\(\int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48})}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx\) [2018]

Optimal result

Integrand size = 458, antiderivative size = 38 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=e^{x+\frac {4 x^2}{\left (5-\frac {1}{4} \left (x^2+\left (1-\left (3-x^2\right )^2\right )^2\right )^2\right )^2}} \] Output:

exp(4*x^2/(5-1/2*(x^2+(1-(-x^2+3)^2)^2)*(1/2*x^2+1/2*(1-(-x^2+3)^2)^2))^2+ 
x)
 

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.34 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=e^{x+\frac {64 x^2}{\left (4076-12160 x^2+15681 x^4-11416 x^6+5112 x^8-1438 x^{10}+248 x^{12}-24 x^{14}+x^{16}\right )^2}} \] Input:

Integrate[(E^((16613776*x + 64*x^2 - 99128320*x^3 + 275697112*x^5 - 474425 
152*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^2 
5 - 14780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(16613776 - 99128320*x^2 + 27 
5697112*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 - 9814 
56*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + x^32))*(6771775 
0976 + 521728*x - 606070548480*x^2 + 1556480*x^3 + 2589662421168*x^4 - 602 
1504*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 + 1014667266 
639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 41770 
29780*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 - 2000418283 
8240*x^10 + 23178449018625*x^12 - 21715716703800*x^14 + 16738275785880*x^1 
6 - 10743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 101466 
7266639*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4 
177029780*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),x]
 

Output:

E^(x + (64*x^2)/(4076 - 12160*x^2 + 15681*x^4 - 11416*x^6 + 5112*x^8 - 143 
8*x^10 + 248*x^12 - 24*x^14 + x^16)^2)
 

Rubi [F]

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.

\(\displaystyle \int \frac {\left (x^{48}-72 x^{46}+2472 x^{44}-53850 x^{42}+835464 x^{40}-9823272 x^{38}[phone] x^{36}-679887504 x^{34}[phone] x^{32}-21348937708 x^{30}[phone] x^{28}-331262302464 x^{26}[phone] x^{24}-2633985825000 x^{22}[phone] x^{20}-10743242067610 x^{18}-1920 x^{17}[phone] x^{16}+39936 x^{15}-21715716703800 x^{14}-349184 x^{13}[phone] x^{12}+1656576 x^{11}-20004182838240 x^{10}-4580352 x^9+13612565902404 x^8+7306240 x^7-7030327854208 x^6-6021504 x^5+2589662421168 x^4+1556480 x^3-606070548480 x^2+521728 x+67717750976\right ) \exp \left (\frac {x^{33}-48 x^{31}+1072 x^{29}-14780 x^{27}+140752 x^{25}-981456 x^{23}+5182726 x^{21}-21141456 x^{19}[phone] x^{17}-168042748 x^{15}[phone] x^{13}-494075008 x^{11}[phone] x^9-474425152 x^7+275697112 x^5-99128320 x^3+64 x^2+16613776 x}{x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+16613776}\right )}{x^{48}-72 x^{46}+2472 x^{44}-53850 x^{42}+835464 x^{40}-9823272 x^{38}[phone] x^{36}-679887504 x^{34}[phone] x^{32}-21348937708 x^{30}[phone] x^{28}-331262302464 x^{26}[phone] x^{24}-2633985825000 x^{22}[phone] x^{20}-10743242067610 x^{18}[phone] x^{16}-21715716703800 x^{14}[phone] x^{12}-20004182838240 x^{10}[phone] x^8-7030327854208 x^6+2589662421168 x^4-606070548480 x^2+67717750976} \, dx\)

\(\Big \downarrow \) 2461

\(\displaystyle \int \frac {\left (x^{48}-72 x^{46}+2472 x^{44}-53850 x^{42}+835464 x^{40}-9823272 x^{38}[phone] x^{36}-679887504 x^{34}[phone] x^{32}-21348937708 x^{30}[phone] x^{28}-331262302464 x^{26}[phone] x^{24}-2633985825000 x^{22}[phone] x^{20}-10743242067610 x^{18}-1920 x^{17}[phone] x^{16}+39936 x^{15}-21715716703800 x^{14}-349184 x^{13}[phone] x^{12}+1656576 x^{11}-20004182838240 x^{10}-4580352 x^9+13612565902404 x^8+7306240 x^7-7030327854208 x^6-6021504 x^5+2589662421168 x^4+1556480 x^3-606070548480 x^2+521728 x+67717750976\right ) \exp \left (\frac {x^{33}-48 x^{31}+1072 x^{29}-14780 x^{27}+140752 x^{25}-981456 x^{23}+5182726 x^{21}-21141456 x^{19}[phone] x^{17}-168042748 x^{15}[phone] x^{13}-494075008 x^{11}[phone] x^9-474425152 x^7+275697112 x^5-99128320 x^3+64 x^2+16613776 x}{x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+16613776}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^3}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (x^{48}-72 x^{46}+2472 x^{44}-53850 x^{42}+835464 x^{40}-9823272 x^{38}[phone] x^{36}-679887504 x^{34}[phone] x^{32}-21348937708 x^{30}[phone] x^{28}-331262302464 x^{26}[phone] x^{24}-2633985825000 x^{22}[phone] x^{20}-10743242067610 x^{18}-1920 x^{17}[phone] x^{16}+39936 x^{15}-21715716703800 x^{14}-349184 x^{13}[phone] x^{12}+1656576 x^{11}-20004182838240 x^{10}-4580352 x^9+13612565902404 x^8+7306240 x^7-7030327854208 x^6-6021504 x^5+2589662421168 x^4+1556480 x^3-606070548480 x^2+521728 x+67717750976\right ) \exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {1920 x \exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}-\frac {512 \left (12 x^{14}-248 x^{12}+2157 x^{10}-10224 x^8+28540 x^6-47043 x^4+42560 x^2-16304\right ) x \exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^3}+\exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \int \left (-\frac {1920 x \exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}-\frac {512 \left (12 x^{14}-248 x^{12}+2157 x^{10}-10224 x^8+28540 x^6-47043 x^4+42560 x^2-16304\right ) x \exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^3}+\exp \left (\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^8-474425152 x^6+275697112 x^4-99128320 x^2+64 x+16613776\right )}{\left (x^{16}-24 x^{14}+248 x^{12}-1438 x^{10}+5112 x^8-11416 x^6+15681 x^4-12160 x^2+4076\right )^2}\right )\right )dx\)

Input:

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 + 673 
34568*x^17 - 21141456*x^19 + 5182726*x^21 - 981456*x^23 + 140752*x^25 - 14 
780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(16613776 - 99128320*x^2 + 27569711 
2*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^2 
2 + 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 - 2 
1715716703800*x^14 + 39936*x^15 + 16738275785880*x^16 - 1920*x^17 - 107432 
42067610*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 + 258 
9662421168*x^4 - 7030327854208*x^6 + 13612565902404*x^8 - 20004182838240*x 
^10 + 23178449018625*x^12 - 21715716703800*x^14 + 16738275785880*x^16 - 10 
743242067610*x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 101466726663 
9*x^24 - 331262302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029 
780*x^32 - 679887504*x^34 + 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 5 
3850*x^42 + 2472*x^44 - 72*x^46 + x^48),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(168\) vs. \(2(56)=112\).

Time = 0.00 (sec) , antiderivative size = 169, normalized size of antiderivative = 4.45

\[{\mathrm e}^{\frac {x \left (x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^{8}-474425152 x^{6}[phone] x^{4}-99128320 x^{2}+64 x [phone]\right )}{x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^{8}-474425152 x^{6}[phone] x^{4}-99128320 x^{2}[phone]}}\]

Input:

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^32-21348937708*x^30+91550677392*x^28-33126 
2302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-1074 
3242067610*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^10-458035 
2*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x^5+2589662 
421168*x^4+1556480*x^3-606070548480*x^2+521728*x[phone])*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 
[phone]*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^4 
4-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029 
780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639 
*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+1673827578 
5880*x^16-21715716703800*x^14+23178449018625*x^12-20004182838240*x^10+1361 
2565902404*x^8-7030327854208*x^6+2589662421168*x^4-606070548480*x^2+677177 
50976),x)
 

Output:

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^16-168042748*x^14+327641456*x^12-494075008*x^ 
10+565203905*x^8-474425152*x^6+275697112*x^4-99128320*x^2+64*x[phone])/( 
x^32-48*x^30+1072*x^28-14780*x^26+140752*x^24-981456*x^22+5182726*x^20-211 
41456*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))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 171 vs. \(2 (29) = 58\).

Time = 0.12 (sec) , antiderivative size = 171, normalized size of antiderivative = 4.50 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] 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}[phone] x^{12}-168042748 x^{14}[phone] 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}}} \left (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}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=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 )} \] Input:

integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+9094 
1519*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^2 
0-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703 
800*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+2 
589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x[phone])*exp((x 
^33-48*x^31+1072*x^29-14780*x^27+140752*x^25-981456*x^23+5182726*x^21-2114 
1456*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^20-2114145 
6*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))/(x^48-72*x^46+24 
72*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4 
177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667 
266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+1673 
8275785880*x^16-21715716703800*x^14+23178449018625*x^12-20004182838240*x^1 
0+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-606070548480*x^2+ 
67717750976),x, algorithm="fricas")
 

Output:

e^((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 - 99 
128320*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^1 
6 - 168042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474 
425152*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (29) = 58\).

Time = 2.91 (sec) , antiderivative size = 170, normalized size of antiderivative = 4.47 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=e^{\frac {x^{33} - 48 x^{31} + 1072 x^{29} - 14780 x^{27} + 140752 x^{25} - 981456 x^{23} + 5182726 x^{21} - 21141456 x^{19} + 67334568 x^{17} - 168042748 x^{15} + 327641456 x^{13} - 494075008 x^{11} + 565203905 x^{9} - 474425152 x^{7} + 275697112 x^{5} - 99128320 x^{3} + 64 x^{2} + 16613776 x}{x^{32} - 48 x^{30} + 1072 x^{28} - 14780 x^{26} + 140752 x^{24} - 981456 x^{22} + 5182726 x^{20} - 21141456 x^{18} + 67334568 x^{16} - 168042748 x^{14} + 327641456 x^{12} - 494075008 x^{10} + 565203905 x^{8} - 474425152 x^{6} + 275697112 x^{4} - 99128320 x^{2} + 16613776}} \] Input:

integrate((x**48-72*x**46+2472*x**44-53850*x**42+835464*x**40-9823272*x**3 
8+90941519*x**36-679887504*x**34+4177029780*x**32-21348937708*x**30+915506 
77392*x**28-331262302464*x**26+1014667266639*x**24-2633985825000*x**22+578 
9669721888*x**20-10743242067610*x**18-1920*x**17+16738275785880*x**16+3993 
6*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**7-7030 
327854208*x**6-6021504*x**5+2589662421168*x**4+1556480*x**3-606070548480*x 
**2+521728*x[phone])*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+565203905*x**9-474425152*x**7+27569 
7112*x**5-99128320*x**3+64*x**2+16613776*x)/(x**32-48*x**30+1072*x**28-147 
80*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**8-474425 
152*x**6+275697112*x**4-99128320*x**2+16613776))/(x**48-72*x**46+2472*x**4 
4-53850*x**42+835464*x**40-9823272*x**38+90941519*x**36-679887504*x**34+41 
77029780*x**32-21348937708*x**30+91550677392*x**28-331262302464*x**26+1014 
667266639*x**24-2633985825000*x**22+5789669721888*x**20-10743242067610*x** 
18+16738275785880*x**16-21715716703800*x**14+23178449018625*x**12-20004182 
838240*x**10+13612565902404*x**8-7030327854208*x**6+2589662421168*x**4-606 
070548480*x**2+67717750976),x)
 

Output:

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 + 275 
697112*x**5 - 99128320*x**3 + 64*x**2 + 16613776*x)/(x**32 - 48*x**30 + 10 
72*x**28 - 14780*x**26 + 140752*x**24 - 981456*x**22 + 5182726*x**20 - 211 
41456*x**18 + 67334568*x**16 - 168042748*x**14 + 327641456*x**12 - 4940750 
08*x**10 + 565203905*x**8 - 474425152*x**6 + 275697112*x**4 - 99128320*x** 
2 + 16613776))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (29) = 58\).

Time = 5.81 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.37 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=e^{\left (x + \frac {64 \, x^{2}}{x^{32} - 48 \, x^{30} + 1072 \, x^{28} - 14780 \, x^{26} + 140752 \, x^{24} - 981456 \, x^{22} + 5182726 \, x^{20} - 21141456 \, x^{18} + 67334568 \, x^{16} - 168042748 \, x^{14} + 327641456 \, x^{12} - 494075008 \, x^{10} + 565203905 \, x^{8} - 474425152 \, x^{6} + 275697112 \, x^{4} - 99128320 \, x^{2} + 16613776}\right )} \] Input:

integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+9094 
1519*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^2 
0-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703 
800*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+2 
589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x[phone])*exp((x 
^33-48*x^31+1072*x^29-14780*x^27+140752*x^25-981456*x^23+5182726*x^21-2114 
1456*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^20-2114145 
6*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))/(x^48-72*x^46+24 
72*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4 
177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667 
266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+1673 
8275785880*x^16-21715716703800*x^14+23178449018625*x^12-20004182838240*x^1 
0+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-606070548480*x^2+ 
67717750976),x, algorithm="maxima")
 

Output:

e^(x + 64*x^2/(x^32 - 48*x^30 + 1072*x^28 - 14780*x^26 + 140752*x^24 - 981 
456*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 + 2756971 
12*x^4 - 99128320*x^2 + 16613776))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1565 vs. \(2 (29) = 58\).

Time = 0.45 (sec) , antiderivative size = 1565, normalized size of antiderivative = 41.18 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=\text {Too large to display} \] Input:

integrate((x^48-72*x^46+2472*x^44-53850*x^42+835464*x^40-9823272*x^38+9094 
1519*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^2 
0-10743242067610*x^18-1920*x^17+16738275785880*x^16+39936*x^15-21715716703 
800*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+2 
589662421168*x^4+1556480*x^3-606070548480*x^2+521728*x[phone])*exp((x 
^33-48*x^31+1072*x^29-14780*x^27+140752*x^25-981456*x^23+5182726*x^21-2114 
1456*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^20-2114145 
6*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))/(x^48-72*x^46+24 
72*x^44-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4 
177029780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667 
266639*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+1673 
8275785880*x^16-21715716703800*x^14+23178449018625*x^12-20004182838240*x^1 
0+13612565902404*x^8-7030327854208*x^6+2589662421168*x^4-606070548480*x^2+ 
67717750976),x, algorithm="giac")
 

Output:

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 + 32764 
1456*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^3 
2 - 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 + 14 
0752*x^24 - 981456*x^22 + 5182726*x^20 - 21141456*x^18 + 67334568*x^16 - 1 
68042748*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 47442515 
2*x^6 + 275697112*x^4 - 99128320*x^2 + 16613776) + 140752*x^25/(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 - 4940750 
08*x^10 + 565203905*x^8 - 474425152*x^6 + 275697112*x^4 - 99128320*x^2 + 1 
6613776) - 981456*x^23/(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 - 1680427 
48*x^14 + 327641456*x^12 - 494075008*x^10 + 565203905*x^8 - 474425152*x...
 

Mupad [B] (verification not implemented)

Time = 3.47 (sec) , antiderivative size = 1582, normalized size of antiderivative = 41.63 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=\text {Too large to display} \] Input:

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 + 67 
334568*x^17 - 21141456*x^19 + 5182726*x^21 - 981456*x^23 + 140752*x^25 - 1 
4780*x^27 + 1072*x^29 - 48*x^31 + x^33)/(275697112*x^4 - 99128320*x^2 - 47 
4425152*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))*(521728*x - 6 
06070548480*x^2 + 1556480*x^3 + 2589662421168*x^4 - 6021504*x^5 - 70303278 
54208*x^6 + 7306240*x^7 + 13612565902404*x^8 - 4580352*x^9 - 2000418283824 
0*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 - 33126230 
2464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 679887 
504*x^34 + 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2472* 
x^44 - 72*x^46 + x^48 + 67717750976))/(2589662421168*x^4 - 606070548480*x^ 
2 - 7030327854208*x^6 + 13612565902404*x^8 - 20004182838240*x^10 + 2317844 
9018625*x^12 - 21715716703800*x^14 + 16738275785880*x^16 - 10743242067610* 
x^18 + 5789669721888*x^20 - 2633985825000*x^22 + 1014667266639*x^24 - 3312 
62302464*x^26 + 91550677392*x^28 - 21348937708*x^30 + 4177029780*x^32 - 67 
9887504*x^34 + 90941519*x^36 - 9823272*x^38 + 835464*x^40 - 53850*x^42 + 2 
472*x^44 - 72*x^46 + x^48 + 67717750976),x)
 

Output:

exp(-(21141456*x^19)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 56520 
3905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^1 
6 - 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((67334568*x^17)/(275697112*x 
^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494075008*x^10 + 32764 
1456*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 + 16 
613776))*exp(-(99128320*x^3)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 
 + 565203905*x^8 - 494075008*x^10 + 327641456*x^12 - 168042748*x^14 + 6733 
4568*x^16 - 21141456*x^18 + 5182726*x^20 - 981456*x^22 + 140752*x^24 - 147 
80*x^26 + 1072*x^28 - 48*x^30 + x^32 + 16613776))*exp(-(168042748*x^15)/(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 + 518 
2726*x^20 - 981456*x^22 + 140752*x^24 - 14780*x^26 + 1072*x^28 - 48*x^30 + 
 x^32 + 16613776))*exp((275697112*x^5)/(275697112*x^4 - 99128320*x^2 - 474 
425152*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((327641456 
*x^13)/(275697112*x^4 - 99128320*x^2 - 474425152*x^6 + 565203905*x^8 - 494 
075008*x^10 + 327641456*x^12 - 168042748*x^14 + 67334568*x^16 - 2114145...
 

Reduce [B] (verification not implemented)

Time = 0.29 (sec) , antiderivative size = 172, normalized size of antiderivative = 4.53 \[ \int \frac {e^{\frac {16613776 x+64 x^2-99128320 x^3+275697112 x^5-474425152 x^7+565203905 x^9-494075008 x^{11}[phone] x^{13}-168042748 x^{15}[phone] x^{17}-21141456 x^{19}+5182726 x^{21}-981456 x^{23}+140752 x^{25}-14780 x^{27}+1072 x^{29}-48 x^{31}+x^{33}}{16613776-99128320 x^2+275697112 x^4-474425152 x^6+565203905 x^8-494075008 x^{10}[phone] x^{12}-168042748 x^{14}[phone] x^{16}-21141456 x^{18}+5182726 x^{20}-981456 x^{22}+140752 x^{24}-14780 x^{26}+1072 x^{28}-48 x^{30}+x^{32}}} \left (67717750976+521728 x-606070548480 x^2+1556480 x^3+2589662421168 x^4-6021504 x^5-7030327854208 x^6+7306240 x^7+13612565902404 x^8-4580352 x^9-20004182838240 x^{10}+1656576 x^{11}[phone] x^{12}-349184 x^{13}-21715716703800 x^{14}+39936 x^{15}[phone] x^{16}-1920 x^{17}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}\right )}{67717750976-606070548480 x^2+2589662421168 x^4-7030327854208 x^6+13612565902404 x^8-20004182838240 x^{10}[phone] x^{12}-21715716703800 x^{14}[phone] x^{16}-10743242067610 x^{18}[phone] x^{20}-2633985825000 x^{22}[phone] x^{24}-331262302464 x^{26}[phone] x^{28}-21348937708 x^{30}[phone] x^{32}-679887504 x^{34}[phone] x^{36}-9823272 x^{38}+835464 x^{40}-53850 x^{42}+2472 x^{44}-72 x^{46}+x^{48}} \, dx=e^{\frac {x^{33}-48 x^{31}+1072 x^{29}-14780 x^{27}+140752 x^{25}-981456 x^{23}+5182726 x^{21}-21141456 x^{19}[phone] x^{17}-168042748 x^{15}[phone] x^{13}-494075008 x^{11}[phone] x^{9}-474425152 x^{7}[phone] x^{5}-99128320 x^{3}+64 x^{2}[phone] x}{x^{32}-48 x^{30}+1072 x^{28}-14780 x^{26}+140752 x^{24}-981456 x^{22}+5182726 x^{20}-21141456 x^{18}[phone] x^{16}-168042748 x^{14}[phone] x^{12}-494075008 x^{10}[phone] x^{8}-474425152 x^{6}[phone] x^{4}-99128320 x^{2}[phone]}} \] Input:

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^32-21348937708*x^30+91550677392*x^28-33126 
2302464*x^26+1014667266639*x^24-2633985825000*x^22+5789669721888*x^20-1074 
3242067610*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^10-458035 
2*x^9+13612565902404*x^8+7306240*x^7-7030327854208*x^6-6021504*x^5+2589662 
421168*x^4+1556480*x^3-606070548480*x^2+521728*x[phone])*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 
[phone]*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^4 
4-53850*x^42+835464*x^40-9823272*x^38+90941519*x^36-679887504*x^34+4177029 
780*x^32-21348937708*x^30+91550677392*x^28-331262302464*x^26+1014667266639 
*x^24-2633985825000*x^22+5789669721888*x^20-10743242067610*x^18+1673827578 
5880*x^16-21715716703800*x^14+23178449018625*x^12-20004182838240*x^10+1361 
2565902404*x^8-7030327854208*x^6+2589662421168*x^4-606070548480*x^2+677177 
50976),x)
 

Output:

e**((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 + 275 
697112*x**5 - 99128320*x**3 + 64*x**2 + 16613776*x)/(x**32 - 48*x**30 + 10 
72*x**28 - 14780*x**26 + 140752*x**24 - 981456*x**22 + 5182726*x**20 - 211 
41456*x**18 + 67334568*x**16 - 168042748*x**14 + 327641456*x**12 - 4940750 
08*x**10 + 565203905*x**8 - 474425152*x**6 + 275697112*x**4 - 99128320*x** 
2 + 16613776))