717750976),x, algorithm="maxima")
[Out]
e^(x + 64*x^2/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x
^18 + 67334568*x^16 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x^6 + 27569
7112*x^4 - 99128320*x^2 + 16613776))
________________________________________________________________________________________
mupad [B] time = 6.60, size = 1582, normalized size = 41.63 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp((16613776*x + 64*x^2 - 99128320*x^3 + 275697112*x^5 - 474425152*x^7 + 565203905*x^9 - 494075008*x^11
+ 327641456*x^13 - 168042748*x^15 + 67334568*x^17 - 21141456*x^19 + 5182726*x^21 - 981456*x^23 + 140752*x^25 -
14780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 4940
75008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 14
0752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*(521728*x - 606070548480*x^2 + 1556480*x^3 +
2589662421168*x^4 - 6021504*x^5 - 7030327854208*x^6 + 7306240*x^7 + 13612565902404*x^8 - 4580352*x^9 - 2000418
2838240*x^10 + 1656576*x^11 + 23178449018625*x^12 - 349184*x^13 - 21715716703800*x^14 + 39936*x^15 + 167382757
85880*x^16 - 1920*x^17 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 1014667266639*x^24 -
331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887504*x^34 + 90941519*x^36 - 9
823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48 + 67717750976))/(2589662421168*x^4 - 60607
0548480*x^2 - 7030327854208*x^6 + 13612565902404*x^8 - 20004182838240*x^10 + 23178449018625*x^12 - 21715716703
800*x^14 + 16738275785880*x^16 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 1014667266639
*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887504*x^34 + 90941519*
x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472*x^44 - 72*x^46 + x^48 + 67717750976),x)
[Out]
exp(-(21141456*x^19)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 32764145
6*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^2
6 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((67334568*x^17)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6
+ 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x
^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(-(99128320*x^3)/(27
5697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14
+ 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30
+ x^32 + 16613776))*exp(-(168042748*x^15)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 4940
75008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 14
0752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((275697112*x^5)/(275697112*x^4 - 99128320
*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 2114
1456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*ex
p((327641456*x^13)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*
x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26
+ 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(-(474425152*x^7)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 +
565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^
20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(-(494075008*x^11)/(2
75697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14
+ 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30
+ x^32 + 16613776))*exp((565203905*x^9)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 49407
5008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140
752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((16613776*x)/(275697112*x^4 - 99128320*x^2
- 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456
*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(x^
33/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748
*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48
*x^30 + x^32 + 16613776))*exp((64*x^2)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 4940750
08*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 14075
2*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(-(48*x^31)/(275697112*x^4 - 99128320*x^2 - 4
74425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^1
8 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((1072*
x^29)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042
748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 -
48*x^30 + x^32 + 16613776))*exp(-(14780*x^27)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 -
494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22
+ 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((140752*x^25)/(275697112*x^4 - 99128
320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 2
1141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))
*exp(-(981456*x^23)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 327641456
*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26
+ 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp((5182726*x^21)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 +
565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 21141456*x^18 + 5182726*x^2
0 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))
________________________________________________________________________________________
sympy [B] time = 7.29, size = 170, normalized size = 4.47 \begin {gather*} e^{\frac {x^{33} - 48 x^{31} + 1072 x^{29} - 14780 x^{27} + 140752 x^{25} - 981456 x^{23} + 5182726 x^{21} - 21141456 x^{19} + 67334568 x^{17} - 168042748 x^{15} + 327641456 x^{13} - 494075008 x^{11} + 565203905 x^{9} - 474425152 x^{7} + 275697112 x^{5} - 99128320 x^{3} + 64 x^{2} + 16613776 x}{x^{32} - 48 x^{30} + 1072 x^{28} - 14780 x^{26} + 140752 x^{24} - 981456 x^{22} + 5182726 x^{20} - 21141456 x^{18} + 67334568 x^{16} - 168042748 x^{14} + 327641456 x^{12} - 494075008 x^{10} + 565203905 x^{8} - 474425152 x^{6} + 275697112 x^{4} - 99128320 x^{2} + 16613776}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x**48-72*x**46+2472*x**44-53850*x**42+835464*x**40-9823272*x**38+90941519*x**36-679887504*x**34+417
7029780*x**32-21348937708*x**30+91550677392*x**28-331262302464*x**26+1014667266639*x**24-2633985825000*x**22+5
789669721888*x**20-10743242067610*x**18-1920*x**17+16738275785880*x**16+39936*x**15-21715716703800*x**14-34918
4*x**13+23178449018625*x**12+1656576*x**11-20004182838240*x**10-4580352*x**9+13612565902404*x**8+7306240*x**7-
7030327854208*x**6-6021504*x**5+2589662421168*x**4+1556480*x**3-606070548480*x**2+521728*x+67717750976)*exp((x
**33-48*x**31+1072*x**29-14780*x**27+140752*x**25-981456*x**23+5182726*x**21-21141456*x**19+67334568*x**17-168
042748*x**15+327641456*x**13-494075008*x**11+565203905*x**9-474425152*x**7+275697112*x**5-99128320*x**3+64*x**
2+16613776*x)/(x**32-48*x**30+1072*x**28-14780*x**26+140752*x**24-981456*x**22+5182726*x**20-21141456*x**18+67
334568*x**16-168042748*x**14+327641456*x**12-494075008*x**10+565203905*x**8-474425152*x**6+275697112*x**4-9912
8320*x**2+16613776))/(x**48-72*x**46+2472*x**44-53850*x**42+835464*x**40-9823272*x**38+90941519*x**36-67988750
4*x**34+4177029780*x**32-21348937708*x**30+91550677392*x**28-331262302464*x**26+1014667266639*x**24-2633985825
000*x**22+5789669721888*x**20-10743242067610*x**18+16738275785880*x**16-21715716703800*x**14+23178449018625*x*
*12-20004182838240*x**10+13612565902404*x**8-7030327854208*x**6+2589662421168*x**4-606070548480*x**2+677177509
76),x)
[Out]
exp((x**33 - 48*x**31 + 1072*x**29 - 14780*x**27 + 140752*x**25 - 981456*x**23 + 5182726*x**21 - 21141456*x**1
9 + 67334568*x**17 - 168042748*x**15 + 327641456*x**13 - 494075008*x**11 + 565203905*x**9 - 474425152*x**7 + 2
75697112*x**5 - 99128320*x**3 + 64*x**2 + 16613776*x)/(x**32 - 48*x**30 + 1072*x**28 - 14780*x**26 + 140752*x*
*24 - 981456*x**22 + 5182726*x**20 - 21141456*x**18 + 67334568*x**16 - 168042748*x**14 + 327641456*x**12 - 494
075008*x**10 + 565203905*x**8 - 474425152*x**6 + 275697112*x**4 - 99128320*x**2 + 16613776))
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