3.49 \(\int \frac{1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx\)

Optimal. Leaf size=1058 \[ \text{result too large to display} \]

[Out]

-13056959628363355534285785425/(106924014357253562723941220352*(3 - 2*x)^(39/2))
- 3948194343291401740321996415/(202881463139404195937734623232*(3 - 2*x)^(37/2)
) - 304688229262620222736480811/(537361713180043545997243056128*(3 - 2*x)^(35/2)
) + 2124315846756567455653862925/(1688851098565851144562763890688*(3 - 2*x)^(33/
2)) + 47657515074514118796095929535/(66632852434325399703658138959872*(3 - 2*x)^
(31/2)) + 34911619993974714062172751985/(124667917457770102671360389021696*(3 -
2*x)^(29/2)) + 149066309808794760843017404825/(162498182065645168309566300173107
2*(3 - 2*x)^(27/2)) + 15848613964169066543734380171/(601845118761648771516912222
863360*(3 - 2*x)^(25/2)) + 11155168222970774232376891145/(1685166332532616560247
354224017408*(3 - 2*x)^(23/2)) + 14011818498091020272474956375/(1011099799519569
9361484125344104448*(3 - 2*x)^(21/2)) + 173441368149804378661935869705/(89650848
8907352010051592447177261056*(3 - 2*x)^(19/2)) - 22724090823469905152713519545/(
1604278348571050965355481221264572416*(3 - 2*x)^(17/2)) - 1011902744127796186785
73275245/(3963511214116714149701777134888943616*(3 - 2*x)^(15/2)) - 460503190416
958283087439337135/(34350430522344855964082068502370844672*(3 - 2*x)^(13/2)) - 2
211619588790911794826342607495/(406920484649315986036049119181931544576*(3 - 2*x
)^(11/2)) - 143401467550777247627940437025/(739855426635119974610998398512602808
32*(3 - 2*x)^(9/2)) - 4611053278117143010907562317585/(7250583181024175751187784
305423507521536*(3 - 2*x)^(7/2)) - 405965372440630510720926890227/(2071595194578
335928910795515835287863296*(3 - 2*x)^(5/2)) - 4986681479187781853417316522775/(
87006998172290109014253411665082090258432*(3 - 2*x)^(3/2)) - 9270277547814767462
08047620505/(58004665448193406009502274443388060172288*Sqrt[3 - 2*x]) + x/(133*(
3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + (113 + 373*x)/(33516*(3 - 2*x)^(39/2)*(1 +
x + 2*x^2)^18) + (40657 + 107329*x)/(7976808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^1
7) + (5*(751303 + 1831285*x))/(595601664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) +
(184959785 + 429411497*x)/(25015269888*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^15) + (4
1652915209 + 92630823167*x)/(4902992898048*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14)
+ (2871555518177 + 6100156355517*x)/(297448235814912*(3 - 2*x)^(39/2)*(1 + x + 2
*x^2)^13) + (77559130805859 + 156274047129113*x)/(7138757659557888*(3 - 2*x)^(39
/2)*(1 + x + 2*x^2)^12) + (5*(2656658801194921 + 5020880176134289*x))/(109936867
9571914752*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^11) + (45187921585208601 + 787529110
37377255*x)/(3420258114223734784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10) + (6063974
149878048635 + 9477172618423641847*x)/(430952522392190582784*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^9) + (691833601144925854831 + 919498192874055581221*x)/(4826668250
7925345271808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^8) + (23*(919498192874055581221 +
908287136092467468517*x))/(1576711628592227945545728*(3 - 2*x)^(39/2)*(1 + x +
2*x^2)^7) + (115*(908287136092467468517 + 298281884944522225747*x))/(10187982830
903626725064704*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + (23*(259931356880226511008
1 - 10426142448623187379187*x))/(20375965661807253450129408*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^5) - (23*(10426142448623187379187 + 27513723463194262383705*x))/(20
018492580021161284337664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) - (115*(26513224428
169016478843 + 30673415406553789342019*x))/(76434244396444433994743808*(3 - 2*x)
^(39/2)*(1 + x + 2*x^2)^3) - (115*(88411609113007981044643 - 5712269536245152162
963*x))/(125891696652967303050166272*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + (115*
(28561347681225760814815 + 965934812839019490346107*x))/(19583152812683802696692
5312*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)) + (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118
912219360725028693061 + 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 +
2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/8120653162747076841330318
42207432842412032 - (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118912219360725028693061
+ 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[
3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/812065316274707684133031842207432842412032 + (
115*(30297118912219360725028693061 - 8061110911143276053983022787*Sqrt[14])*Sqrt
[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*
x])/1624130632549415368266063684414865684824064 - (115*(302971189122193607250286
93061 - 8061110911143276053983022787*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 +
Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/1624130632549415368266063
684414865684824064

_______________________________________________________________________________________

Rubi [A]  time = 5.37521, antiderivative size = 1058, normalized size of antiderivative = 1., number of steps used = 49, number of rules used = 9, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.45 \[ \text{result too large to display} \]

Warning: Unable to verify antiderivative.

[In]  Int[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]

[Out]

-13056959628363355534285785425/(106924014357253562723941220352*(3 - 2*x)^(39/2))
- 3948194343291401740321996415/(202881463139404195937734623232*(3 - 2*x)^(37/2)
) - 304688229262620222736480811/(537361713180043545997243056128*(3 - 2*x)^(35/2)
) + 2124315846756567455653862925/(1688851098565851144562763890688*(3 - 2*x)^(33/
2)) + 47657515074514118796095929535/(66632852434325399703658138959872*(3 - 2*x)^
(31/2)) + 34911619993974714062172751985/(124667917457770102671360389021696*(3 -
2*x)^(29/2)) + 149066309808794760843017404825/(162498182065645168309566300173107
2*(3 - 2*x)^(27/2)) + 15848613964169066543734380171/(601845118761648771516912222
863360*(3 - 2*x)^(25/2)) + 11155168222970774232376891145/(1685166332532616560247
354224017408*(3 - 2*x)^(23/2)) + 14011818498091020272474956375/(1011099799519569
9361484125344104448*(3 - 2*x)^(21/2)) + 173441368149804378661935869705/(89650848
8907352010051592447177261056*(3 - 2*x)^(19/2)) - 22724090823469905152713519545/(
1604278348571050965355481221264572416*(3 - 2*x)^(17/2)) - 1011902744127796186785
73275245/(3963511214116714149701777134888943616*(3 - 2*x)^(15/2)) - 460503190416
958283087439337135/(34350430522344855964082068502370844672*(3 - 2*x)^(13/2)) - 2
211619588790911794826342607495/(406920484649315986036049119181931544576*(3 - 2*x
)^(11/2)) - 143401467550777247627940437025/(739855426635119974610998398512602808
32*(3 - 2*x)^(9/2)) - 4611053278117143010907562317585/(7250583181024175751187784
305423507521536*(3 - 2*x)^(7/2)) - 405965372440630510720926890227/(2071595194578
335928910795515835287863296*(3 - 2*x)^(5/2)) - 4986681479187781853417316522775/(
87006998172290109014253411665082090258432*(3 - 2*x)^(3/2)) - 9270277547814767462
08047620505/(58004665448193406009502274443388060172288*Sqrt[3 - 2*x]) + x/(133*(
3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + (113 + 373*x)/(33516*(3 - 2*x)^(39/2)*(1 +
x + 2*x^2)^18) + (40657 + 107329*x)/(7976808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^1
7) + (5*(751303 + 1831285*x))/(595601664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) +
(184959785 + 429411497*x)/(25015269888*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^15) + (4
1652915209 + 92630823167*x)/(4902992898048*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14)
+ (2871555518177 + 6100156355517*x)/(297448235814912*(3 - 2*x)^(39/2)*(1 + x + 2
*x^2)^13) + (77559130805859 + 156274047129113*x)/(7138757659557888*(3 - 2*x)^(39
/2)*(1 + x + 2*x^2)^12) + (5*(2656658801194921 + 5020880176134289*x))/(109936867
9571914752*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^11) + (45187921585208601 + 787529110
37377255*x)/(3420258114223734784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10) + (6063974
149878048635 + 9477172618423641847*x)/(430952522392190582784*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^9) + (691833601144925854831 + 919498192874055581221*x)/(4826668250
7925345271808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^8) + (23*(919498192874055581221 +
908287136092467468517*x))/(1576711628592227945545728*(3 - 2*x)^(39/2)*(1 + x +
2*x^2)^7) + (115*(908287136092467468517 + 298281884944522225747*x))/(10187982830
903626725064704*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + (23*(259931356880226511008
1 - 10426142448623187379187*x))/(20375965661807253450129408*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^5) - (23*(10426142448623187379187 + 27513723463194262383705*x))/(20
018492580021161284337664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) - (115*(26513224428
169016478843 + 30673415406553789342019*x))/(76434244396444433994743808*(3 - 2*x)
^(39/2)*(1 + x + 2*x^2)^3) - (115*(88411609113007981044643 - 5712269536245152162
963*x))/(125891696652967303050166272*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + (115*
(28561347681225760814815 + 965934812839019490346107*x))/(19583152812683802696692
5312*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)) + (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118
912219360725028693061 + 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 +
2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/8120653162747076841330318
42207432842412032 - (115*Sqrt[(7 + 2*Sqrt[14])/2]*(30297118912219360725028693061
+ 8061110911143276053983022787*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[
3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/812065316274707684133031842207432842412032 + (
115*(30297118912219360725028693061 - 8061110911143276053983022787*Sqrt[14])*Sqrt
[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*
x])/1624130632549415368266063684414865684824064 - (115*(302971189122193607250286
93061 - 8061110911143276053983022787*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 +
Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/1624130632549415368266063
684414865684824064

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x}{133 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{19}} + \frac{\int \frac{- 79426075962231715392089154535476326400 x + 13068536369629429401640635068702208000}{\left (- 2 x + 3\right )^{\frac{41}{2}} \left (2 x^{2} + x + 1\right )^{9}}\, dx}{49475578698391671468350845128120729600} + \frac{146216 x + 44296}{13138272 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{18}} + \frac{589021552 x + 223125616}{43776722304 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{17}} + \frac{2110519336800 x + 865861681440}{137283801145344 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{16}} + \frac{6928434268875840 x + 2984274342235200}{403614375367311360 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{15}} + \frac{20924013532366815360 x + 9408813737133390720}{1107517846007902371840 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{14}} + \frac{57873497074462503141120 x + 27243065619141593598720}{2821955471628135243448320 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{13}} + \frac{145295342948683106164016640 x + 72110377354780278913835520}{6637239269269374092590448640 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{12}} + \frac{326770416680301421681066214400 x + 172901458108932896335179801600}{14309887864544770543625007267840 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{11}} + \frac{645802967231886306826540424448000 x + 370557652515461812186329087129600}{28047380214507750265505014244966400 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{10}} + \frac{1088028437838790621809440473088716800 x + 696175598675973438759010577554944000}{49475578698391671468350845128120729600 \left (- 2 x + 3\right )^{\frac{39}{2}} \left (2 x^{2} + x + 1\right )^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(3-2*x)**(41/2)/(2*x**2+x+1)**20,x)

[Out]

x/(133*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**19) + Integral((-7942607596223171539
2089154535476326400*x + 13068536369629429401640635068702208000)/((-2*x + 3)**(41
/2)*(2*x**2 + x + 1)**9), x)/49475578698391671468350845128120729600 + (146216*x
+ 44296)/(13138272*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**18) + (589021552*x + 223
125616)/(43776722304*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**17) + (2110519336800*x
+ 865861681440)/(137283801145344*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**16) + (69
28434268875840*x + 2984274342235200)/(403614375367311360*(-2*x + 3)**(39/2)*(2*x
**2 + x + 1)**15) + (20924013532366815360*x + 9408813737133390720)/(110751784600
7902371840*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**14) + (57873497074462503141120*x
+ 27243065619141593598720)/(2821955471628135243448320*(-2*x + 3)**(39/2)*(2*x**
2 + x + 1)**13) + (145295342948683106164016640*x + 72110377354780278913835520)/(
6637239269269374092590448640*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**12) + (3267704
16680301421681066214400*x + 172901458108932896335179801600)/(1430988786454477054
3625007267840*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**11) + (6458029672318863068265
40424448000*x + 370557652515461812186329087129600)/(2804738021450775026550501424
4966400*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**10) + (1088028437838790621809440473
088716800*x + 696175598675973438759010577554944000)/(494755786983916714683508451
28120729600*(-2*x + 3)**(39/2)*(2*x**2 + x + 1)**9)

_______________________________________________________________________________________

Mathematica [C]  time = 6.16477, size = 1242, normalized size = 1.17 \[ \text{result too large to display} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]

[Out]

-(393*Sqrt[3 - 2*x] + 287*(3 - 2*x)^(3/2))/(150276832468*(14 - 7*(3 - 2*x) + (3
- 2*x)^2)^19) - (-4226921*Sqrt[3 - 2*x] + 1313129*(3 - 2*x)^(3/2))/(757395235638
72*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^18) - (-3401932701*Sqrt[3 - 2*x] + 760755809
*(3 - 2*x)^(3/2))/(36052013216403072*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^17) - (5*(
-146490500023*Sqrt[3 - 2*x] + 16144709919*(3 - 2*x)^(3/2)))/(1615130192094857625
6*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^16) - (9745709632283*Sqrt[3 - 2*x] - 45579120
48927*(3 - 2*x)^(3/2))/(452236453786560135168*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^1
5) - (435856117815771*Sqrt[3 - 2*x] - 123609208162571*(3 - 2*x)^(3/2))/(93303520
99175345946624*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^14) - (127435522656997631*Sqrt[3
- 2*x] - 31270302414674811*(3 - 2*x)^(3/2))/(3396248164099825924571136*(14 - 7*
(3 - 2*x) + (3 - 2*x)^2)^13) + (5*(-1540359167602841319*Sqrt[3 - 2*x] + 34202655
7757088031*(3 - 2*x)^(3/2)))/(380379794379180503551967232*(14 - 7*(3 - 2*x) + (3
- 2*x)^2)^12) + (5*(-21084628139481190687*Sqrt[3 - 2*x] + 4158669924550257827*(
3 - 2*x)^(3/2)))/(13017441852087510566000656384*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)
^11) - (1633293973597342712581*Sqrt[3 - 2*x] - 237080744154193384005*(3 - 2*x)^(
3/2))/(728976743716900591696036757504*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^10) - (73
50432513431022017155*Sqrt[3 - 2*x] + 5131564318471376538977*(3 - 2*x)^(3/2))/(61
234046472219649702467087630336*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^9) - (-113207386
492327172550771*Sqrt[3 - 2*x] + 43421160367342900895387*(3 - 2*x)^(3/2))/(279927
069587289827211278114881536*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^8) - (-224637967205
02183624842107*Sqrt[3 - 2*x] + 7094978194424786431173663*(3 - 2*x)^(3/2))/(54865
705639108806133410510516781056*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^7) - (5*(-186257
412289925530757362143*Sqrt[3 - 2*x] + 55540178588722046667113711*(3 - 2*x)^(3/2)
))/(3072479515790093143470988588939739136*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^6) -
(23*(-255056047077847659080618951*Sqrt[3 - 2*x] + 74443988473272328189316355*(3
- 2*x)^(3/2)))/(28676475480707536005729226830104231936*(14 - 7*(3 - 2*x) + (3 -
2*x)^2)^5) - (23*(-1110057788286806589656260577*Sqrt[3 - 2*x] + 3215339539099846
40923113289*(3 - 2*x)^(3/2)))/(188927367872896707802451376763039645696*(14 - 7*(
3 - 2*x) + (3 - 2*x)^2)^4) - (23*(-4820387670797872511726954245*Sqrt[3 - 2*x] +
1394304490531377203111252689*(3 - 2*x)^(3/2)))/(12207614539479479581081473575457
94633728*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^3) - (23*(-174904025701511085811282262
13*Sqrt[3 - 2*x] + 5072167085782230110284731077*(3 - 2*x)^(3/2)))/(6214785583735
007786732386547505863589888*(14 - 7*(3 - 2*x) + (3 - 2*x)^2)^2) - (115*(-8278238
6138609724168863115877*Sqrt[3 - 2*x] + 24217623575858523510208130121*(3 - 2*x)^(
3/2)))/(174013996344580218028506823330164180516864*(14 - 7*(3 - 2*x) + (3 - 2*x)
^2)) + 1/(3111898385606868039*(3 - 2*x)^(39/2)) + 10/(2952313853011644037*(3 - 2
*x)^(37/2)) + 143/(7819642097165976098*(3 - 2*x)^(35/2)) + 355/(5266289575642392
066*(3 - 2*x)^(33/2)) + 52865/(277038748585308867472*(3 - 2*x)^(31/2)) + 14333/(
32395660116830472406*(3 - 2*x)^(29/2)) + 1478345/(1689042692987850837168*(3 - 2*
x)^(27/2)) + 475387/(312785683886639043920*(3 - 2*x)^(25/2)) + 16575515/(7006399
319060714583808*(3 - 2*x)^(23/2)) + 246866015/(73567192850137503129984*(3 - 2*x)
^(21/2)) + 8192823353/(1863702218870150079292928*(3 - 2*x)^(19/2)) + 8972680075/
(1667523037936450070946304*(3 - 2*x)^(17/2)) + 102495360575/(1647905119843080070
1116416*(3 - 2*x)^(15/2)) + 122484655975/(17852305464966700759542784*(3 - 2*x)^(
13/2)) + 10815878546425/(1480368099325700262983624704*(3 - 2*x)^(11/2)) + 769045
155125/(100934188590388654294338048*(3 - 2*x)^(9/2)) + 838467657280275/(10550987
1806486273289014706176*(3 - 2*x)^(7/2)) + 9270470094105/(10766313449641456458062
72512*(3 - 2*x)^(5/2)) + 320421783064625/(30145677658996078082575630336*(3 - 2*x
)^(3/2)) + 683151246370725/(30145677658996078082575630336*Sqrt[3 - 2*x]) - (115*
(-117022014202441653827938545631*I + 8061110911143276053983022787*Sqrt[7])*ArcTa
n[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[-7 - I*Sqrt[7]]])/(580046654481934060095022744433
88060172288*Sqrt[14*(-7 - I*Sqrt[7])]) - (115*(117022014202441653827938545631*I
+ 8061110911143276053983022787*Sqrt[7])*ArcTan[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[-7 +
I*Sqrt[7]]])/(58004665448193406009502274443388060172288*Sqrt[14*(-7 + I*Sqrt[7]
)])

_______________________________________________________________________________________

Maple [A]  time = 0.138, size = 989, normalized size = 0.9 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x)

[Out]

-7192279694031133468210490184035/3248261265098830736532127368829731369648128*ln(
3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)*14^(1/2)
+13457531633280790190212932747565/812065316274707684133031842207432842412032/(-7
+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))
^(1/2))*(7+2*14^(1/2))-3484168674905226483378299702015/8120653162747076841330318
42207432842412032/(-7+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)-(7+2*14^(1/2))^(
1/2))/(-7+2*14^(1/2))^(1/2))*14^(1/2)+7192279694031133468210490184035/3248261265
098830736532127368829731369648128*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))
^(1/2))*(7+2*14^(1/2))^(1/2)*14^(1/2)+13457531633280790190212932747565/812065316
274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)+
(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))-34841686749052264833
78299702015/812065316274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*arc
tan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*14^(1/2)+13457
531633280790190212932747565/1624130632549415368266063684414865684824064*ln(3-2*x
+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)-1345753163328
0790190212932747565/1624130632549415368266063684414865684824064*ln(3-2*x+14^(1/2
)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2)[phone]/30145
677658996078082575630336/(3-2*x)^(1/2)+1/30145677658996078082575630336*(-5059022
664167725408892162874688680417923742003781/29480655519744*(3-2*x)^(47/2)-4479632
9357069082297154473725670903546220392558695/9070970929152*(3-2*x)^(43/2)-1939242
920901534821454026903132433081580221023737/501171143835648*(3-2*x)^(51/2)-100630
4725834560333245233940167063186576585913370455/10720238370816*(3-2*x)^(39/2)+138
05722741822612586258592099428566280191230197271405/39307540692992*(3-2*x)^(37/2)
-928342237074576734557978321305/1924145348608*(3-2*x)^(75/2)+3395565446412935417
59958988614814460549873/9826885173248*(3-2*x)^(61/2)+133883313322119397348791732
981953297/824633720832*(3-2*x)^(69/2)+490738543064879423955077165987434152441563
270473/1002342287671296*(3-2*x)^(53/2)-75593011640468285657019519019203244129463
2160945523631/3915399561216*(3-2*x)^(23/2)+8535085022072145119870938660211240879
08041634697244059/7830799122432*(3-2*x)^(25/2)-688617380989400554399451644246187
1486007042005189775/125627793408*(3-2*x)^(27/2)+13632998796724539514184825376514
7208279814148352958009/5527622909952*(3-2*x)^(29/2)-5506609142081759016786540198
6871791412011888132876913/5527622909952*(3-2*x)^(31/2)+2737487528928439357869138
774910126923363791747141675/755914244096*(3-2*x)^(33/2)-116645721702158768842036
68230743495214488310113371105/9826885173248*(3-2*x)^(35/2)+126466293333827227169
04430763732665179119615389552413/25098715136*(3-2*x)^(17/2)-25936732036850444416
95042001860835122939346700333136537/6199382638592*(3-2*x)^(19/2)[phone]
378942268937217995835353849465/1048576*(3-2*x)^(1/2)-503502693505289734438057515
605193725/103079215104*(3-2*x)^(67/2)-3254850748003483429666738850178379/8246337
20832*(3-2*x)^(71/2)+360433340020130123942335063779145/5772436045824*(3-2*x)^(73
/2)+1808668971148992206490172102870787954874541181/334114095890432*(3-2*x)^(57/2
)+129886852748727110357425618672922324659/1133871366144*(3-2*x)^(65/2)[phone]
17693223698395672584150593863016075796143/29480655519744*(3-2*x)^(45/2)-11968977
253082880651292892111395530933265219/25701084299264*(3-2*x)^(59/2)[phone]
7571533836489036461787385135079265/2680059592704*(3-2*x)^(49/2)-6424339671914037
4998473027009027485263697/29480655519744*(3-2*x)^(63/2)+267223998479033784429201
9294315182385216573077301785/117922622078976*(3-2*x)^(41/2)+11863238464538262372
12517196312193819452761764018822545/3915399561216*(3-2*x)^(21/2)-176509423589632
62675871173166229809316744939271143/51904512*(3-2*x)^(11/2)-22397546321209486953
062074374795737299957063565/3145728*(3-2*x)^(3/2)+404531566689883337048499233527
781983599187634017/12582912*(3-2*x)^(5/2)-11885980275522548300826832180646971886
05612952419/12582912*(3-2*x)^(7/2)+383158337916629409182357295398999362577247144
5345/18874368*(3-2*x)^(9/2)+9977850126168010187169130424774568330973123412551261
/21592276992*(3-2*x)^(13/2)-1255696718499588580979726331572072320357969297077745
/2399141888*(3-2*x)^(15/2)-55011835288361289002011693179378316699033102675/10023
42287671296*(3-2*x)^(55/2))/((3-2*x)^2-7+14*x)^19-719227969403113346821049018403
5/1624130632549415368266063684414865684824064/(-7+2*14^(1/2))^(1/2)*arctan((2*(3
-2*x)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))*14^(1/2)
-7192279694031133468210490184035/1624130632549415368266063684414865684824064/(-7
+2*14^(1/2))^(1/2)*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))
^(1/2))*(7+2*14^(1/2))*14^(1/2)+52865/277038748585308867472/(3-2*x)^(31/2)+14333
/32395660116830472406/(3-2*x)^(29/2)+1478345/1689042692987850837168/(3-2*x)^(27/
2)+475387/312785683886639043920/(3-2*x)^(25/2)[phone]/7006399319060714583808/(
3-2*x)^(23/2)[phone]/73567192850137503129984/(3-2*x)^(21/2)+355/5266289575642
392066/(3-2*x)^(33/2)+1/3111898385606868039/(3-2*x)^(39/2)+10/295231385301164403
7/(3-2*x)^(37/2)+143/7819642097165976098/(3-2*x)^(35/2)[phone]/1863702218870
150079292928/(3-2*x)^(19/2)[phone]/1667523037936450070946304/(3-2*x)^(17/2)+
102495360575/16479051198430800701116416/(3-2*x)^(15/2)[phone]/178523054649
66700759542784/(3-2*x)^(13/2)[phone]/1480368099325700262983624704/(3-2*x
)^(11/2)[phone]/1076631344964145645806272512/(3-2*x)^(5/2)[phone]
5/30145677658996078082575630336/(3-2*x)^(3/2)[phone]/100934188590388654294
338048/(3-2*x)^(9/2)[phone]/105509871806486273289014706176/(3-2*x)^(7/2
)

_______________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{20}{\left (-2 \, x + 3\right )}^{\frac{41}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)),x, algorithm="maxima")

[Out]

integrate(1/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)), x)

_______________________________________________________________________________________

Fricas [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/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)),x, algorithm="fricas")

[Out]

Timed out

_______________________________________________________________________________________

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/(3-2*x)**(41/2)/(2*x**2+x+1)**20,x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.227316, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)),x, algorithm="giac")

[Out]

Done