3.50 \(\int \frac{1}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )^5} \, dx\)
Optimal. Leaf size=378 \[ -\frac{63043297-29625922 x}{41160000000 \left (x^2-2 x+3\right )^{3/2}}-\frac{31 (7434109-3088870 x)}{411600000000 \sqrt{x^2-2 x+3}}+\frac{3 (8233 x+8822)}{343000 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )}+\frac{8878 x+5485}{117600 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^2}-\frac{30316369-15043110 x}{6860000000 \left (x^2-2 x+3\right )^{5/2}}+\frac{67 x+28}{1050 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^3}-\frac{4878869-2578034 x}{411600000 \left (x^2-2 x+3\right )^{7/2}}-\frac{1-10 x}{280 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^4}-\frac{3450497-2004270 x}{123480000 \left (x^2-2 x+3\right )^{9/2}}+\frac{\sqrt{\frac{1}{70} \left (151363871237318045+110320475741093888 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (151363871237318045+110320475741093888 \sqrt{2}\right )}} \left (\left (932587773+620347970 \sqrt{2}\right ) x+312239803 \sqrt{2}+308108167\right )}{\sqrt{x^2-2 x+3}}\right )}{137200000000}-\frac{\sqrt{\frac{1}{70} \left (110320475741093888 \sqrt{2}-151363871237318045\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (110320475741093888 \sqrt{2}-151363871237318045\right )}} \left (\left (932587773-620347970 \sqrt{2}\right ) x-312239803 \sqrt{2}+308108167\right )}{\sqrt{x^2-2 x+3}}\right )}{137200000000} \]
[Out]
-(3450497 - 2004270*x)/(123480000*(3 - 2*x + x^2)^(9/2)) - (4878869 - 2578034*x)
/(411600000*(3 - 2*x + x^2)^(7/2)) - (30316369 - 15043110*x)/(6860000000*(3 - 2*
x + x^2)^(5/2)) - (63043297 - 29625922*x)/(41160000000*(3 - 2*x + x^2)^(3/2)) -
(31*(7434109 - 3088870*x))/(411600000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(280*
(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^4) + (28 + 67*x)/(1050*(3 - 2*x + x^2)^(9/
2)*(1 + x + 2*x^2)^3) + (5485 + 8878*x)/(117600*(3 - 2*x + x^2)^(9/2)*(1 + x + 2
*x^2)^2) + (3*(8822 + 8233*x))/(343000*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)) +
(Sqrt[(151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(1
51363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 + 312239803*Sqrt[2]
+ (932587773 + 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000 - (Sqr
t[(-151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-15
1363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 - 312239803*Sqrt[2]
+ (932587773 - 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000
_______________________________________________________________________________________
Rubi [A] time = 1.58625, antiderivative size = 378, normalized size of antiderivative = 1.,
number of steps used = 14, number of rules used = 6, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.261
\[ -\frac{63043297-29625922 x}{41160000000 \left (x^2-2 x+3\right )^{3/2}}-\frac{31 (7434109-3088870 x)}{411600000000 \sqrt{x^2-2 x+3}}+\frac{3 (8233 x+8822)}{343000 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )}+\frac{8878 x+5485}{117600 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^2}-\frac{30316369-15043110 x}{6860000000 \left (x^2-2 x+3\right )^{5/2}}+\frac{67 x+28}{1050 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^3}-\frac{4878869-2578034 x}{411600000 \left (x^2-2 x+3\right )^{7/2}}-\frac{1-10 x}{280 \left (x^2-2 x+3\right )^{9/2} \left (2 x^2+x+1\right )^4}-\frac{3450497-2004270 x}{123480000 \left (x^2-2 x+3\right )^{9/2}}+\frac{\sqrt{\frac{1}{70} \left (151363871237318045+110320475741093888 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (151363871237318045+110320475741093888 \sqrt{2}\right )}} \left (\left (932587773+620347970 \sqrt{2}\right ) x+312239803 \sqrt{2}+308108167\right )}{\sqrt{x^2-2 x+3}}\right )}{137200000000}-\frac{\sqrt{\frac{1}{70} \left (110320475741093888 \sqrt{2}-151363871237318045\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (110320475741093888 \sqrt{2}-151363871237318045\right )}} \left (\left (932587773-620347970 \sqrt{2}\right ) x-312239803 \sqrt{2}+308108167\right )}{\sqrt{x^2-2 x+3}}\right )}{137200000000} \]
Antiderivative was successfully verified.
[In] Int[1/((3 - 2*x + x^2)^(11/2)*(1 + x + 2*x^2)^5),x]
[Out]
-(3450497 - 2004270*x)/(123480000*(3 - 2*x + x^2)^(9/2)) - (4878869 - 2578034*x)
/(411600000*(3 - 2*x + x^2)^(7/2)) - (30316369 - 15043110*x)/(6860000000*(3 - 2*
x + x^2)^(5/2)) - (63043297 - 29625922*x)/(41160000000*(3 - 2*x + x^2)^(3/2)) -
(31*(7434109 - 3088870*x))/(411600000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(280*
(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)^4) + (28 + 67*x)/(1050*(3 - 2*x + x^2)^(9/
2)*(1 + x + 2*x^2)^3) + (5485 + 8878*x)/(117600*(3 - 2*x + x^2)^(9/2)*(1 + x + 2
*x^2)^2) + (3*(8822 + 8233*x))/(343000*(3 - 2*x + x^2)^(9/2)*(1 + x + 2*x^2)) +
(Sqrt[(151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7*(1
51363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 + 312239803*Sqrt[2]
+ (932587773 + 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000 - (Sqr
t[(-151363871237318045 + 110320475741093888*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-15
1363871237318045 + 110320475741093888*Sqrt[2]))]*(308108167 - 312239803*Sqrt[2]
+ (932587773 - 620347970*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/137200000000
_______________________________________________________________________________________
Rubi in Sympy [A] time = 79.0556, size = 379, normalized size = 1. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2-2*x+3)**(11/2)/(2*x**2+x+1)**5,x)
[Out]
-(-25336765062000000000000*x + 60979022483400000000000)/(10890936000000000000000
0000*sqrt(x**2 - 2*x + 3)) - (-391950948060000000000*x + 834062819310000000000)/
(544546800000000000000000*(x**2 - 2*x + 3)**(3/2)) - (-1990203453000000000*x + 4
010855618700000000)/(907578000000000000000*(x**2 - 2*x + 3)**(5/2)) - (-56845649
70000000*x + 10757906145000000)/(907578000000000000*(x**2 - 2*x + 3)**(7/2)) - (
-10522417500000*x + 18115109250000)/(648270000000000*(x**2 - 2*x + 3)**(9/2)) -
(-50*x + 5)/(1400*(x**2 - 2*x + 3)**(9/2)*(2*x**2 + x + 1)**4) + (93800*x + 3920
0)/(1470000*(x**2 - 2*x + 3)**(9/2)*(2*x**2 + x + 1)**3) + (77682500*x + 4799375
0)/(1029000000*(x**2 - 2*x + 3)**(9/2)*(2*x**2 + x + 1)**2) + (25933950000*x + 2
7789300000)/(360150000000*(x**2 - 2*x + 3)**(9/2)*(2*x**2 + x + 1)) + sqrt(70)*(
1222881314823000000000000 + 1239279778107000000000000*sqrt(2))*(1052869259358000
000000000*sqrt(2) + 1765714407786000000000000)*atan(sqrt(35)*(x*(246216109293000
0000000000*sqrt(2) + 3701440871037000000000000) + 1222881314823000000000000 + 12
39279778107000000000000*sqrt(2))/(27783000000000000*sqrt(151363871237318045 + 11
0320475741093888*sqrt(2))*sqrt(x**2 - 2*x + 3)))/(302582874888000000000000000000
000000000000000*sqrt(151363871237318045 + 110320475741093888*sqrt(2))) + sqrt(70
)*(-1239279778107000000000000*sqrt(2) + 1222881314823000000000000)*(-10528692593
58000000000000*sqrt(2) + 1765714407786000000000000)*atanh(sqrt(35)*(x*(-24621610
92930000000000000*sqrt(2) + 3701440871037000000000000) - 12392797781070000000000
00*sqrt(2) + 1222881314823000000000000)/(27783000000000000*sqrt(-151363871237318
045 + 110320475741093888*sqrt(2))*sqrt(x**2 - 2*x + 3)))/(3025828748880000000000
00000000000000000000000*sqrt(-151363871237318045 + 110320475741093888*sqrt(2)))
_______________________________________________________________________________________
Mathematica [C] time = 6.46651, size = 1236, normalized size = 3.27 \[ \text{result too large to display} \]
Antiderivative was successfully verified.
[In] Integrate[1/((3 - 2*x + x^2)^(11/2)*(1 + x + 2*x^2)^5),x]
[Out]
Sqrt[3 - 2*x + x^2]*(1/(225000*(3 - 2*x + x^2)^5) + (1 + 2*x)/(350000*(3 - 2*x +
x^2)^4) + (3*(-38 + 45*x))/(8750000*(3 - 2*x + x^2)^3) + (-2003 + 1198*x)/(5250
0000*(3 - 2*x + x^2)^2) + (-97229 + 29420*x)/(1050000000*(3 - 2*x + x^2)) + (-79
7 - 1998*x)/(28000000*(1 + x + 2*x^2)^4) + (-14087 - 5995*x)/(105000000*(1 + x +
2*x^2)^3) + (-795589 + 1892994*x)/(11760000000*(1 + x + 2*x^2)^2) + (3035369 +
14037055*x)/(34300000000*(1 + x + 2*x^2))) + ((310173985*I + 44900803*Sqrt[7])*A
rcTan[(9627448535205165 + (357977536529228045*I)*Sqrt[7] - 2892591314086740000*x
+ (36106220736881480*I)*Sqrt[7]*x + 464983088285203040*x^2 - (10385697256225243
80*I)*Sqrt[7]*x^2 + 12836598046940220*x^3 + (328748064746064540*I)*Sqrt[7]*x^3 -
487447134867348425*x^4 - (428071291440525685*I)*Sqrt[7]*x^4 + (3585415461585551
36*I)*Sqrt[10*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (220640951482187776*I)*Sqr
t[10*(-5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2] + (579182497640742912*I)*Sqrt[10*(-
5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] - (275801189352734720*I)*Sqrt[10*(-5 + I
*Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])/(4321741285513437647*I + 827387564543169945*
Sqrt[7] + (3694994885631086104*I)*x + 285423303382928480*Sqrt[7]*x + (5471192788
852131980*I)*x^2 - 70525532316488480*Sqrt[7]*x^2 - (6268363351511187532*I)*x^3 +
137879256656321740*Sqrt[7]*x^3 + (2092254277956040633*I)*x^4 + 7056287385156831
5*Sqrt[7]*x^4)])/(68600000000*Sqrt[70*(-5 + I*Sqrt[7])]) - ((I/68600000000)*(-31
0173985*I + 44900803*Sqrt[7])*ArcTan[(35*(15210275631276955*I + 2363964470123342
7*Sqrt[7] - (80355173705781000*I)*x + 8154951525226528*Sqrt[7]*x + (328010215889
57180*I)*x^2 - 2015015209042528*Sqrt[7]*x^2 - (22632774169109180*I)*x^3 + 393940
7333037764*Sqrt[7]*x^3 - (9346476174243955*I)*x^4 + 2016082110044809*Sqrt[7]*x^4
))/(-9627448535205165 + (357977536529228045*I)*Sqrt[7] + 2892591314086740000*x +
(36106220736881480*I)*Sqrt[7]*x - 464983088285203040*x^2 - (1038569725622524380
*I)*Sqrt[7]*x^2 - 12836598046940220*x^3 + (328748064746064540*I)*Sqrt[7]*x^3 + 4
87447134867348425*x^4 - (428071291440525685*I)*Sqrt[7]*x^4 - (27580118935273472*
I)*Sqrt[70*(5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - (27580118935273472*I)*Sqrt[70*
(5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] + (55160237870546944*I)*Sqrt[70*(5 + I*
Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])])/Sqrt[70*(5 + I*Sqrt[7])] - ((-310173985*I +
44900803*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/(1
37200000000*Sqrt[70*(5 + I*Sqrt[7])]) + ((I/137200000000)*(310173985*I + 4490080
3*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/Sqrt[70*(-
5 + I*Sqrt[7])] - ((I/137200000000)*(310173985*I + 44900803*Sqrt[7])*Log[(1 + x
+ 2*x^2)*(-13*I + 15*Sqrt[7] + (22*I)*x - 10*Sqrt[7]*x + (9*I)*x^2 + 5*Sqrt[7]*x
^2 + I*Sqrt[70*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - I*Sqrt[70*(-5 + I*Sqrt[7]
)]*x*Sqrt[3 - 2*x + x^2])])/Sqrt[70*(-5 + I*Sqrt[7])] + ((-310173985*I + 4490080
3*Sqrt[7])*Log[(1 + x + 2*x^2)*(-163*I + 15*Sqrt[7] + (122*I)*x - 10*Sqrt[7]*x -
(41*I)*x^2 + 5*Sqrt[7]*x^2 - (13*I)*Sqrt[10*(5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2
] + (5*I)*Sqrt[10*(5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2])])/(137200000000*Sqrt[7
0*(5 + I*Sqrt[7])])
_______________________________________________________________________________________
Maple [B] time = 0.765, size = 21028, normalized size = 55.6 \[ \text{output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2-2*x+3)^(11/2)/(2*x^2+x+1)^5,x)
[Out]
result too large to display
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{5}{\left (x^{2} - 2 \, x + 3\right )}^{\frac{11}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^5*(x^2 - 2*x + 3)^(11/2)),x, algorithm="maxima")
[Out]
integrate(1/((2*x^2 + x + 1)^5*(x^2 - 2*x + 3)^(11/2)), x)
_______________________________________________________________________________________
Fricas [A] time = 0.362639, size = 6251, normalized size = 16.54 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^5*(x^2 - 2*x + 3)^(11/2)),x, algorithm="fricas")
[Out]
1/4939200000000*(4*sqrt(205487899)*sqrt(35)*sqrt(7)*(250540991585065591119917936
640*x^32 - 5884831549275969411796256686080*x^31 + 703366989013471329022024708300
80*x^30 - 564011472262755728213727938611200*x^29 + 33877828431307192657415395726
88640*x^28 - 16164416998187353864497620912156160*x^27 + 635159303509111899447500
96784965760*x^26 - 210557817277442257216056696290868480*x^25 + 59907998562460880
7889894068082206400*x^24 - 1481788240195926502419500474927552000*x^23 + 32181812
05607145182585261559186346560*x^22 - 6187184772955802395440882682138814720*x^21
+ 10603803272759527543249407132512637520*x^20 - 16301932856715307988417262259057
211200*x^19 + 22613684765066685707216182128734364240*x^18 - 28462902342004920706
947119363091816160*x^17 + 32676135176862669211706329839458900360*x^16 - 34375259
168148954959453196199877528480*x^15 + 33264095254764270345104132253135996400*x^1
4 - 29690304639514302322193623022642067720*x^13 + 244846318871224837097785946631
37626775*x^12 - 18669195666477658318850179379968512720*x^11 + 131586975136960148
49995752136862496980*x^10 - 8560917034642778106789153295046959300*x^9 + 51239419
61010059680373987398344568415*x^8 - 2804226320624950569135022727301669360*x^7 +
1388535812396865496182258810064197360*x^6 - 610465831798347956368523388448548480
*x^5 + 230216298955627150529634520155221125*x^4 - 699643834043733205950021672946
09600*x^3 + 15304284300591900638465660638051420*x^2 - 110320475741093888*sqrt(2)
*(1655223201792*x^32 - 38878706663424*x^31 + 464686178586624*x^30 - 372619613684
7360*x^29 + 22381713783067392*x^28 - 106791778421442048*x^27 + 41962411394279692
8*x^26 - 1391070508148646144*x^25 + 3957879649400169920*x^24 - 97895767866077056
00*x^23 + 21261224222796687168*x^22 - 40876232368919362816*x^21 + 70055048051289
600656*x^20 - 107700290191151927360*x^19 + 149399487342732477072*x^18 - 18804290
6866321790048*x^17 + 215878035555994176808*x^16 - 227103461923573594144*x^15 + 2
19762450463563231920*x^14 - 196151858411205186216*x^13 + 161760079779763942595*x
^12 - 123339840041530707216*x^11 + 86934203030952873444*x^10 - 56558523276802427
540*x^9 + 33851816283004633387*x^8 - 18526391388525625008*x^7 + 9173495637012543
408*x^6 - 4033101339230550144*x^5 + 1520946161549206025*x^4 - 462226440381394880
*x^3 + 101109228876664076*x^2 - 12595090393724612*x + 382982001236017) - 1906441
640578113609130057188223540*x + 57969638321298857545326138026765)*sqrt(x^2 - 2*x
+ 3)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(333970685698292085
76933551323217920*sqrt(2) - 47252236251429967028491746144535113)) - 4*sqrt(20548
7899)*sqrt(35)*sqrt(7)*(250540991585065591119917936640*x^33 - 613537254086103500
2916174622720*x^32 + 76472071442208167905118645452800*x^31 - 6399824617217937649
36606748190720*x^30 + 4016371453241338690241233684412160*x^29 - 2004894230094991
2243052144039937280*x^28 + 82541853673704441299545848818052480*x^27 - 2871591044
33155596834389825111898240*x^26 + 858868629564315376337541934649544640*x^25 - 22
36946999108419783878615048450148800*x^24 + 5124102521174037211790204381357664960
*x^23 - 10405933975960152123149730201711967680*x^22 + 18860766060525068433557020
025072619600*x^21 - 30691274851422616119553452520028489680*x^20 + 45081528653462
797168790944458441243760*x^19 - 60080156394086663140994853987619185680*x^18 + 72
999815962536691617826033044526479080*x^17 - 812317437826085642926362400967153272
40*x^16 + 83109945593953060776505494062289747840*x^15 - 784274949941308099024346
83204783737480*x^14 + 68411527510419695509612014370957102335*x^13 - 552310579433
03058323856167435958954875*x^12 + 41285051865108979303210529619078972420*x^11 -
28556677261894993605897587670410952880*x^10 + 1824396790085912527116454319620964
2035*x^9 - 10724669541859622266496198594992688955*x^8 + 576224566416395989571926
7159339201680*x^7 - 2797454333407067178417649149855271440*x^6 + 1202776750515386
982146365413070444165*x^5 - 441963914431106016828531333461331825*x^4 + 130380975
576388033973331946562853820*x^3 - 27619638829652562290439255223888360*x^2 - 1103
20475741093888*sqrt(2)*(1655223201792*x^33 - 40533929865216*x^32 + 5052201084518
40*x^31 - 4228105798895616*x^30 + 26534545003438848*x^29 - 132455269127702784*x^
28 + 545320709618281344*x^27 - 1897144292662342272*x^26 + 5674198357530944192*x^
25 - 14778605890709480640*x^24 + 33852877039198730688*x^23 - 6874780547628209990
4*x^22 + 124605468308576372880*x^21 - 202764864564694271504*x^20 + 2978354628812
38465328*x^19 - 396925342242926100304*x^18 + 482280318056102498824*x^17 - 536665
342387075938472*x^16 + 549073863627919009152*x^15 - 518138802562515874344*x^14 +
451967348292510885963*x^13 - 364889306092787766775*x^12 + 272753673169336497876
*x^11 - 188662439910260964464*x^10 + 120530531835136900623*x^9 - 708535627041726
04599*x^8 + 38068831201664625104*x^7 - 18481651602455633232*x^6 + 79462604958722
01737*x^5 - 2919877186136224485*x^4 + 861374478008482796*x^3 - 18247180521928320
8*x^2 + 22036451262907845*x - 663344282706293) + 3335522571486217667919065790563
025*x - 100406358593566432873987763957185)*sqrt((151363871237318045*sqrt(2) - 22
0640951482187776)/(33397068569829208576933551323217920*sqrt(2) - 472522362514299
67028491746144535113)) - 3602042876982878244*(337802213083473608^(1/4)*(4096*x^3
3 - 94208*x^32 + 1105920*x^31 - 8726528*x^30 + 51652864*x^29 - 243142912*x^28 +
943504512*x^27 - 3091758976*x^26 + 8703838016*x^25 - 21323296320*x^24 + 45922747
584*x^23 - 87669031872*x^22 + 149429442480*x^21 - 228892406512*x^20 + 3170206495
84*x^19 - 399317439952*x^18 + 459889940952*x^17 - 486569477336*x^16 + 4747417294
56*x^15 - 428370113832*x^14 + 358128604129*x^13 - 277690283125*x^12 + 1997414265
98*x^11 - 133169510462*x^10 + 82124768139*x^9 - 46688819967*x^8 + 24352777172*x^
7 - 11572941916*x^6 + 4956109991*x^5 - 1881604195*x^4 + 618995238*x^3 - 16980305
4*x^2 + 35318565*x - 4164129)*sqrt(x^2 - 2*x + 3) - 337802213083473608^(1/4)*(40
96*x^34 - 98304*x^33 + 1204224*x^32 - 9922560*x^31 + 61393152*x^30 - 302465536*x
^29 + 1230167680*x^28 - 4231534592*x^27 + 12524632256*x^26 - 32311376256*x^25 +
73387152384*x^24 - 147941398656*x^23 + 266538692976*x^22 - 431807810720*x^21 + 6
32607571360*x^20 - 842579391296*x^19 + 1025439024680*x^18 - 1145619691952*x^17 +
1179623583016*x^16 - 1123076849304*x^15 + 990931422841*x^14 - 811490311782*x^13
+ 617205254013*x^12 - 435943782908*x^11 + 285629584397*x^10 - 173202055986*x^9
+ 96858530705*x^8 - 49702089632*x^7 + 23230667691*x^6 - 9779204266*x^5 + 3646868
583*x^4 - 1176696972*x^3 + 315300087*x^2 - 63577710*x + 7212483))*arctan(1438415
293*(2*sqrt(205487899)*sqrt(35)*sqrt(7)*(110320475741093888*sqrt(2) - 1513638712
37318045)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(33397068569829
208576933551323217920*sqrt(2) - 47252236251429967028491746144535113)) + 5*337802
213083473608^(1/4)*sqrt(7)*(932587773*sqrt(2) - 1240695940))/(4*sqrt(1438415293)
*sqrt(205487899)*sqrt(35)*sqrt(7)*(110320475741093888*sqrt(2) - 1513638712373180
45)*sqrt(-(337802213083473608^(1/4)*sqrt(205487899)*sqrt(35)*(sqrt(2)*(246617419
2810249028691853897589514172583272025134182276224653*x - 59538591941389670823830
53517413008702994628754686755712968393) - 34876850013287180536911996198234945304
11356729552573436743740*x + 8420033386949216111074907415002522875577900779820937
989193046)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(3339706856982
9208576933551323217920*sqrt(2) - 47252236251429967028491746144535113)) + 3375919
1906238865443158698053056851590355903161284193415069696*x^2 - 596779698385758914
2192330688404962508573690130033831464558990*sqrt(2)*(4*x^2 - 3*x + 7) - (3378022
13083473608^(1/4)*sqrt(205487899)*sqrt(35)*(246617419281024902869185389758951417
2583272025134182276224653*sqrt(2) - 34876850013287180536911996198234945304113567
29552573436743740)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(33397
068569829208576933551323217920*sqrt(2) - 47252236251429967028491746144535113)) -
5967796983857589142192330688404962508573690130033831464558990*sqrt(2)*(4*x + 1)
+ 33759191906238865443158698053056851590355903161284193415069696*x + 8439797976
559716360789674513264212897588975790321048353767424)*sqrt(x^2 - 2*x + 3) - 20548
78990*sqrt(2)*(14521042389599762130499788428916104954126009459160005*sqrt(2) - 2
0535997539591653425756410389071652578405543458111488) - 253193939296791490823690
23539792638692766927370963145061302272*x + 5907858583591801452552772159284949028
3122830532247338476371968)/(1452104238959976213049978842891610495412600945916000
5*sqrt(2) - 20535997539591653425756410389071652578405543458111488))*sqrt((151363
871237318045*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*
sqrt(2) - 47252236251429967028491746144535113)) + 11507322344*sqrt(205487899)*sq
rt(35)*sqrt(x^2 - 2*x + 3)*(110320475741093888*sqrt(2) - 151363871237318045)*sqr
t((151363871237318045*sqrt(2) - 220640951482187776)/(333970685698292085769335513
23217920*sqrt(2) - 47252236251429967028491746144535113)) - 2876830586*sqrt(20548
7899)*sqrt(35)*(110320475741093888*sqrt(2)*(4*x + 1) - 605455484949272180*x - 15
1363871237318045)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(333970
68569829208576933551323217920*sqrt(2) - 47252236251429967028491746144535113)) +
50344535255*337802213083473608^(1/4)*(42834985*sqrt(2) - 179603212))) + 36020428
76982878244*(337802213083473608^(1/4)*(4096*x^33 - 94208*x^32 + 1105920*x^31 - 8
726528*x^30 + 51652864*x^29 - 243142912*x^28 + 943504512*x^27 - 3091758976*x^26
+ 8703838016*x^25 - 21323296320*x^24 + 45922747584*x^23 - 87669031872*x^22 + 149
429442480*x^21 - 228892406512*x^20 + 317020649584*x^19 - 399317439952*x^18 + 459
889940952*x^17 - 486569477336*x^16 + 474741729456*x^15 - 428370113832*x^14 + 358
128604129*x^13 - 277690283125*x^12 + 199741426598*x^11 - 133169510462*x^10 + 821
24768139*x^9 - 46688819967*x^8 + 24352777172*x^7 - 11572941916*x^6 + 4956109991*
x^5 - 1881604195*x^4 + 618995238*x^3 - 169803054*x^2 + 35318565*x - 4164129)*sqr
t(x^2 - 2*x + 3) - 337802213083473608^(1/4)*(4096*x^34 - 98304*x^33 + 1204224*x^
32 - 9922560*x^31 + 61393152*x^30 - 302465536*x^29 + 1230167680*x^28 - 423153459
2*x^27 + 12524632256*x^26 - 32311376256*x^25 + 73387152384*x^24 - 147941398656*x
^23 + 266538692976*x^22 - 431807810720*x^21 + 632607571360*x^20 - 842579391296*x
^19 + 1025439024680*x^18 - 1145619691952*x^17 + 1179623583016*x^16 - 11230768493
04*x^15 + 990931422841*x^14 - 811490311782*x^13 + 617205254013*x^12 - 4359437829
08*x^11 + 285629584397*x^10 - 173202055986*x^9 + 96858530705*x^8 - 49702089632*x
^7 + 23230667691*x^6 - 9779204266*x^5 + 3646868583*x^4 - 1176696972*x^3 + 315300
087*x^2 - 63577710*x + 7212483))*arctan(1438415293*(2*sqrt(205487899)*sqrt(35)*s
qrt(7)*(110320475741093888*sqrt(2) - 151363871237318045)*sqrt((15136387123731804
5*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqrt(2) - 4
7252236251429967028491746144535113)) - 5*337802213083473608^(1/4)*sqrt(7)*(93258
7773*sqrt(2) - 1240695940))/(4*sqrt(1438415293)*sqrt(205487899)*sqrt(35)*sqrt(7)
*(110320475741093888*sqrt(2) - 151363871237318045)*sqrt((337802213083473608^(1/4
)*sqrt(205487899)*sqrt(35)*(sqrt(2)*(2466174192810249028691853897589514172583272
025134182276224653*x - 595385919413896708238305351741300870299462875468675571296
8393) - 3487685001328718053691199619823494530411356729552573436743740*x + 842003
3386949216111074907415002522875577900779820937989193046)*sqrt((15136387123731804
5*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqrt(2) - 4
7252236251429967028491746144535113)) - 33759191906238865443158698053056851590355
903161284193415069696*x^2 + 5967796983857589142192330688404962508573690130033831
464558990*sqrt(2)*(4*x^2 - 3*x + 7) - (337802213083473608^(1/4)*sqrt(205487899)*
sqrt(35)*(2466174192810249028691853897589514172583272025134182276224653*sqrt(2)
- 3487685001328718053691199619823494530411356729552573436743740)*sqrt((151363871
237318045*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqr
t(2) - 47252236251429967028491746144535113)) + 596779698385758914219233068840496
2508573690130033831464558990*sqrt(2)*(4*x + 1) - 3375919190623886544315869805305
6851590355903161284193415069696*x - 84397979765597163607896745132642128975889757
90321048353767424)*sqrt(x^2 - 2*x + 3) + 2054878990*sqrt(2)*(1452104238959976213
0499788428916104954126009459160005*sqrt(2) - 20535997539591653425756410389071652
578405543458111488) + 2531939392967914908236902353979263869276692737096314506130
2272*x - 59078585835918014525527721592849490283122830532247338476371968)/(145210
42389599762130499788428916104954126009459160005*sqrt(2) - 2053599753959165342575
6410389071652578405543458111488))*sqrt((151363871237318045*sqrt(2) - 22064095148
2187776)/(33397068569829208576933551323217920*sqrt(2) - 472522362514299670284917
46144535113)) + 11507322344*sqrt(205487899)*sqrt(35)*sqrt(x^2 - 2*x + 3)*(110320
475741093888*sqrt(2) - 151363871237318045)*sqrt((151363871237318045*sqrt(2) - 22
0640951482187776)/(33397068569829208576933551323217920*sqrt(2) - 472522362514299
67028491746144535113)) - 2876830586*sqrt(205487899)*sqrt(35)*(110320475741093888
*sqrt(2)*(4*x + 1) - 605455484949272180*x - 151363871237318045)*sqrt((1513638712
37318045*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqrt
(2) - 47252236251429967028491746144535113)) - 50344535255*337802213083473608^(1/
4)*(42834985*sqrt(2) - 179603212))) - 9*(337802213083473608^(1/4)*sqrt(7)*(61998
6416588054712320*x^33 - 14259687581525258383360*x^32 + 167396332478774772326400*
x^31 - 1320881060540850564597760*x^30 + 7818377455534700703130880*x^29 - 3680305
2424234552531447040*x^28 + 142812495466196598236519040*x^27 - 467980607540086291
795521920*x^26 + 1317446616724297757953798720*x^25 - 322757667853565771561809440
0*x^24 + 6951044852168434341663353280*x^23 - 13269924051773739762905730240*x^22
+ 22618218890606943234793551600*x^21 - 34646040746482226380773109040*x^20 + 4798
5472783203500447904943280*x^19 - 60442233563710008375813533840*x^18 + 6961072180
5596326893894078840*x^17 - 73649039715495444774051328120*x^16 + 7185874600835966
3290416833520*x^15 - 64839758751982121623037698440*x^14 + 5420773192178240354947
3207805*x^13 - 42032276258786891981721490625*x^12 + 3023363557633788572374836091
0*x^11 - 20157052634306846278448886790*x^10 + 12430722829986195489825768255*x^9
- 7067000533707311734925404515*x^8 + 3686130628133706280779668740*x^7 - 17517252
90010384786403674220*x^6 + 750175994515709494869087595*x^5 - 2848068950915774740
21198775*x^4 + 93693515501145037746469710*x^3 - 25702047601359362810309430*x^2 -
110320475741093888*sqrt(2)*(4096*x^33 - 94208*x^32 + 1105920*x^31 - 8726528*x^3
0 + 51652864*x^29 - 243142912*x^28 + 943504512*x^27 - 3091758976*x^26 + 87038380
16*x^25 - 21323296320*x^24 + 45922747584*x^23 - 87669031872*x^22 + 149429442480*
x^21 - 228892406512*x^20 + 317020649584*x^19 - 399317439952*x^18 + 459889940952*
x^17 - 486569477336*x^16 + 474741729456*x^15 - 428370113832*x^14 + 358128604129*
x^13 - 277690283125*x^12 + 199741426598*x^11 - 133169510462*x^10 + 82124768139*x
^9 - 46688819967*x^8 + 24352777172*x^7 - 11572941916*x^6 + 4956109991*x^5 - 1881
604195*x^4 + 618995238*x^3 - 169803054*x^2 + 35318565*x - 4164129) + 53459547249
46847798005425*x - 630298685771581953407805)*sqrt(x^2 - 2*x + 3) - 3378022130834
73608^(1/4)*sqrt(7)*(619986416588054712320*x^34 - 14879673998113313095680*x^33 +
182276006476888085422080*x^32 - 1501917094184562540595200*x^31 + 92927051541810
94809027840*x^30 - 45782354444830385683397120*x^29 + 186202942315830268839785600
*x^28 - 640501457119745148723312640*x^27 + 1895776824091944217337859520*x^26 - 4
890774995113719620333339520*x^25 + 11108163483925213995887969280*x^24 - 22392982
816835520879607547520*x^23 + 40344328403382311629919551920*x^22 - 65360101861090
282575800442400*x^21 + 95753930975087526647353191200*x^20 - 12753607849134556071
5656736320*x^19 + 155214420493384520883764350600*x^18 - 173405431539558491799550
873840*x^17 + 178552392128137577493252323720*x^16 - 1699932596076634980455848906
80*x^15 + 149991216291917485508694465845*x^14 - 122830315062901722450544706190*x
^13 + 93422576595419908569093564585*x^12 - 65986138622795843157630974860*x^11 +
43233999634236175350258543865*x^10 - 26216533700303655122578067370*x^9 + 1466088
2169867436203483071725*x^8 - 7523100695283688215881009440*x^7 + 3516283793137448
501472784095*x^6 - 1480218215322255324062779970*x^5 + 55200414661663251548948023
5*x^4 - 178109408955150036952459740*x^3 + 47725041769783177235169915*x^2 - 11032
0475741093888*sqrt(2)*(4096*x^34 - 98304*x^33 + 1204224*x^32 - 9922560*x^31 + 61
393152*x^30 - 302465536*x^29 + 1230167680*x^28 - 4231534592*x^27 + 12524632256*x
^26 - 32311376256*x^25 + 73387152384*x^24 - 147941398656*x^23 + 266538692976*x^2
2 - 431807810720*x^21 + 632607571360*x^20 - 842579391296*x^19 + 1025439024680*x^
18 - 1145619691952*x^17 + 1179623583016*x^16 - 1123076849304*x^15 + 990931422841
*x^14 - 811490311782*x^13 + 617205254013*x^12 - 435943782908*x^11 + 285629584397
*x^10 - 173202055986*x^9 + 96858530705*x^8 - 49702089632*x^7 + 23230667691*x^6 -
9779204266*x^5 + 3646868583*x^4 - 1176696972*x^3 + 315300087*x^2 - 63577710*x +
7212483) - 9623368310003547842776950*x + 1091709348113345365155735))*log(-15815
54340224321978368*(337802213083473608^(1/4)*sqrt(205487899)*sqrt(35)*(sqrt(2)*(2
466174192810249028691853897589514172583272025134182276224653*x - 595385919413896
7082383053517413008702994628754686755712968393) - 348768500132871805369119961982
3494530411356729552573436743740*x + 84200333869492161110749074150025228755779007
79820937989193046)*sqrt((151363871237318045*sqrt(2) - 220640951482187776)/(33397
068569829208576933551323217920*sqrt(2) - 47252236251429967028491746144535113)) +
33759191906238865443158698053056851590355903161284193415069696*x^2 - 5967796983
857589142192330688404962508573690130033831464558990*sqrt(2)*(4*x^2 - 3*x + 7) -
(337802213083473608^(1/4)*sqrt(205487899)*sqrt(35)*(2466174192810249028691853897
589514172583272025134182276224653*sqrt(2) - 348768500132871805369119961982349453
0411356729552573436743740)*sqrt((151363871237318045*sqrt(2) - 220640951482187776
)/(33397068569829208576933551323217920*sqrt(2) - 4725223625142996702849174614453
5113)) - 5967796983857589142192330688404962508573690130033831464558990*sqrt(2)*(
4*x + 1) + 33759191906238865443158698053056851590355903161284193415069696*x + 84
39797976559716360789674513264212897588975790321048353767424)*sqrt(x^2 - 2*x + 3)
- 2054878990*sqrt(2)*(14521042389599762130499788428916104954126009459160005*sqr
t(2) - 20535997539591653425756410389071652578405543458111488) - 2531939392967914
9082369023539792638692766927370963145061302272*x + 59078585835918014525527721592
849490283122830532247338476371968)/(14521042389599762130499788428916104954126009
459160005*sqrt(2) - 20535997539591653425756410389071652578405543458111488)) + 9*
(337802213083473608^(1/4)*sqrt(7)*(619986416588054712320*x^33 - 1425968758152525
8383360*x^32 + 167396332478774772326400*x^31 - 1320881060540850564597760*x^30 +
7818377455534700703130880*x^29 - 36803052424234552531447040*x^28 + 1428124954661
96598236519040*x^27 - 467980607540086291795521920*x^26 + 13174466167242977579537
98720*x^25 - 3227576678535657715618094400*x^24 + 6951044852168434341663353280*x^
23 - 13269924051773739762905730240*x^22 + 22618218890606943234793551600*x^21 - 3
4646040746482226380773109040*x^20 + 47985472783203500447904943280*x^19 - 6044223
3563710008375813533840*x^18 + 69610721805596326893894078840*x^17 - 7364903971549
5444774051328120*x^16 + 71858746008359663290416833520*x^15 - 6483975875198212162
3037698440*x^14 + 54207731921782403549473207805*x^13 - 4203227625878689198172149
0625*x^12 + 30233635576337885723748360910*x^11 - 20157052634306846278448886790*x
^10 + 12430722829986195489825768255*x^9 - 7067000533707311734925404515*x^8 + 368
6130628133706280779668740*x^7 - 1751725290010384786403674220*x^6 + 7501759945157
09494869087595*x^5 - 284806895091577474021198775*x^4 + 9369351550114503774646971
0*x^3 - 25702047601359362810309430*x^2 - 110320475741093888*sqrt(2)*(4096*x^33 -
94208*x^32 + 1105920*x^31 - 8726528*x^30 + 51652864*x^29 - 243142912*x^28 + 943
504512*x^27 - 3091758976*x^26 + 8703838016*x^25 - 21323296320*x^24 + 45922747584
*x^23 - 87669031872*x^22 + 149429442480*x^21 - 228892406512*x^20 + 317020649584*
x^19 - 399317439952*x^18 + 459889940952*x^17 - 486569477336*x^16 + 474741729456*
x^15 - 428370113832*x^14 + 358128604129*x^13 - 277690283125*x^12 + 199741426598*
x^11 - 133169510462*x^10 + 82124768139*x^9 - 46688819967*x^8 + 24352777172*x^7 -
11572941916*x^6 + 4956109991*x^5 - 1881604195*x^4 + 618995238*x^3 - 169803054*x
^2 + 35318565*x - 4164129) + 5345954724946847798005425*x - 630298685771581953407
805)*sqrt(x^2 - 2*x + 3) - 337802213083473608^(1/4)*sqrt(7)*(6199864165880547123
20*x^34 - 14879673998113313095680*x^33 + 182276006476888085422080*x^32 - 1501917
094184562540595200*x^31 + 9292705154181094809027840*x^30 - 457823544448303856833
97120*x^29 + 186202942315830268839785600*x^28 - 640501457119745148723312640*x^27
+ 1895776824091944217337859520*x^26 - 4890774995113719620333339520*x^25 + 11108
163483925213995887969280*x^24 - 22392982816835520879607547520*x^23 + 40344328403
382311629919551920*x^22 - 65360101861090282575800442400*x^21 + 95753930975087526
647353191200*x^20 - 127536078491345560715656736320*x^19 + 1552144204933845208837
64350600*x^18 - 173405431539558491799550873840*x^17 + 17855239212813757749325232
3720*x^16 - 169993259607663498045584890680*x^15 + 149991216291917485508694465845
*x^14 - 122830315062901722450544706190*x^13 + 93422576595419908569093564585*x^12
- 65986138622795843157630974860*x^11 + 43233999634236175350258543865*x^10 - 262
16533700303655122578067370*x^9 + 14660882169867436203483071725*x^8 - 75231006952
83688215881009440*x^7 + 3516283793137448501472784095*x^6 - 148021821532225532406
2779970*x^5 + 552004146616632515489480235*x^4 - 178109408955150036952459740*x^3
+ 47725041769783177235169915*x^2 - 110320475741093888*sqrt(2)*(4096*x^34 - 98304
*x^33 + 1204224*x^32 - 9922560*x^31 + 61393152*x^30 - 302465536*x^29 + 123016768
0*x^28 - 4231534592*x^27 + 12524632256*x^26 - 32311376256*x^25 + 73387152384*x^2
4 - 147941398656*x^23 + 266538692976*x^22 - 431807810720*x^21 + 632607571360*x^2
0 - 842579391296*x^19 + 1025439024680*x^18 - 1145619691952*x^17 + 1179623583016*
x^16 - 1123076849304*x^15 + 990931422841*x^14 - 811490311782*x^13 + 617205254013
*x^12 - 435943782908*x^11 + 285629584397*x^10 - 173202055986*x^9 + 96858530705*x
^8 - 49702089632*x^7 + 23230667691*x^6 - 9779204266*x^5 + 3646868583*x^4 - 11766
96972*x^3 + 315300087*x^2 - 63577710*x + 7212483) - 9623368310003547842776950*x
+ 1091709348113345365155735))*log(1581554340224321978368*(337802213083473608^(1/
4)*sqrt(205487899)*sqrt(35)*(sqrt(2)*(246617419281024902869185389758951417258327
2025134182276224653*x - 59538591941389670823830535174130087029946287546867557129
68393) - 3487685001328718053691199619823494530411356729552573436743740*x + 84200
33386949216111074907415002522875577900779820937989193046)*sqrt((1513638712373180
45*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqrt(2) -
47252236251429967028491746144535113)) - 3375919190623886544315869805305685159035
5903161284193415069696*x^2 + 596779698385758914219233068840496250857369013003383
1464558990*sqrt(2)*(4*x^2 - 3*x + 7) - (337802213083473608^(1/4)*sqrt(205487899)
*sqrt(35)*(2466174192810249028691853897589514172583272025134182276224653*sqrt(2)
- 3487685001328718053691199619823494530411356729552573436743740)*sqrt((15136387
1237318045*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sq
rt(2) - 47252236251429967028491746144535113)) + 59677969838575891421923306884049
62508573690130033831464558990*sqrt(2)*(4*x + 1) - 337591919062388654431586980530
56851590355903161284193415069696*x - 8439797976559716360789674513264212897588975
790321048353767424)*sqrt(x^2 - 2*x + 3) + 2054878990*sqrt(2)*(145210423895997621
30499788428916104954126009459160005*sqrt(2) - 2053599753959165342575641038907165
2578405543458111488) + 253193939296791490823690235397926386927669273709631450613
02272*x - 59078585835918014525527721592849490283122830532247338476371968)/(14521
042389599762130499788428916104954126009459160005*sqrt(2) - 205359975395916534257
56410389071652578405543458111488)))/(sqrt(205487899)*sqrt(35)*sqrt(7)*(619986416
588054712320*x^33 - 14259687581525258383360*x^32 + 167396332478774772326400*x^31
- 1320881060540850564597760*x^30 + 7818377455534700703130880*x^29 - 36803052424
234552531447040*x^28 + 142812495466196598236519040*x^27 - 4679806075400862917955
21920*x^26 + 1317446616724297757953798720*x^25 - 3227576678535657715618094400*x^
24 + 6951044852168434341663353280*x^23 - 13269924051773739762905730240*x^22 + 22
618218890606943234793551600*x^21 - 34646040746482226380773109040*x^20 + 47985472
783203500447904943280*x^19 - 60442233563710008375813533840*x^18 + 69610721805596
326893894078840*x^17 - 73649039715495444774051328120*x^16 + 71858746008359663290
416833520*x^15 - 64839758751982121623037698440*x^14 + 54207731921782403549473207
805*x^13 - 42032276258786891981721490625*x^12 + 30233635576337885723748360910*x^
11 - 20157052634306846278448886790*x^10 + 12430722829986195489825768255*x^9 - 70
67000533707311734925404515*x^8 + 3686130628133706280779668740*x^7 - 175172529001
0384786403674220*x^6 + 750175994515709494869087595*x^5 - 28480689509157747402119
8775*x^4 + 93693515501145037746469710*x^3 - 25702047601359362810309430*x^2 - 110
320475741093888*sqrt(2)*(4096*x^33 - 94208*x^32 + 1105920*x^31 - 8726528*x^30 +
51652864*x^29 - 243142912*x^28 + 943504512*x^27 - 3091758976*x^26 + 8703838016*x
^25 - 21323296320*x^24 + 45922747584*x^23 - 87669031872*x^22 + 149429442480*x^21
- 228892406512*x^20 + 317020649584*x^19 - 399317439952*x^18 + 459889940952*x^17
- 486569477336*x^16 + 474741729456*x^15 - 428370113832*x^14 + 358128604129*x^13
- 277690283125*x^12 + 199741426598*x^11 - 133169510462*x^10 + 82124768139*x^9 -
46688819967*x^8 + 24352777172*x^7 - 11572941916*x^6 + 4956109991*x^5 - 18816041
95*x^4 + 618995238*x^3 - 169803054*x^2 + 35318565*x - 4164129) + 534595472494684
7798005425*x - 630298685771581953407805)*sqrt(x^2 - 2*x + 3)*sqrt((1513638712373
18045*sqrt(2) - 220640951482187776)/(33397068569829208576933551323217920*sqrt(2)
- 47252236251429967028491746144535113)) - sqrt(205487899)*sqrt(35)*sqrt(7)*(619
986416588054712320*x^34 - 14879673998113313095680*x^33 + 18227600647688808542208
0*x^32 - 1501917094184562540595200*x^31 + 9292705154181094809027840*x^30 - 45782
354444830385683397120*x^29 + 186202942315830268839785600*x^28 - 6405014571197451
48723312640*x^27 + 1895776824091944217337859520*x^26 - 4890774995113719620333339
520*x^25 + 11108163483925213995887969280*x^24 - 22392982816835520879607547520*x^
23 + 40344328403382311629919551920*x^22 - 65360101861090282575800442400*x^21 + 9
5753930975087526647353191200*x^20 - 127536078491345560715656736320*x^19 + 155214
420493384520883764350600*x^18 - 173405431539558491799550873840*x^17 + 1785523921
28137577493252323720*x^16 - 169993259607663498045584890680*x^15 + 14999121629191
7485508694465845*x^14 - 122830315062901722450544706190*x^13 + 934225765954199085
69093564585*x^12 - 65986138622795843157630974860*x^11 + 432339996342361753502585
43865*x^10 - 26216533700303655122578067370*x^9 + 14660882169867436203483071725*x
^8 - 7523100695283688215881009440*x^7 + 3516283793137448501472784095*x^6 - 14802
18215322255324062779970*x^5 + 552004146616632515489480235*x^4 - 1781094089551500
36952459740*x^3 + 47725041769783177235169915*x^2 - 110320475741093888*sqrt(2)*(4
096*x^34 - 98304*x^33 + 1204224*x^32 - 9922560*x^31 + 61393152*x^30 - 302465536*
x^29 + 1230167680*x^28 - 4231534592*x^27 + 12524632256*x^26 - 32311376256*x^25 +
73387152384*x^24 - 147941398656*x^23 + 266538692976*x^22 - 431807810720*x^21 +
632607571360*x^20 - 842579391296*x^19 + 1025439024680*x^18 - 1145619691952*x^17
+ 1179623583016*x^16 - 1123076849304*x^15 + 990931422841*x^14 - 811490311782*x^1
3 + 617205254013*x^12 - 435943782908*x^11 + 285629584397*x^10 - 173202055986*x^9
+ 96858530705*x^8 - 49702089632*x^7 + 23230667691*x^6 - 9779204266*x^5 + 364686
8583*x^4 - 1176696972*x^3 + 315300087*x^2 - 63577710*x + 7212483) - 962336831000
3547842776950*x + 1091709348113345365155735)*sqrt((151363871237318045*sqrt(2) -
220640951482187776)/(33397068569829208576933551323217920*sqrt(2) - 4725223625142
9967028491746144535113)))
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2-2*x+3)**(11/2)/(2*x**2+x+1)**5,x)
[Out]
Timed out
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{5}{\left (x^{2} - 2 \, x + 3\right )}^{\frac{11}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x^2 + x + 1)^5*(x^2 - 2*x + 3)^(11/2)),x, algorithm="giac")
[Out]
integrate(1/((2*x^2 + x + 1)^5*(x^2 - 2*x + 3)^(11/2)), x)