3.13.65 \(\int \frac {-5083731656658 x^3-13122 e^{9 x} x^3+5083731656658 x^4-2259436291848 x^5+585779779368 x^6-97629963228 x^7+10847773692 x^8-803538792 x^9+38263752 x^{10}-1062882 x^{11}+13122 x^{12}+e^{24} (-36+20 x)+e^{8 x} (-1062882 x^3+118098 x^4)+e^{7 x} (-38263752 x^3+8503056 x^4-472392 x^5)+e^{6 x} (-803538792 x^3+267846264 x^4-29760696 x^5+1102248 x^6)+e^{5 x} (-10847773692 x^3+4821232752 x^4-803538792 x^5+59521392 x^6-1653372 x^7)+e^{4 x} (-97629963228 x^3+54238868460 x^4-12053081880 x^5+1339231320 x^6-74401740 x^7+1653372 x^8)+e^{3 x} (-585779779368 x^3+390519852912 x^4-108477736920 x^5+16070775840 x^6-1339231320 x^7+59521392 x^8-1102248 x^9)+e^{2 x} (-2259436291848 x^3+1757339338104 x^4-585779779368 x^5+108477736920 x^6-12053081880 x^7+803538792 x^8-29760696 x^9+472392 x^{10})+e^x (e^{24} (-4-16 x)-5083731656658 x^3+4518872583696 x^4-1757339338104 x^5+390519852912 x^6-54238868460 x^7+4821232752 x^8-267846264 x^9+8503056 x^{10}-118098 x^{11})}{2541865828329 x^3+6561 e^{9 x} x^3-2541865828329 x^4+1129718145924 x^5-292889889684 x^6+48814981614 x^7-5423886846 x^8+401769396 x^9-19131876 x^{10}+531441 x^{11}-6561 x^{12}+e^{8 x} (531441 x^3-59049 x^4)+e^{7 x} (19131876 x^3-4251528 x^4+236196 x^5)+e^{6 x} (401769396 x^3-133923132 x^4+14880348 x^5-551124 x^6)+e^{5 x} (5423886846 x^3-2410616376 x^4+401769396 x^5-29760696 x^6+826686 x^7)+e^{4 x} (48814981614 x^3-27119434230 x^4+6026540940 x^5-669615660 x^6+37200870 x^7-826686 x^8)+e^{3 x} (292889889684 x^3-195259926456 x^4+54238868460 x^5-8035387920 x^6+669615660 x^7-29760696 x^8+551124 x^9)+e^{2 x} (1129718145924 x^3-878669669052 x^4+292889889684 x^5-54238868460 x^6+6026540940 x^7-401769396 x^8+14880348 x^9-236196 x^{10})+e^x (2541865828329 x^3-2259436291848 x^4+878669669052 x^5-195259926456 x^6+27119434230 x^7-2410616376 x^8+133923132 x^9-4251528 x^{10}+59049 x^{11})} \, dx\)
Optimal. Leaf size=26 \[ 2 \left (\frac {e^{24}}{6561 \left (9+e^x-x\right )^8 x^2}-x\right ) \]
________________________________________________________________________________________
Rubi [F] time = 21.83, 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*} \int \frac {-5083731656658 x^3-13122 e^{9 x} x^3+5083731656658 x^4-2259436291848 x^5+585779779368 x^6-97629963228 x^7+10847773692 x^8-803538792 x^9+38263752 x^{10}-1062882 x^{11}+13122 x^{12}+e^{24} (-36+20 x)+e^{8 x} \left (-1062882 x^3+118098 x^4\right )+e^{7 x} \left (-38263752 x^3+8503056 x^4-472392 x^5\right )+e^{6 x} \left (-803538792 x^3+267846264 x^4-29760696 x^5+1102248 x^6\right )+e^{5 x} \left (-10847773692 x^3+4821232752 x^4-803538792 x^5+59521392 x^6-1653372 x^7\right )+e^{4 x} \left (-97629963228 x^3+54238868460 x^4-12053081880 x^5+1339231320 x^6-74401740 x^7+1653372 x^8\right )+e^{3 x} \left (-585779779368 x^3+390519852912 x^4-108477736920 x^5+16070775840 x^6-1339231320 x^7+59521392 x^8-1102248 x^9\right )+e^{2 x} \left (-2259436291848 x^3+1757339338104 x^4-585779779368 x^5+108477736920 x^6-12053081880 x^7+803538792 x^8-29760696 x^9+472392 x^{10}\right )+e^x \left (e^{24} (-4-16 x)-5083731656658 x^3+4518872583696 x^4-1757339338104 x^5+390519852912 x^6-54238868460 x^7+4821232752 x^8-267846264 x^9+8503056 x^{10}-118098 x^{11}\right )}{2541865828329 x^3+6561 e^{9 x} x^3-2541865828329 x^4+1129718145924 x^5-292889889684 x^6+48814981614 x^7-5423886846 x^8+401769396 x^9-19131876 x^{10}+531441 x^{11}-6561 x^{12}+e^{8 x} \left (531441 x^3-59049 x^4\right )+e^{7 x} \left (19131876 x^3-4251528 x^4+236196 x^5\right )+e^{6 x} \left (401769396 x^3-133923132 x^4+14880348 x^5-551124 x^6\right )+e^{5 x} \left (5423886846 x^3-2410616376 x^4+401769396 x^5-29760696 x^6+826686 x^7\right )+e^{4 x} \left (48814981614 x^3-27119434230 x^4+6026540940 x^5-669615660 x^6+37200870 x^7-826686 x^8\right )+e^{3 x} \left (292889889684 x^3-195259926456 x^4+54238868460 x^5-8035387920 x^6+669615660 x^7-29760696 x^8+551124 x^9\right )+e^{2 x} \left (1129718145924 x^3-878669669052 x^4+292889889684 x^5-54238868460 x^6+6026540940 x^7-401769396 x^8+14880348 x^9-236196 x^{10}\right )+e^x \left (2541865828329 x^3-2259436291848 x^4+878669669052 x^5-195259926456 x^6+27119434230 x^7-2410616376 x^8+133923132 x^9-4251528 x^{10}+59049 x^{11}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-5083731656658*x^3 - 13122*E^(9*x)*x^3 + 5083731656658*x^4 - 2259436291848*x^5 + 585779779368*x^6 - 97629
963228*x^7 + 10847773692*x^8 - 803538792*x^9 + 38263752*x^10 - 1062882*x^11 + 13122*x^12 + E^24*(-36 + 20*x) +
E^(8*x)*(-1062882*x^3 + 118098*x^4) + E^(7*x)*(-38263752*x^3 + 8503056*x^4 - 472392*x^5) + E^(6*x)*(-80353879
2*x^3 + 267846264*x^4 - 29760696*x^5 + 1102248*x^6) + E^(5*x)*(-10847773692*x^3 + 4821232752*x^4 - 803538792*x
^5 + 59521392*x^6 - 1653372*x^7) + E^(4*x)*(-97629963228*x^3 + 54238868460*x^4 - 12053081880*x^5 + 1339231320*
x^6 - 74401740*x^7 + 1653372*x^8) + E^(3*x)*(-585779779368*x^3 + 390519852912*x^4 - 108477736920*x^5 + 1607077
5840*x^6 - 1339231320*x^7 + 59521392*x^8 - 1102248*x^9) + E^(2*x)*(-2259436291848*x^3 + 1757339338104*x^4 - 58
5779779368*x^5 + 108477736920*x^6 - 12053081880*x^7 + 803538792*x^8 - 29760696*x^9 + 472392*x^10) + E^x*(E^24*
(-4 - 16*x) - 5083731656658*x^3 + 4518872583696*x^4 - 1757339338104*x^5 + 390519852912*x^6 - 54238868460*x^7 +
4821232752*x^8 - 267846264*x^9 + 8503056*x^10 - 118098*x^11))/(2541865828329*x^3 + 6561*E^(9*x)*x^3 - 2541865
828329*x^4 + 1129718145924*x^5 - 292889889684*x^6 + 48814981614*x^7 - 5423886846*x^8 + 401769396*x^9 - 1913187
6*x^10 + 531441*x^11 - 6561*x^12 + E^(8*x)*(531441*x^3 - 59049*x^4) + E^(7*x)*(19131876*x^3 - 4251528*x^4 + 23
6196*x^5) + E^(6*x)*(401769396*x^3 - 133923132*x^4 + 14880348*x^5 - 551124*x^6) + E^(5*x)*(5423886846*x^3 - 24
10616376*x^4 + 401769396*x^5 - 29760696*x^6 + 826686*x^7) + E^(4*x)*(48814981614*x^3 - 27119434230*x^4 + 60265
40940*x^5 - 669615660*x^6 + 37200870*x^7 - 826686*x^8) + E^(3*x)*(292889889684*x^3 - 195259926456*x^4 + 542388
68460*x^5 - 8035387920*x^6 + 669615660*x^7 - 29760696*x^8 + 551124*x^9) + E^(2*x)*(1129718145924*x^3 - 8786696
69052*x^4 + 292889889684*x^5 - 54238868460*x^6 + 6026540940*x^7 - 401769396*x^8 + 14880348*x^9 - 236196*x^10)
+ E^x*(2541865828329*x^3 - 2259436291848*x^4 + 878669669052*x^5 - 195259926456*x^6 + 27119434230*x^7 - 2410616
376*x^8 + 133923132*x^9 - 4251528*x^10 + 59049*x^11)),x]
[Out]
-2*x - (4*E^24*Defer[Int][1/((9 + E^x - x)^8*x^3), x])/6561 + (160*E^24*Defer[Int][1/((9 + E^x - x)^9*x^2), x]
)/6561 - (16*E^24*Defer[Int][1/((9 + E^x - x)^8*x^2), x])/6561 - (16*E^24*Defer[Int][1/((9 + E^x - x)^9*x), x]
)/6561
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 27, normalized size = 1.04 \begin {gather*} \frac {2 \left (-6561 (-9+x)+\frac {e^{24}}{\left (9+e^x-x\right )^8 x^2}\right )}{6561} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-5083731656658*x^3 - 13122*E^(9*x)*x^3 + 5083731656658*x^4 - 2259436291848*x^5 + 585779779368*x^6 -
97629963228*x^7 + 10847773692*x^8 - 803538792*x^9 + 38263752*x^10 - 1062882*x^11 + 13122*x^12 + E^24*(-36 + 2
0*x) + E^(8*x)*(-1062882*x^3 + 118098*x^4) + E^(7*x)*(-38263752*x^3 + 8503056*x^4 - 472392*x^5) + E^(6*x)*(-80
3538792*x^3 + 267846264*x^4 - 29760696*x^5 + 1102248*x^6) + E^(5*x)*(-10847773692*x^3 + 4821232752*x^4 - 80353
8792*x^5 + 59521392*x^6 - 1653372*x^7) + E^(4*x)*(-97629963228*x^3 + 54238868460*x^4 - 12053081880*x^5 + 13392
31320*x^6 - 74401740*x^7 + 1653372*x^8) + E^(3*x)*(-585779779368*x^3 + 390519852912*x^4 - 108477736920*x^5 + 1
6070775840*x^6 - 1339231320*x^7 + 59521392*x^8 - 1102248*x^9) + E^(2*x)*(-2259436291848*x^3 + 1757339338104*x^
4 - 585779779368*x^5 + 108477736920*x^6 - 12053081880*x^7 + 803538792*x^8 - 29760696*x^9 + 472392*x^10) + E^x*
(E^24*(-4 - 16*x) - 5083731656658*x^3 + 4518872583696*x^4 - 1757339338104*x^5 + 390519852912*x^6 - 54238868460
*x^7 + 4821232752*x^8 - 267846264*x^9 + 8503056*x^10 - 118098*x^11))/(2541865828329*x^3 + 6561*E^(9*x)*x^3 - 2
541865828329*x^4 + 1129718145924*x^5 - 292889889684*x^6 + 48814981614*x^7 - 5423886846*x^8 + 401769396*x^9 - 1
9131876*x^10 + 531441*x^11 - 6561*x^12 + E^(8*x)*(531441*x^3 - 59049*x^4) + E^(7*x)*(19131876*x^3 - 4251528*x^
4 + 236196*x^5) + E^(6*x)*(401769396*x^3 - 133923132*x^4 + 14880348*x^5 - 551124*x^6) + E^(5*x)*(5423886846*x^
3 - 2410616376*x^4 + 401769396*x^5 - 29760696*x^6 + 826686*x^7) + E^(4*x)*(48814981614*x^3 - 27119434230*x^4 +
6026540940*x^5 - 669615660*x^6 + 37200870*x^7 - 826686*x^8) + E^(3*x)*(292889889684*x^3 - 195259926456*x^4 +
54238868460*x^5 - 8035387920*x^6 + 669615660*x^7 - 29760696*x^8 + 551124*x^9) + E^(2*x)*(1129718145924*x^3 - 8
78669669052*x^4 + 292889889684*x^5 - 54238868460*x^6 + 6026540940*x^7 - 401769396*x^8 + 14880348*x^9 - 236196*
x^10) + E^x*(2541865828329*x^3 - 2259436291848*x^4 + 878669669052*x^5 - 195259926456*x^6 + 27119434230*x^7 - 2
410616376*x^8 + 133923132*x^9 - 4251528*x^10 + 59049*x^11)),x]
[Out]
(2*(-6561*(-9 + x) + E^24/((9 + E^x - x)^8*x^2)))/6561
________________________________________________________________________________________
fricas [B] time = 0.68, size = 531, normalized size = 20.42 \begin {gather*} -\frac {2 \, {\left (6561 \, x^{11} - 472392 \, x^{10} + 14880348 \, x^{9} - 267846264 \, x^{8} + 3013270470 \, x^{7} - 21695547384 \, x^{6} + 97629963228 \, x^{5} - 251048476872 \, x^{4} + 6561 \, x^{3} e^{\left (8 \, x\right )} + 282429536481 \, x^{3} - 52488 \, {\left (x^{4} - 9 \, x^{3}\right )} e^{\left (7 \, x\right )} + 183708 \, {\left (x^{5} - 18 \, x^{4} + 81 \, x^{3}\right )} e^{\left (6 \, x\right )} - 367416 \, {\left (x^{6} - 27 \, x^{5} + 243 \, x^{4} - 729 \, x^{3}\right )} e^{\left (5 \, x\right )} + 459270 \, {\left (x^{7} - 36 \, x^{6} + 486 \, x^{5} - 2916 \, x^{4} + 6561 \, x^{3}\right )} e^{\left (4 \, x\right )} - 367416 \, {\left (x^{8} - 45 \, x^{7} + 810 \, x^{6} - 7290 \, x^{5} + 32805 \, x^{4} - 59049 \, x^{3}\right )} e^{\left (3 \, x\right )} + 183708 \, {\left (x^{9} - 54 \, x^{8} + 1215 \, x^{7} - 14580 \, x^{6} + 98415 \, x^{5} - 354294 \, x^{4} + 531441 \, x^{3}\right )} e^{\left (2 \, x\right )} - 52488 \, {\left (x^{10} - 63 \, x^{9} + 1701 \, x^{8} - 25515 \, x^{7} + 229635 \, x^{6} - 1240029 \, x^{5} + 3720087 \, x^{4} - 4782969 \, x^{3}\right )} e^{x} - e^{24}\right )}}{6561 \, {\left (x^{10} - 72 \, x^{9} + 2268 \, x^{8} - 40824 \, x^{7} + 459270 \, x^{6} - 3306744 \, x^{5} + 14880348 \, x^{4} - 38263752 \, x^{3} + x^{2} e^{\left (8 \, x\right )} + 43046721 \, x^{2} - 8 \, {\left (x^{3} - 9 \, x^{2}\right )} e^{\left (7 \, x\right )} + 28 \, {\left (x^{4} - 18 \, x^{3} + 81 \, x^{2}\right )} e^{\left (6 \, x\right )} - 56 \, {\left (x^{5} - 27 \, x^{4} + 243 \, x^{3} - 729 \, x^{2}\right )} e^{\left (5 \, x\right )} + 70 \, {\left (x^{6} - 36 \, x^{5} + 486 \, x^{4} - 2916 \, x^{3} + 6561 \, x^{2}\right )} e^{\left (4 \, x\right )} - 56 \, {\left (x^{7} - 45 \, x^{6} + 810 \, x^{5} - 7290 \, x^{4} + 32805 \, x^{3} - 59049 \, x^{2}\right )} e^{\left (3 \, x\right )} + 28 \, {\left (x^{8} - 54 \, x^{7} + 1215 \, x^{6} - 14580 \, x^{5} + 98415 \, x^{4} - 354294 \, x^{3} + 531441 \, x^{2}\right )} e^{\left (2 \, x\right )} - 8 \, {\left (x^{9} - 63 \, x^{8} + 1701 \, x^{7} - 25515 \, x^{6} + 229635 \, x^{5} - 1240029 \, x^{4} + 3720087 \, x^{3} - 4782969 \, x^{2}\right )} e^{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-13122*x^3*exp(x)^9+(118098*x^4-1062882*x^3)*exp(x)^8+(-472392*x^5+8503056*x^4-38263752*x^3)*exp(x)
^7+(1102248*x^6-29760696*x^5+267846264*x^4-803538792*x^3)*exp(x)^6+(-1653372*x^7+59521392*x^6-803538792*x^5+48
21232752*x^4-10847773692*x^3)*exp(x)^5+(1653372*x^8-74401740*x^7+1339231320*x^6-12053081880*x^5+54238868460*x^
4-97629963228*x^3)*exp(x)^4+(-1102248*x^9+59521392*x^8-1339231320*x^7+16070775840*x^6-108477736920*x^5+3905198
52912*x^4-585779779368*x^3)*exp(x)^3+(472392*x^10-29760696*x^9+803538792*x^8-12053081880*x^7+108477736920*x^6-
585779779368*x^5+1757339338104*x^4-2259436291848*x^3)*exp(x)^2+((-16*x-4)*exp(3)^8-118098*x^11+8503056*x^10-26
7846264*x^9+4821232752*x^8-54238868460*x^7+390519852912*x^6-1757339338104*x^5+4518872583696*x^4-5083731656658*
x^3)*exp(x)+(20*x-36)*exp(3)^8+13122*x^12-1062882*x^11+38263752*x^10-803538792*x^9+10847773692*x^8-97629963228
*x^7+585779779368*x^6-2259436291848*x^5+5083731656658*x^4-5083731656658*x^3)/(6561*x^3*exp(x)^9+(-59049*x^4+53
1441*x^3)*exp(x)^8+(236196*x^5-4251528*x^4+19131876*x^3)*exp(x)^7+(-551124*x^6+14880348*x^5-133923132*x^4+4017
69396*x^3)*exp(x)^6+(826686*x^7-29760696*x^6+401769396*x^5-2410616376*x^4+5423886846*x^3)*exp(x)^5+(-826686*x^
8+37200870*x^7-669615660*x^6+6026540940*x^5-27119434230*x^4+48814981614*x^3)*exp(x)^4+(551124*x^9-29760696*x^8
+669615660*x^7-8035387920*x^6+54238868460*x^5-195259926456*x^4+292889889684*x^3)*exp(x)^3+(-236196*x^10+148803
48*x^9-401769396*x^8+6026540940*x^7-54238868460*x^6+292889889684*x^5-878669669052*x^4+1129718145924*x^3)*exp(x
)^2+(59049*x^11-4251528*x^10+133923132*x^9-2410616376*x^8+27119434230*x^7-195259926456*x^6+878669669052*x^5-22
59436291848*x^4+2541865828329*x^3)*exp(x)-6561*x^12+531441*x^11-19131876*x^10+401769396*x^9-5423886846*x^8+488
14981614*x^7-292889889684*x^6+1129718145924*x^5-2541865828329*x^4+2541865828329*x^3),x, algorithm="fricas")
[Out]
-2/6561*(6561*x^11 - 472392*x^10 + 14880348*x^9 - 267846264*x^8 + 3013270470*x^7 - 21695547384*x^6 + 976299632
28*x^5 - 251048476872*x^4 + 6561*x^3*e^(8*x) + 282429536481*x^3 - 52488*(x^4 - 9*x^3)*e^(7*x) + 183708*(x^5 -
18*x^4 + 81*x^3)*e^(6*x) - 367416*(x^6 - 27*x^5 + 243*x^4 - 729*x^3)*e^(5*x) + 459270*(x^7 - 36*x^6 + 486*x^5
- 2916*x^4 + 6561*x^3)*e^(4*x) - 367416*(x^8 - 45*x^7 + 810*x^6 - 7290*x^5 + 32805*x^4 - 59049*x^3)*e^(3*x) +
183708*(x^9 - 54*x^8 + 1215*x^7 - 14580*x^6 + 98415*x^5 - 354294*x^4 + 531441*x^3)*e^(2*x) - 52488*(x^10 - 63*
x^9 + 1701*x^8 - 25515*x^7 + 229635*x^6 - 1240029*x^5 + 3720087*x^4 - 4782969*x^3)*e^x - e^24)/(x^10 - 72*x^9
+ 2268*x^8 - 40824*x^7 + 459270*x^6 - 3306744*x^5 + 14880348*x^4 - 38263752*x^3 + x^2*e^(8*x) + 43046721*x^2 -
8*(x^3 - 9*x^2)*e^(7*x) + 28*(x^4 - 18*x^3 + 81*x^2)*e^(6*x) - 56*(x^5 - 27*x^4 + 243*x^3 - 729*x^2)*e^(5*x)
+ 70*(x^6 - 36*x^5 + 486*x^4 - 2916*x^3 + 6561*x^2)*e^(4*x) - 56*(x^7 - 45*x^6 + 810*x^5 - 7290*x^4 + 32805*x^
3 - 59049*x^2)*e^(3*x) + 28*(x^8 - 54*x^7 + 1215*x^6 - 14580*x^5 + 98415*x^4 - 354294*x^3 + 531441*x^2)*e^(2*x
) - 8*(x^9 - 63*x^8 + 1701*x^7 - 25515*x^6 + 229635*x^5 - 1240029*x^4 + 3720087*x^3 - 4782969*x^2)*e^x)
________________________________________________________________________________________
giac [B] time = 5.92, size = 713, normalized size = 27.42 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-13122*x^3*exp(x)^9+(118098*x^4-1062882*x^3)*exp(x)^8+(-472392*x^5+8503056*x^4-38263752*x^3)*exp(x)
^7+(1102248*x^6-29760696*x^5+267846264*x^4-803538792*x^3)*exp(x)^6+(-1653372*x^7+59521392*x^6-803538792*x^5+48
21232752*x^4-10847773692*x^3)*exp(x)^5+(1653372*x^8-74401740*x^7+1339231320*x^6-12053081880*x^5+54238868460*x^
4-97629963228*x^3)*exp(x)^4+(-1102248*x^9+59521392*x^8-1339231320*x^7+16070775840*x^6-108477736920*x^5+3905198
52912*x^4-585779779368*x^3)*exp(x)^3+(472392*x^10-29760696*x^9+803538792*x^8-12053081880*x^7+108477736920*x^6-
585779779368*x^5+1757339338104*x^4-2259436291848*x^3)*exp(x)^2+((-16*x-4)*exp(3)^8-118098*x^11+8503056*x^10-26
7846264*x^9+4821232752*x^8-54238868460*x^7+390519852912*x^6-1757339338104*x^5+4518872583696*x^4-5083731656658*
x^3)*exp(x)+(20*x-36)*exp(3)^8+13122*x^12-1062882*x^11+38263752*x^10-803538792*x^9+10847773692*x^8-97629963228
*x^7+585779779368*x^6-2259436291848*x^5+5083731656658*x^4-5083731656658*x^3)/(6561*x^3*exp(x)^9+(-59049*x^4+53
1441*x^3)*exp(x)^8+(236196*x^5-4251528*x^4+19131876*x^3)*exp(x)^7+(-551124*x^6+14880348*x^5-133923132*x^4+4017
69396*x^3)*exp(x)^6+(826686*x^7-29760696*x^6+401769396*x^5-2410616376*x^4+5423886846*x^3)*exp(x)^5+(-826686*x^
8+37200870*x^7-669615660*x^6+6026540940*x^5-27119434230*x^4+48814981614*x^3)*exp(x)^4+(551124*x^9-29760696*x^8
+669615660*x^7-8035387920*x^6+54238868460*x^5-195259926456*x^4+292889889684*x^3)*exp(x)^3+(-236196*x^10+148803
48*x^9-401769396*x^8+6026540940*x^7-54238868460*x^6+292889889684*x^5-878669669052*x^4+1129718145924*x^3)*exp(x
)^2+(59049*x^11-4251528*x^10+133923132*x^9-2410616376*x^8+27119434230*x^7-195259926456*x^6+878669669052*x^5-22
59436291848*x^4+2541865828329*x^3)*exp(x)-6561*x^12+531441*x^11-19131876*x^10+401769396*x^9-5423886846*x^8+488
14981614*x^7-292889889684*x^6+1129718145924*x^5-2541865828329*x^4+2541865828329*x^3),x, algorithm="giac")
[Out]
-2/6561*(6561*x^11 - 52488*x^10*e^x - 472392*x^10 + 183708*x^9*e^(2*x) + 3306744*x^9*e^x + 14880348*x^9 - 3674
16*x^8*e^(3*x) - 9920232*x^8*e^(2*x) - 89282088*x^8*e^x - 267846264*x^8 + 459270*x^7*e^(4*x) + 16533720*x^7*e^
(3*x) + 223205220*x^7*e^(2*x) + 1339231320*x^7*e^x + 3013270470*x^7 - 367416*x^6*e^(5*x) - 16533720*x^6*e^(4*x
) - 297606960*x^6*e^(3*x) - 2678462640*x^6*e^(2*x) - 12053081880*x^6*e^x - 21695547384*x^6 + 183708*x^5*e^(6*x
) + 9920232*x^5*e^(5*x) + 223205220*x^5*e^(4*x) + 2678462640*x^5*e^(3*x) + 18079622820*x^5*e^(2*x) + 650866421
52*x^5*e^x + 97629963228*x^5 - 52488*x^4*e^(7*x) - 3306744*x^4*e^(6*x) - 89282088*x^4*e^(5*x) - 1339231320*x^4
*e^(4*x) - 12053081880*x^4*e^(3*x) - 65086642152*x^4*e^(2*x) - 195259926456*x^4*e^x - 251048476872*x^4 + 6561*
x^3*e^(8*x) + 472392*x^3*e^(7*x) + 14880348*x^3*e^(6*x) + 267846264*x^3*e^(5*x) + 3013270470*x^3*e^(4*x) + 216
95547384*x^3*e^(3*x) + 97629963228*x^3*e^(2*x) + 251048476872*x^3*e^x + 282429536481*x^3 - e^24)/(x^10 - 8*x^9
*e^x - 72*x^9 + 28*x^8*e^(2*x) + 504*x^8*e^x + 2268*x^8 - 56*x^7*e^(3*x) - 1512*x^7*e^(2*x) - 13608*x^7*e^x -
40824*x^7 + 70*x^6*e^(4*x) + 2520*x^6*e^(3*x) + 34020*x^6*e^(2*x) + 204120*x^6*e^x + 459270*x^6 - 56*x^5*e^(5*
x) - 2520*x^5*e^(4*x) - 45360*x^5*e^(3*x) - 408240*x^5*e^(2*x) - 1837080*x^5*e^x - 3306744*x^5 + 28*x^4*e^(6*x
) + 1512*x^4*e^(5*x) + 34020*x^4*e^(4*x) + 408240*x^4*e^(3*x) + 2755620*x^4*e^(2*x) + 9920232*x^4*e^x + 148803
48*x^4 - 8*x^3*e^(7*x) - 504*x^3*e^(6*x) - 13608*x^3*e^(5*x) - 204120*x^3*e^(4*x) - 1837080*x^3*e^(3*x) - 9920
232*x^3*e^(2*x) - 29760696*x^3*e^x - 38263752*x^3 + x^2*e^(8*x) + 72*x^2*e^(7*x) + 2268*x^2*e^(6*x) + 40824*x^
2*e^(5*x) + 459270*x^2*e^(4*x) + 3306744*x^2*e^(3*x) + 14880348*x^2*e^(2*x) + 38263752*x^2*e^x + 43046721*x^2)
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maple [A] time = 0.16, size = 21, normalized size = 0.81
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\(-2 x +\frac {2 \,{\mathrm e}^{24}}{6561 x^{2} \left (x -{\mathrm e}^{x}-9\right )^{8}}\) |
\(21\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-13122*x^3*exp(x)^9+(118098*x^4-1062882*x^3)*exp(x)^8+(-472392*x^5+8503056*x^4-38263752*x^3)*exp(x)^7+(11
02248*x^6-29760696*x^5+267846264*x^4-803538792*x^3)*exp(x)^6+(-1653372*x^7+59521392*x^6-803538792*x^5+48212327
52*x^4-10847773692*x^3)*exp(x)^5+(1653372*x^8-74401740*x^7+1339231320*x^6-12053081880*x^5+54238868460*x^4-9762
9963228*x^3)*exp(x)^4+(-1102248*x^9+59521392*x^8-1339231320*x^7+16070775840*x^6-108477736920*x^5+390519852912*
x^4-585779779368*x^3)*exp(x)^3+(472392*x^10-29760696*x^9+803538792*x^8-12053081880*x^7+108477736920*x^6-585779
779368*x^5+1757339338104*x^4-2259436291848*x^3)*exp(x)^2+((-16*x-4)*exp(3)^8-118098*x^11+8503056*x^10-26784626
4*x^9+4821232752*x^8-54238868460*x^7+390519852912*x^6-1757339338104*x^5+4518872583696*x^4-5083731656658*x^3)*e
xp(x)+(20*x-36)*exp(3)^8+13122*x^12-1062882*x^11+38263752*x^10-803538792*x^9+10847773692*x^8-97629963228*x^7+5
85779779368*x^6-2259436291848*x^5+5083731656658*x^4-5083731656658*x^3)/(6561*x^3*exp(x)^9+(-59049*x^4+531441*x
^3)*exp(x)^8+(236196*x^5-4251528*x^4+19131876*x^3)*exp(x)^7+(-551124*x^6+14880348*x^5-133923132*x^4+401769396*
x^3)*exp(x)^6+(826686*x^7-29760696*x^6+401769396*x^5-2410616376*x^4+5423886846*x^3)*exp(x)^5+(-826686*x^8+3720
0870*x^7-669615660*x^6+6026540940*x^5-27119434230*x^4+48814981614*x^3)*exp(x)^4+(551124*x^9-29760696*x^8+66961
5660*x^7-8035387920*x^6+54238868460*x^5-195259926456*x^4+292889889684*x^3)*exp(x)^3+(-236196*x^10+14880348*x^9
-401769396*x^8+6026540940*x^7-54238868460*x^6+292889889684*x^5-878669669052*x^4+1129718145924*x^3)*exp(x)^2+(5
9049*x^11-4251528*x^10+133923132*x^9-2410616376*x^8+27119434230*x^7-195259926456*x^6+878669669052*x^5-22594362
91848*x^4+2541865828329*x^3)*exp(x)-6561*x^12+531441*x^11-19131876*x^10+401769396*x^9-5423886846*x^8+488149816
14*x^7-292889889684*x^6+1129718145924*x^5-2541865828329*x^4+2541865828329*x^3),x,method=_RETURNVERBOSE)
[Out]
-2*x+2/6561*exp(24)/x^2/(x-exp(x)-9)^8
________________________________________________________________________________________
maxima [B] time = 2.28, size = 531, normalized size = 20.42 \begin {gather*} -\frac {2 \, {\left (6561 \, x^{11} - 472392 \, x^{10} + 14880348 \, x^{9} - 267846264 \, x^{8} + 3013270470 \, x^{7} - 21695547384 \, x^{6} + 97629963228 \, x^{5} - 251048476872 \, x^{4} + 6561 \, x^{3} e^{\left (8 \, x\right )} + 282429536481 \, x^{3} - 52488 \, {\left (x^{4} - 9 \, x^{3}\right )} e^{\left (7 \, x\right )} + 183708 \, {\left (x^{5} - 18 \, x^{4} + 81 \, x^{3}\right )} e^{\left (6 \, x\right )} - 367416 \, {\left (x^{6} - 27 \, x^{5} + 243 \, x^{4} - 729 \, x^{3}\right )} e^{\left (5 \, x\right )} + 459270 \, {\left (x^{7} - 36 \, x^{6} + 486 \, x^{5} - 2916 \, x^{4} + 6561 \, x^{3}\right )} e^{\left (4 \, x\right )} - 367416 \, {\left (x^{8} - 45 \, x^{7} + 810 \, x^{6} - 7290 \, x^{5} + 32805 \, x^{4} - 59049 \, x^{3}\right )} e^{\left (3 \, x\right )} + 183708 \, {\left (x^{9} - 54 \, x^{8} + 1215 \, x^{7} - 14580 \, x^{6} + 98415 \, x^{5} - 354294 \, x^{4} + 531441 \, x^{3}\right )} e^{\left (2 \, x\right )} - 52488 \, {\left (x^{10} - 63 \, x^{9} + 1701 \, x^{8} - 25515 \, x^{7} + 229635 \, x^{6} - 1240029 \, x^{5} + 3720087 \, x^{4} - 4782969 \, x^{3}\right )} e^{x} - e^{24}\right )}}{6561 \, {\left (x^{10} - 72 \, x^{9} + 2268 \, x^{8} - 40824 \, x^{7} + 459270 \, x^{6} - 3306744 \, x^{5} + 14880348 \, x^{4} - 38263752 \, x^{3} + x^{2} e^{\left (8 \, x\right )} + 43046721 \, x^{2} - 8 \, {\left (x^{3} - 9 \, x^{2}\right )} e^{\left (7 \, x\right )} + 28 \, {\left (x^{4} - 18 \, x^{3} + 81 \, x^{2}\right )} e^{\left (6 \, x\right )} - 56 \, {\left (x^{5} - 27 \, x^{4} + 243 \, x^{3} - 729 \, x^{2}\right )} e^{\left (5 \, x\right )} + 70 \, {\left (x^{6} - 36 \, x^{5} + 486 \, x^{4} - 2916 \, x^{3} + 6561 \, x^{2}\right )} e^{\left (4 \, x\right )} - 56 \, {\left (x^{7} - 45 \, x^{6} + 810 \, x^{5} - 7290 \, x^{4} + 32805 \, x^{3} - 59049 \, x^{2}\right )} e^{\left (3 \, x\right )} + 28 \, {\left (x^{8} - 54 \, x^{7} + 1215 \, x^{6} - 14580 \, x^{5} + 98415 \, x^{4} - 354294 \, x^{3} + 531441 \, x^{2}\right )} e^{\left (2 \, x\right )} - 8 \, {\left (x^{9} - 63 \, x^{8} + 1701 \, x^{7} - 25515 \, x^{6} + 229635 \, x^{5} - 1240029 \, x^{4} + 3720087 \, x^{3} - 4782969 \, x^{2}\right )} e^{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-13122*x^3*exp(x)^9+(118098*x^4-1062882*x^3)*exp(x)^8+(-472392*x^5+8503056*x^4-38263752*x^3)*exp(x)
^7+(1102248*x^6-29760696*x^5+267846264*x^4-803538792*x^3)*exp(x)^6+(-1653372*x^7+59521392*x^6-803538792*x^5+48
21232752*x^4-10847773692*x^3)*exp(x)^5+(1653372*x^8-74401740*x^7+1339231320*x^6-12053081880*x^5+54238868460*x^
4-97629963228*x^3)*exp(x)^4+(-1102248*x^9+59521392*x^8-1339231320*x^7+16070775840*x^6-108477736920*x^5+3905198
52912*x^4-585779779368*x^3)*exp(x)^3+(472392*x^10-29760696*x^9+803538792*x^8-12053081880*x^7+108477736920*x^6-
585779779368*x^5+1757339338104*x^4-2259436291848*x^3)*exp(x)^2+((-16*x-4)*exp(3)^8-118098*x^11+8503056*x^10-26
7846264*x^9+4821232752*x^8-54238868460*x^7+390519852912*x^6-1757339338104*x^5+4518872583696*x^4-5083731656658*
x^3)*exp(x)+(20*x-36)*exp(3)^8+13122*x^12-1062882*x^11+38263752*x^10-803538792*x^9+10847773692*x^8-97629963228
*x^7+585779779368*x^6-2259436291848*x^5+5083731656658*x^4-5083731656658*x^3)/(6561*x^3*exp(x)^9+(-59049*x^4+53
1441*x^3)*exp(x)^8+(236196*x^5-4251528*x^4+19131876*x^3)*exp(x)^7+(-551124*x^6+14880348*x^5-133923132*x^4+4017
69396*x^3)*exp(x)^6+(826686*x^7-29760696*x^6+401769396*x^5-2410616376*x^4+5423886846*x^3)*exp(x)^5+(-826686*x^
8+37200870*x^7-669615660*x^6+6026540940*x^5-27119434230*x^4+48814981614*x^3)*exp(x)^4+(551124*x^9-29760696*x^8
+669615660*x^7-8035387920*x^6+54238868460*x^5-195259926456*x^4+292889889684*x^3)*exp(x)^3+(-236196*x^10+148803
48*x^9-401769396*x^8+6026540940*x^7-54238868460*x^6+292889889684*x^5-878669669052*x^4+1129718145924*x^3)*exp(x
)^2+(59049*x^11-4251528*x^10+133923132*x^9-2410616376*x^8+27119434230*x^7-195259926456*x^6+878669669052*x^5-22
59436291848*x^4+2541865828329*x^3)*exp(x)-6561*x^12+531441*x^11-19131876*x^10+401769396*x^9-5423886846*x^8+488
14981614*x^7-292889889684*x^6+1129718145924*x^5-2541865828329*x^4+2541865828329*x^3),x, algorithm="maxima")
[Out]
-2/6561*(6561*x^11 - 472392*x^10 + 14880348*x^9 - 267846264*x^8 + 3013270470*x^7 - 21695547384*x^6 + 976299632
28*x^5 - 251048476872*x^4 + 6561*x^3*e^(8*x) + 282429536481*x^3 - 52488*(x^4 - 9*x^3)*e^(7*x) + 183708*(x^5 -
18*x^4 + 81*x^3)*e^(6*x) - 367416*(x^6 - 27*x^5 + 243*x^4 - 729*x^3)*e^(5*x) + 459270*(x^7 - 36*x^6 + 486*x^5
- 2916*x^4 + 6561*x^3)*e^(4*x) - 367416*(x^8 - 45*x^7 + 810*x^6 - 7290*x^5 + 32805*x^4 - 59049*x^3)*e^(3*x) +
183708*(x^9 - 54*x^8 + 1215*x^7 - 14580*x^6 + 98415*x^5 - 354294*x^4 + 531441*x^3)*e^(2*x) - 52488*(x^10 - 63*
x^9 + 1701*x^8 - 25515*x^7 + 229635*x^6 - 1240029*x^5 + 3720087*x^4 - 4782969*x^3)*e^x - e^24)/(x^10 - 72*x^9
+ 2268*x^8 - 40824*x^7 + 459270*x^6 - 3306744*x^5 + 14880348*x^4 - 38263752*x^3 + x^2*e^(8*x) + 43046721*x^2 -
8*(x^3 - 9*x^2)*e^(7*x) + 28*(x^4 - 18*x^3 + 81*x^2)*e^(6*x) - 56*(x^5 - 27*x^4 + 243*x^3 - 729*x^2)*e^(5*x)
+ 70*(x^6 - 36*x^5 + 486*x^4 - 2916*x^3 + 6561*x^2)*e^(4*x) - 56*(x^7 - 45*x^6 + 810*x^5 - 7290*x^4 + 32805*x^
3 - 59049*x^2)*e^(3*x) + 28*(x^8 - 54*x^7 + 1215*x^6 - 14580*x^5 + 98415*x^4 - 354294*x^3 + 531441*x^2)*e^(2*x
) - 8*(x^9 - 63*x^8 + 1701*x^7 - 25515*x^6 + 229635*x^5 - 1240029*x^4 + 3720087*x^3 - 4782969*x^2)*e^x)
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{6\,x}\,\left (-1102248\,x^6+29760696\,x^5-267846264\,x^4+803538792\,x^3\right )+{\mathrm {e}}^{3\,x}\,\left (1102248\,x^9-59521392\,x^8+1339231320\,x^7-16070775840\,x^6+108477736920\,x^5-390519852912\,x^4+585779779368\,x^3\right )+{\mathrm {e}}^x\,\left (5083731656658\,x^3-4518872583696\,x^4+1757339338104\,x^5-390519852912\,x^6+54238868460\,x^7-4821232752\,x^8+267846264\,x^9-8503056\,x^{10}+118098\,x^{11}+{\mathrm {e}}^{24}\,\left (16\,x+4\right )\right )+{\mathrm {e}}^{8\,x}\,\left (1062882\,x^3-118098\,x^4\right )+13122\,x^3\,{\mathrm {e}}^{9\,x}+{\mathrm {e}}^{2\,x}\,\left (-472392\,x^{10}+29760696\,x^9-803538792\,x^8+12053081880\,x^7-108477736920\,x^6+585779779368\,x^5-1757339338104\,x^4+2259436291848\,x^3\right )+{\mathrm {e}}^{7\,x}\,\left (472392\,x^5-8503056\,x^4+38263752\,x^3\right )+{\mathrm {e}}^{4\,x}\,\left (-1653372\,x^8+74401740\,x^7-1339231320\,x^6+12053081880\,x^5-54238868460\,x^4+97629963228\,x^3\right )+5083731656658\,x^3-5083731656658\,x^4+2259436291848\,x^5-585779779368\,x^6+97629963228\,x^7-10847773692\,x^8+803538792\,x^9-38263752\,x^{10}+1062882\,x^{11}-13122\,x^{12}+{\mathrm {e}}^{5\,x}\,\left (1653372\,x^7-59521392\,x^6+803538792\,x^5-4821232752\,x^4+10847773692\,x^3\right )-{\mathrm {e}}^{24}\,\left (20\,x-36\right )}{{\mathrm {e}}^x\,\left (59049\,x^{11}-4251528\,x^{10}+133923132\,x^9-2410616376\,x^8+27119434230\,x^7-195259926456\,x^6+878669669052\,x^5-2259436291848\,x^4+2541865828329\,x^3\right )+{\mathrm {e}}^{8\,x}\,\left (531441\,x^3-59049\,x^4\right )+6561\,x^3\,{\mathrm {e}}^{9\,x}+{\mathrm {e}}^{4\,x}\,\left (-826686\,x^8+37200870\,x^7-669615660\,x^6+6026540940\,x^5-27119434230\,x^4+48814981614\,x^3\right )+{\mathrm {e}}^{7\,x}\,\left (236196\,x^5-4251528\,x^4+19131876\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (-236196\,x^{10}+14880348\,x^9-401769396\,x^8+6026540940\,x^7-54238868460\,x^6+292889889684\,x^5-878669669052\,x^4+1129718145924\,x^3\right )+{\mathrm {e}}^{3\,x}\,\left (551124\,x^9-29760696\,x^8+669615660\,x^7-8035387920\,x^6+54238868460\,x^5-195259926456\,x^4+292889889684\,x^3\right )+2541865828329\,x^3-2541865828329\,x^4+1129718145924\,x^5-292889889684\,x^6+48814981614\,x^7-5423886846\,x^8+401769396\,x^9-19131876\,x^{10}+531441\,x^{11}-6561\,x^{12}+{\mathrm {e}}^{6\,x}\,\left (-551124\,x^6+14880348\,x^5-133923132\,x^4+401769396\,x^3\right )+{\mathrm {e}}^{5\,x}\,\left (826686\,x^7-29760696\,x^6+401769396\,x^5-2410616376\,x^4+5423886846\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(6*x)*(803538792*x^3 - 267846264*x^4 + 29760696*x^5 - 1102248*x^6) + exp(3*x)*(585779779368*x^3 - 390
519852912*x^4 + 108477736920*x^5 - 16070775840*x^6 + 1339231320*x^7 - 59521392*x^8 + 1102248*x^9) + exp(x)*(50
83731656658*x^3 - 4518872583696*x^4 + 1757339338104*x^5 - 390519852912*x^6 + 54238868460*x^7 - 4821232752*x^8
+ 267846264*x^9 - 8503056*x^10 + 118098*x^11 + exp(24)*(16*x + 4)) + exp(8*x)*(1062882*x^3 - 118098*x^4) + 131
22*x^3*exp(9*x) + exp(2*x)*(2259436291848*x^3 - 1757339338104*x^4 + 585779779368*x^5 - 108477736920*x^6 + 1205
3081880*x^7 - 803538792*x^8 + 29760696*x^9 - 472392*x^10) + exp(7*x)*(38263752*x^3 - 8503056*x^4 + 472392*x^5)
+ exp(4*x)*(97629963228*x^3 - 54238868460*x^4 + 12053081880*x^5 - 1339231320*x^6 + 74401740*x^7 - 1653372*x^8
) + 5083731656658*x^3 - 5083731656658*x^4 + 2259436291848*x^5 - 585779779368*x^6 + 97629963228*x^7 - 108477736
92*x^8 + 803538792*x^9 - 38263752*x^10 + 1062882*x^11 - 13122*x^12 + exp(5*x)*(10847773692*x^3 - 4821232752*x^
4 + 803538792*x^5 - 59521392*x^6 + 1653372*x^7) - exp(24)*(20*x - 36))/(exp(x)*(2541865828329*x^3 - 2259436291
848*x^4 + 878669669052*x^5 - 195259926456*x^6 + 27119434230*x^7 - 2410616376*x^8 + 133923132*x^9 - 4251528*x^1
0 + 59049*x^11) + exp(8*x)*(531441*x^3 - 59049*x^4) + 6561*x^3*exp(9*x) + exp(4*x)*(48814981614*x^3 - 27119434
230*x^4 + 6026540940*x^5 - 669615660*x^6 + 37200870*x^7 - 826686*x^8) + exp(7*x)*(19131876*x^3 - 4251528*x^4 +
236196*x^5) + exp(2*x)*(1129718145924*x^3 - 878669669052*x^4 + 292889889684*x^5 - 54238868460*x^6 + 602654094
0*x^7 - 401769396*x^8 + 14880348*x^9 - 236196*x^10) + exp(3*x)*(292889889684*x^3 - 195259926456*x^4 + 54238868
460*x^5 - 8035387920*x^6 + 669615660*x^7 - 29760696*x^8 + 551124*x^9) + 2541865828329*x^3 - 2541865828329*x^4
+ 1129718145924*x^5 - 292889889684*x^6 + 48814981614*x^7 - 5423886846*x^8 + 401769396*x^9 - 19131876*x^10 + 53
1441*x^11 - 6561*x^12 + exp(6*x)*(401769396*x^3 - 133923132*x^4 + 14880348*x^5 - 551124*x^6) + exp(5*x)*(54238
86846*x^3 - 2410616376*x^4 + 401769396*x^5 - 29760696*x^6 + 826686*x^7)),x)
[Out]
int(-(exp(6*x)*(803538792*x^3 - 267846264*x^4 + 29760696*x^5 - 1102248*x^6) + exp(3*x)*(585779779368*x^3 - 390
519852912*x^4 + 108477736920*x^5 - 16070775840*x^6 + 1339231320*x^7 - 59521392*x^8 + 1102248*x^9) + exp(x)*(50
83731656658*x^3 - 4518872583696*x^4 + 1757339338104*x^5 - 390519852912*x^6 + 54238868460*x^7 - 4821232752*x^8
+ 267846264*x^9 - 8503056*x^10 + 118098*x^11 + exp(24)*(16*x + 4)) + exp(8*x)*(1062882*x^3 - 118098*x^4) + 131
22*x^3*exp(9*x) + exp(2*x)*(2259436291848*x^3 - 1757339338104*x^4 + 585779779368*x^5 - 108477736920*x^6 + 1205
3081880*x^7 - 803538792*x^8 + 29760696*x^9 - 472392*x^10) + exp(7*x)*(38263752*x^3 - 8503056*x^4 + 472392*x^5)
+ exp(4*x)*(97629963228*x^3 - 54238868460*x^4 + 12053081880*x^5 - 1339231320*x^6 + 74401740*x^7 - 1653372*x^8
) + 5083731656658*x^3 - 5083731656658*x^4 + 2259436291848*x^5 - 585779779368*x^6 + 97629963228*x^7 - 108477736
92*x^8 + 803538792*x^9 - 38263752*x^10 + 1062882*x^11 - 13122*x^12 + exp(5*x)*(10847773692*x^3 - 4821232752*x^
4 + 803538792*x^5 - 59521392*x^6 + 1653372*x^7) - exp(24)*(20*x - 36))/(exp(x)*(2541865828329*x^3 - 2259436291
848*x^4 + 878669669052*x^5 - 195259926456*x^6 + 27119434230*x^7 - 2410616376*x^8 + 133923132*x^9 - 4251528*x^1
0 + 59049*x^11) + exp(8*x)*(531441*x^3 - 59049*x^4) + 6561*x^3*exp(9*x) + exp(4*x)*(48814981614*x^3 - 27119434
230*x^4 + 6026540940*x^5 - 669615660*x^6 + 37200870*x^7 - 826686*x^8) + exp(7*x)*(19131876*x^3 - 4251528*x^4 +
236196*x^5) + exp(2*x)*(1129718145924*x^3 - 878669669052*x^4 + 292889889684*x^5 - 54238868460*x^6 + 602654094
0*x^7 - 401769396*x^8 + 14880348*x^9 - 236196*x^10) + exp(3*x)*(292889889684*x^3 - 195259926456*x^4 + 54238868
460*x^5 - 8035387920*x^6 + 669615660*x^7 - 29760696*x^8 + 551124*x^9) + 2541865828329*x^3 - 2541865828329*x^4
+ 1129718145924*x^5 - 292889889684*x^6 + 48814981614*x^7 - 5423886846*x^8 + 401769396*x^9 - 19131876*x^10 + 53
1441*x^11 - 6561*x^12 + exp(6*x)*(401769396*x^3 - 133923132*x^4 + 14880348*x^5 - 551124*x^6) + exp(5*x)*(54238
86846*x^3 - 2410616376*x^4 + 401769396*x^5 - 29760696*x^6 + 826686*x^7)), x)
________________________________________________________________________________________
sympy [B] time = 1.73, size = 275, normalized size = 10.58 \begin {gather*} - 2 x + \frac {2 e^{24}}{6561 x^{10} - 472392 x^{9} + 14880348 x^{8} - 267846264 x^{7} + 3013270470 x^{6} - 21695547384 x^{5} + 97629963228 x^{4} - 251048476872 x^{3} + 6561 x^{2} e^{8 x} + 282429536481 x^{2} + \left (- 52488 x^{3} + 472392 x^{2}\right ) e^{7 x} + \left (183708 x^{4} - 3306744 x^{3} + 14880348 x^{2}\right ) e^{6 x} + \left (- 367416 x^{5} + 9920232 x^{4} - 89282088 x^{3} + 267846264 x^{2}\right ) e^{5 x} + \left (459270 x^{6} - 16533720 x^{5} + 223205220 x^{4} - 1339231320 x^{3} + 3013270470 x^{2}\right ) e^{4 x} + \left (- 367416 x^{7} + 16533720 x^{6} - 297606960 x^{5} + 2678462640 x^{4} - 12053081880 x^{3} + 21695547384 x^{2}\right ) e^{3 x} + \left (183708 x^{8} - 9920232 x^{7} + 223205220 x^{6} - 2678462640 x^{5} + 18079622820 x^{4} - 65086642152 x^{3} + 97629963228 x^{2}\right ) e^{2 x} + \left (- 52488 x^{9} + 3306744 x^{8} - 89282088 x^{7} + 1339231320 x^{6} - 12053081880 x^{5} + 65086642152 x^{4} - 195259926456 x^{3} + 251048476872 x^{2}\right ) e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-13122*x**3*exp(x)**9+(118098*x**4-1062882*x**3)*exp(x)**8+(-472392*x**5+8503056*x**4-38263752*x**3
)*exp(x)**7+(1102248*x**6-29760696*x**5+267846264*x**4-803538792*x**3)*exp(x)**6+(-1653372*x**7+59521392*x**6-
803538792*x**5+4821232752*x**4-10847773692*x**3)*exp(x)**5+(1653372*x**8-74401740*x**7+1339231320*x**6-1205308
1880*x**5+54238868460*x**4-97629963228*x**3)*exp(x)**4+(-1102248*x**9+59521392*x**8-1339231320*x**7+1607077584
0*x**6-108477736920*x**5+390519852912*x**4-585779779368*x**3)*exp(x)**3+(472392*x**10-29760696*x**9+803538792*
x**8-12053081880*x**7+108477736920*x**6-585779779368*x**5+1757339338104*x**4-2259436291848*x**3)*exp(x)**2+((-
16*x-4)*exp(3)**8-118098*x**11+8503056*x**10-267846264*x**9+4821232752*x**8-54238868460*x**7+390519852912*x**6
-1757339338104*x**5+4518872583696*x**4-5083731656658*x**3)*exp(x)+(20*x-36)*exp(3)**8+13122*x**12-1062882*x**1
1+38263752*x**10-803538792*x**9+10847773692*x**8-97629963228*x**7+585779779368*x**6-2259436291848*x**5+5083731
656658*x**4-5083731656658*x**3)/(6561*x**3*exp(x)**9+(-59049*x**4+531441*x**3)*exp(x)**8+(236196*x**5-4251528*
x**4+19131876*x**3)*exp(x)**7+(-551124*x**6+14880348*x**5-133923132*x**4+401769396*x**3)*exp(x)**6+(826686*x**
7-29760696*x**6+401769396*x**5-2410616376*x**4+5423886846*x**3)*exp(x)**5+(-826686*x**8+37200870*x**7-66961566
0*x**6+6026540940*x**5-27119434230*x**4+48814981614*x**3)*exp(x)**4+(551124*x**9-29760696*x**8+669615660*x**7-
8035387920*x**6+54238868460*x**5-195259926456*x**4+292889889684*x**3)*exp(x)**3+(-236196*x**10+14880348*x**9-4
01769396*x**8+6026540940*x**7-54238868460*x**6+292889889684*x**5-878669669052*x**4+1129718145924*x**3)*exp(x)*
*2+(59049*x**11-4251528*x**10+133923132*x**9-2410616376*x**8+27119434230*x**7-195259926456*x**6+878669669052*x
**5-2259436291848*x**4+2541865828329*x**3)*exp(x)-6561*x**12+531441*x**11-19131876*x**10+401769396*x**9-542388
6846*x**8+48814981614*x**7-292889889684*x**6+1129718145924*x**5-2541865828329*x**4+2541865828329*x**3),x)
[Out]
-2*x + 2*exp(24)/(6561*x**10 - 472392*x**9 + 14880348*x**8 - 267846264*x**7 + 3013270470*x**6 - 21695547384*x*
*5 + 97629963228*x**4 - 251048476872*x**3 + 6561*x**2*exp(8*x) + 282429536481*x**2 + (-52488*x**3 + 472392*x**
2)*exp(7*x) + (183708*x**4 - 3306744*x**3 + 14880348*x**2)*exp(6*x) + (-367416*x**5 + 9920232*x**4 - 89282088*
x**3 + 267846264*x**2)*exp(5*x) + (459270*x**6 - 16533720*x**5 + 223205220*x**4 - 1339231320*x**3 + 3013270470
*x**2)*exp(4*x) + (-367416*x**7 + 16533720*x**6 - 297606960*x**5 + 2678462640*x**4 - 12053081880*x**3 + 216955
47384*x**2)*exp(3*x) + (183708*x**8 - 9920232*x**7 + 223205220*x**6 - 2678462640*x**5 + 18079622820*x**4 - 650
86642152*x**3 + 97629963228*x**2)*exp(2*x) + (-52488*x**9 + 3306744*x**8 - 89282088*x**7 + 1339231320*x**6 - 1
2053081880*x**5 + 65086642152*x**4 - 195259926456*x**3 + 251048476872*x**2)*exp(x))
________________________________________________________________________________________