3.49 \(\int \frac {1}{(3-2 x)^{41/2} (1+x+2 x^2)^{20}} \, dx\)
Optimal. Leaf size=1058 \[ \text {result too large to display} \]
[Out]
1/33516*(113+373*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^18+1/7976808*(40657+107329*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^17+5/5
95601664*(751303+1831285*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^16+1/25015269888*(184959785+429411497*x)/(3-2*x)^(39/2)
/(2*x^2+x+1)^15+1/4902992898048*(41652915209+92630823167*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^14+1/297448235814912*(2
871555518177+6100156355517*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^13+1/7138757659557888*(77559130805859+156274047129113
*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^12+5/1099368679571914752*(2656658801194921+5020880176134289*x)/(3-2*x)^(39/2)/(
2*x^2+x+1)^11+1/3420258114223734784*(45187921585208601+78752911037377255*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^10+1/43
0952522392190582784*(6063974149878048635+9477172618423641847*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^9+1/482666825079253
45271808*(691833601144925854831+919498192874055581221*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^8+23/157671162859222794554
5728*(919498192874055581221+908287136092467468517*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^7+115/101879828309036267250647
04*(908287136092467468517+298281884944522225747*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^6+23/20375965661807253450129408*
(2599313568802265110081-10426142448623187379187*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^5-23/20018492580021161284337664*
(10426142448623187379187+27513723463194262383705*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^4-115/7643424439644443399474380
8*(26513224428169016478843+30673415406553789342019*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^3-115/12589169665296730305016
6272*(88411609113007981044643-5712269536245152162963*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^2+115/195831528126838026966
925312*(28561347681225760814815+965934812839019490346107*x)/(3-2*x)^(39/2)/(2*x^2+x+1)+1/133*x/(3-2*x)^(39/2)/
(2*x^2+x+1)^19+115/3248261265098830736532127368829731369648128*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^
(1/2))*(30297118912219360725028693061-8061110911143276053983022787*14^(1/2))*(-14+4*14^(1/2))^(1/2)-115/324826
1265098830736532127368829731369648128*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(30297118912219360
725028693061-8061110911143276053983022787*14^(1/2))*(-14+4*14^(1/2))^(1/2)+115/1624130632549415368266063684414
865684824064*arctan((-2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(30297118912219360725028693
061+8061110911143276053983022787*14^(1/2))*(14+4*14^(1/2))^(1/2)-115/16241306325494153682660636844148656848240
64*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(30297118912219360725028693061+8061110
911143276053983022787*14^(1/2))*(14+4*14^(1/2))^(1/2)-927027754781476746208047620505/5800466544819340600950227
4443388060172288/(3-2*x)^(1/2)+11155168222970774232376891145/1685166332532616560247354224017408/(3-2*x)^(23/2)
+14011818498091020272474956375/10110997995195699361484125344104448/(3-2*x)^(21/2)-1305695962836335553428578542
5/106924014357253562723941220352/(3-2*x)^(39/2)-3948194343291401740321996415/202881463139404195937734623232/(3
-2*x)^(37/2)-304688229262620222736480811/537361713180043545997243056128/(3-2*x)^(35/2)+21243158467565674556538
62925/1688851098565851144562763890688/(3-2*x)^(33/2)+47657515074514118796095929535/666328524343253997036581389
59872/(3-2*x)^(31/2)+34911619993974714062172751985/124667917457770102671360389021696/(3-2*x)^(29/2)+1490663098
08794760843017404825/1624981820656451683095663001731072/(3-2*x)^(27/2)+15848613964169066543734380171/601845118
761648771516912222863360/(3-2*x)^(25/2)-101190274412779618678573275245/3963511214116714149701777134888943616/(
3-2*x)^(15/2)-460503190416958283087439337135/34350430522344855964082068502370844672/(3-2*x)^(13/2)-22116195887
90911794826342607495/406920484649315986036049119181931544576/(3-2*x)^(11/2)-4986681479187781853417316522775/87
006998172290109014253411665082090258432/(3-2*x)^(3/2)+173441368149804378661935869705/8965084889073520100515924
47177261056/(3-2*x)^(19/2)-22724090823469905152713519545/1604278348571050965355481221264572416/(3-2*x)^(17/2)-
143401467550777247627940437025/73985542663511997461099839851260280832/(3-2*x)^(9/2)-46110532781171430109075623
17585/7250583181024175751187784305423507521536/(3-2*x)^(7/2)-405965372440630510720926890227/207159519457833592
8910795515835287863296/(3-2*x)^(5/2)
________________________________________________________________________________________
Rubi [A] time = 2.49, antiderivative size = 1058, normalized size of antiderivative = 1.00,
number of steps used = 49, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used
= {740, 822, 828, 826, 1169, 634, 618, 204, 628} \[ \text {result too large to display} \]
Antiderivative was successfully verified.
[In]
Int[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]
[Out]
-13056959628363355534285785425/(106924014357253562723941220352*(3 - 2*x)^(39/2)) - 394819434329140174032199641
5/(202881463139404195937734623232*(3 - 2*x)^(37/2)) - 304688229262620222736480811/(537361713180043545997243056
128*(3 - 2*x)^(35/2)) + 2124315846756567455653862925/(1688851098565851144562763890688*(3 - 2*x)^(33/2)) + 4765
7515074514118796095929535/(66632852434325399703658138959872*(3 - 2*x)^(31/2)) + 34911619993974714062172751985/
(124667917457770102671360389021696*(3 - 2*x)^(29/2)) + 149066309808794760843017404825/(16249818206564516830956
63001731072*(3 - 2*x)^(27/2)) + 15848613964169066543734380171/(601845118761648771516912222863360*(3 - 2*x)^(25
/2)) + 11155168222970774232376891145/(1685166332532616560247354224017408*(3 - 2*x)^(23/2)) + 14011818498091020
272474956375/(10110997995195699361484125344104448*(3 - 2*x)^(21/2)) + 173441368149804378661935869705/(89650848
8907352010051592447177261056*(3 - 2*x)^(19/2)) - 22724090823469905152713519545/(160427834857105096535548122126
4572416*(3 - 2*x)^(17/2)) - 101190274412779618678573275245/(3963511214116714149701777134888943616*(3 - 2*x)^(1
5/2)) - 460503190416958283087439337135/(34350430522344855964082068502370844672*(3 - 2*x)^(13/2)) - 22116195887
90911794826342607495/(406920484649315986036049119181931544576*(3 - 2*x)^(11/2)) - 1434014675507772476279404370
25/(73985542663511997461099839851260280832*(3 - 2*x)^(9/2)) - 4611053278117143010907562317585/(725058318102417
5751187784305423507521536*(3 - 2*x)^(7/2)) - 405965372440630510720926890227/(207159519457833592891079551583528
7863296*(3 - 2*x)^(5/2)) - 4986681479187781853417316522775/(87006998172290109014253411665082090258432*(3 - 2*x
)^(3/2)) - 927027754781476746208047620505/(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 + 107
329*x)/(7976808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^17) + (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) + (41652915209
+ 92630823167*x)/(4902992898048*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14) + (2871555518177 + 6100156355517*x)/(297
448235814912*(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))/(1099368679571914752*(3 - 2*x)
^(39/2)*(1 + x + 2*x^2)^11) + (45187921585208601 + 78752911037377255*x)/(3420258114223734784*(3 - 2*x)^(39/2)*
(1 + x + 2*x^2)^10) + (6063974149878048635 + 9477172618423641847*x)/(430952522392190582784*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^9) + (691833601144925854831 + 919498192874055581221*x)/(48266682507925345271808*(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))/(101879828309036267250
64704*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + (23*(2599313568802265110081 - 10426142448623187379187*x))/(2037596
5661807253450129408*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^5) - (23*(10426142448623187379187 + 275137234631942623837
05*x))/(20018492580021161284337664*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) - (115*(26513224428169016478843 + 30673
415406553789342019*x))/(76434244396444433994743808*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^3) - (115*(884116091130079
81044643 - 5712269536245152162963*x))/(125891696652967303050166272*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + (115*
(28561347681225760814815 + 965934812839019490346107*x))/(195831528126838026966925312*(3 - 2*x)^(39/2)*(1 + x +
2*x^2)) + (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]]])/81206531627470768413303184220743284
2412032 - (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]]])/812065316274707684133031842207432842
412032 + (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*(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
Rule 204
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])
Rule 618
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]
Rule 628
Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]
Rule 634
Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] && !NiceSqrtQ[b^2 - 4*a*c]
Rule 740
Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m + 1)*(
b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e
+ a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*Simp[b*c*d*e*(2*p - m
+ 2) + b^2*e^2*(m + p + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3) - c*e*(2*c*d - b*e)*(m + 2*p + 4)*x
, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b
*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && LtQ[p, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]
Rule 822
Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[((d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x
)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*
c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2
*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -
b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b,
c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] ||
IntegerQ[p] || IntegersQ[2*m, 2*p])
Rule 826
Int[((f_.) + (g_.)*(x_))/(Sqrt[(d_.) + (e_.)*(x_)]*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)), x_Symbol] :> Dist[2,
Subst[Int[(e*f - d*g + g*x^2)/(c*d^2 - b*d*e + a*e^2 - (2*c*d - b*e)*x^2 + c*x^4), x], x, Sqrt[d + e*x]], x] /
; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0]
Rule 828
Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[((
e*f - d*g)*(d + e*x)^(m + 1))/((m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/(c*d^2 - b*d*e + a*e^2), Int[((d
+ e*x)^(m + 1)*Simp[c*d*f - f*b*e + a*e*g - c*(e*f - d*g)*x, x])/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,
d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && FractionQ[m] && LtQ[m, -1]
Rule 1169
Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[a/c, 2]}, With[{r =
Rt[2*q - b/c, 2]}, Dist[1/(2*c*q*r), Int[(d*r - (d - e*q)*x)/(q - r*x + x^2), x], x] + Dist[1/(2*c*q*r), Int[(
d*r + (d - e*q)*x)/(q + r*x + x^2), x], x]]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2
- b*d*e + a*e^2, 0] && NegQ[b^2 - 4*a*c]
Rubi steps
\begin {align*} \int \frac {1}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{20}} \, dx &=\frac {x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac {\int \frac {3640-3164 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{19}} \, dx}{3724} \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 6.18, size = 1100, normalized size = 1.04 \[ \text {result too large to display} \]
Antiderivative was successfully verified.
[In]
Integrate[1/((3 - 2*x)^(41/2)*(1 + x + 2*x^2)^20),x]
[Out]
x/(133*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^19) + ((44296 + 146216*x)/(3528*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^18) +
((223125616 + 589021552*x)/(3332*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^17) + ((865861681440 + 2110519336800*x)/(31
36*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^16) + ((2984274342235200 + 6928434268875840*x)/(2940*(3 - 2*x)^(39/2)*(1 +
x + 2*x^2)^15) + ((9408813737133390720 + 20924013532366815360*x)/(2744*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^14) +
((27243065619141593598720 + 57873497074462503141120*x)/(2548*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^13) + ((7211037
7354780278913835520 + 145295342948683106164016640*x)/(2352*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^12) + ((1729014581
08932896335179801600 + 326770416680301421681066214400*x)/(2156*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^11) + ((370557
652515461812186329087129600 + 645802967231886306826540424448000*x)/(1960*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^10)
+ ((696175598675973438759010577554944000 + 1088028437838790621809440473088716800*x)/(1764*(3 - 2*x)^(39/2)*(1
+ x + 2*x^2)^9) + ((1111965063471244015489248163496668569600 + 1477884081820868038735185945420330393600*x)/(15
68*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^8) + ((1427636023038958525418189623276039160217600 + 141022945428029359210
8580217248432347955200*x)/(1372*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^7) + ((12833088033950671688188079976960734366
39232000 + 421439161286999121770135584246204836237312000*x)/(1176*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^6) + ((3599
09043739097249991695788946258930146664448000 - 1443636121324398194831693460992758930913796096000*x)/(980*(3 -
2*x)^(39/2)*(1 + x + 2*x^2)^5) + ((-1152021624816869759475691381872221626869209284608000 - 3040089329780519199
031170166260953381570260254720000*x)/(784*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^4) + ((-225574628269714524568112826
3365627409125133109002240000 - 2609695511325529255410382651665073470845732989009920000*x)/(588*(3 - 2*x)^(39/2
)*(1 + x + 2*x^2)^3) + ((-1790251120769313069211522499042240401000172830460805120000 + 11566803321414359689429
5804604678509924267822733393920000*x)/(392*(3 - 2*x)^(39/2)*(1 + x + 2*x^2)^2) + ((728708609249104660434063569
00947461252288728322038169600000 + 2464467090087282692969213073458776810025190662610343034880000*x)/(196*(3 -
2*x)^(39/2)*(1 + x + 2*x^2)) + (-530550566665897087493026465460148012491929957574880460800000/(3 - 2*x)^(39/2)
+ (-1708089006242241264480481073293611769771298388785813753364480000/(37*(3 - 2*x)^(37/2)) + (-69674095008990
9200017539783692427216704271188038402697920512000/(3 - 2*x)^(35/2) + (7573666677621473556024460064742611515974
09525795681824661504000000/(3 - 2*x)^(33/2) + (616772664905423340350737254793402194192083509401081655628275875
8400000/(31*(3 - 2*x)^(31/2)) + (980445504127015992472138196645778610361943940861637274650890661068800000/(29*
(3 - 2*x)^(29/2)) + (4496423323436580179825935667807239175646629240803415910250222313472000000/(3 - 2*x)^(27/2
) + (487904184130260773926886832047572655461484781443782543411352841560457216000/(3 - 2*x)^(25/2) + (429268867
21523802306414887155091882259902542088067698170622802545418240000000/(3 - 2*x)^(23/2) + (289369259398036472323
1826294558630623656919099359688069727689450554368000000000/(3 - 2*x)^(21/2) + (1187674764929302643741666332431
40666046068763101817907661320807641190359040000000/(3 - 2*x)^(19/2) + (-23130641371662285970537372414163682847
22516912423159767489332810437803253760000000/(3 - 2*x)^(17/2) + (-99223951965379086042262394895796485235598584
6800936213338418761762097950023680000000/(3 - 2*x)^(15/2) + (-109415183151546322431572415879018096250836012099
731766901467841654602614755123200000000/(3 - 2*x)^(13/2) + (-8073268485314233063840337934095431560069216535225
849300748018943930634745621913600000000/(3 - 2*x)^(11/2) + (-4433798722621123130520736149457228398171520393809
63932483996666511839997547213824000000000/(3 - 2*x)^(9/2) + (-183301908922166977441737067901437000873585615761
36178754174544727578117325359791923200000000/(3 - 2*x)^(7/2) + (-553541210002735957048844214716028245499086746
401723523324780660557661668413725058949120000000/(3 - 2*x)^(5/2) + (-11332385663391839740343974428370683887566
771471384841151672642393999283182139266339840000000000/(3 - 2*x)^(3/2) + (-13272202629081314874038396353552342
7142665518975435293064356777236410088640362467513344000000000/Sqrt[3 - 2*x] + ((Sqrt[(7 - I*Sqrt[7])/2]*(-1858
108368071384082365375489497327979997317265656094102900994881309741240965074545186816000000000 - (3853414006278
103146767987622401496699336335555921865837542016885265897482833115690092544000000000*I)*Sqrt[7])*ArcTanh[(Sqrt
[2]*Sqrt[3 - 2*x])/Sqrt[7 - I*Sqrt[7]]])/(-14 + (2*I)*Sqrt[7]) + (Sqrt[(7 + I*Sqrt[7])/2]*(-185810836807138408
2365375489497327979997317265656094102900994881309741240965074545186816000000000 + (385341400627810314676798762
2401496699336335555921865837542016885265897482833115690092544000000000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2
*x])/Sqrt[7 + I*Sqrt[7]]])/(-14 - (2*I)*Sqrt[7]))/7)/42)/70)/98)/126)/154)/182)/210)/238)/266)/294)/322)/350)/
378)/406)/434)/462)/490)/518)/546)/196)/392)/588)/784)/980)/1176)/1372)/1568)/1764)/1960)/2156)/2352)/2548)/27
44)/2940)/3136)/3332)/3528)/3724
________________________________________________________________________________________
fricas [B] time = 151.30, size = 2763, normalized size = 2.61 \[ \text {result too large to display} \]
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, algorithm="fricas")
[Out]
1/392164866433134591452265700785383646021637848990793338705942972429050741081771910613067676554567307313820760
631947790705447918522595322425206164852572160*(616525316537858546962128448983043227187951381815778781478549978
900*579590499192185855665304541951571706717845859384545414208024478076585205782332794174344701326^(1/4)*sqrt(1
2868460882463048970358421717432178503450051394)*sqrt(14)*sqrt(7)*(549755813888*x^58 - 11269994184704*x^57 + 10
7064944754688*x^56 - 630638638006272*x^55 + 2618521301286912*x^54 - 8342252417974272*x^53 + 21849572376576000*
x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363618304*x^49 + 323261995581177856*x^48 -
517079841212727296*x^47 + 778117896260812800*x^46 - 1105641165387988992*x^45 + 1491287028233404416*x^44 - 1919
929663119949824*x^43 + 2363050939901804544*x^42 - 2786274020645928960*x^41 + 3161145685194047488*x^40 - 345375
3931369283584*x^39 + 3634098467102523392*x^38 - 3697893960325791744*x^37 + 3640651752731836416*x^36 - 34617982
12247617536*x^35 + 3194540251789393920*x^34 - 2861544579495297024*x^33 + 2477632938217930752*x^32 - 2088430257
127768064*x^31 + 1712761005459316736*x^30 - 1355447485390974976*x^29 + 1048940886155151360*x^28 - 790511024135
089152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 282845069599813728*x^24 - 186113897194906128
*x^23 + 123982890381352520*x^22 - 78116367732251996*x^21 + 46488580159296898*x^20 - 29591055660829971*x^19 + 1
6200795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441*x^16 - 2296849711499532*x^15 + 14482898824007
88*x^14 - 756896247319212*x^13 + 182213447974992*x^12 - 240797810407770*x^11 + 25549234281774*x^10 - 265002817
27302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164*x^6 + 3755740313808*x^5 + 1820618017974*x^
4 + 463742325333*x^3 + 139858796529*x^2 + 19758444939*x + 3486784401)*sqrt(37814840288016788880034681293391537
27662345024772741260943*sqrt(14) + 14149022371848728385570789036684124101210161640127797919744)*arctan(1/34885
55476273159707600878934940824497561724963674913242575009589894914045286581081812447079130476773106112671051669
99787145808229165832263016823558232093156487983192678515257488180949060050957316309922278384344605468898548205
7622250395943920813921700*579590499192185855665304541951571706717845859384545414208024478076585205782332794174
344701326^(3/4)*sqrt(1634857335323112850812492677092639503349451327418417311)*sqrt(643423044123152448517921085
87160892517250256970)*sqrt(12868460882463048970358421717432178503450051394)*sqrt(57959049919218585566530454195
1571706717845859384545414208024478076585205782332794174344701326^(1/4)*sqrt(1286846088246304897035842171743217
8503450051394)*sqrt(-2*x + 3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 14149
022371848728385570789036684124101210161640127797919744)*(8061110911143276053983022787*sqrt(14) - 3029711891221
9360725028693061) - 210380976680132535569563443287236823905478719259451204168457324874865216162080856741370745
650892815340*x + 963732050599621794425456308219340060829468062999882820661390*sqrt(166789371965963959581098742
817586289130679764812156476721038706576007991289033281726) + 3155714650201988033543451649308552358582180788891
76806252685987312297824243121285112056118476339223010)*(30297118912219360725028693061*sqrt(14)*sqrt(7) - 11285
5552756005864755762319018*sqrt(7))*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) +
14149022371848728385570789036684124101210161640127797919744) - 1/331641722680775415760424069447358035430711841
28057805445740643992848947205475131833297639875732592434272266883677954804521721584006729715127306903510*57959
0499192185855665304541951571706717845859384545414208024478076585205782332794174344701326^(3/4)*sqrt(1286846088
2463048970358421717432178503450051394)*(30297118912219360725028693061*sqrt(14)*sqrt(7) - 112855552756005864755
762319018*sqrt(7))*sqrt(-2*x + 3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1
4149022371848728385570789036684124101210161640127797919744) + 2/7*sqrt(14)*sqrt(7) + sqrt(7)) + 61652531653785
8546962128448983043227187951381815778781478549978900*579590499192185855665304541951571706717845859384545414208
024478076585205782332794174344701326^(1/4)*sqrt(12868460882463048970358421717432178503450051394)*sqrt(14)*sqrt
(7)*(549755813888*x^58 - 11269994184704*x^57 + 107064944754688*x^56 - 630638638006272*x^55 + 2618521301286912*
x^54 - 8342252417974272*x^53 + 21849572376576000*x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188
583312363618304*x^49 + 323261995581177856*x^48 - 517079841212727296*x^47 + 778117896260812800*x^46 - 110564116
5387988992*x^45 + 1491287028233404416*x^44 - 1919929663119949824*x^43 + 2363050939901804544*x^42 - 27862740206
45928960*x^41 + 3161145685194047488*x^40 - 3453753931369283584*x^39 + 3634098467102523392*x^38 - 3697893960325
791744*x^37 + 3640651752731836416*x^36 - 3461798212247617536*x^35 + 3194540251789393920*x^34 - 286154457949529
7024*x^33 + 2477632938217930752*x^32 - 2088430257127768064*x^31 + 1712761005459316736*x^30 - 13554474853909749
76*x^29 + 1048940886155151360*x^28 - 790511024135089152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^
25 + 282845069599813728*x^24 - 186113897194906128*x^23 + 123982890381352520*x^22 - 78116367732251996*x^21 + 46
488580159296898*x^20 - 29591055660829971*x^19 + 16200795673453545*x^18 - 8941894120163277*x^17 + 5578893209169
441*x^16 - 2296849711499532*x^15 + 1448289882400788*x^14 - 756896247319212*x^13 + 182213447974992*x^12 - 24079
7810407770*x^11 + 25549234281774*x^10 - 26500281727302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354
811164*x^6 + 3755740313808*x^5 + 1820618017974*x^4 + 463742325333*x^3 + 139858796529*x^2 + 19758444939*x + 348
6784401)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 14149022371848728385570789
036684124101210161640127797919744)*arctan(1/882212681369915578508303477421571883476414798304262215955022242191
75844282483036150488446475189965496243820538044661002745074619234209862134823250046493206397567627980015263931
446769927917308008043494406341475991998227625530289790494302092900288913988891810201600*5795904991921858556653
04541951571706717845859384545414208024478076585205782332794174344701326^(3/4)*sqrt(163485733532311285081249267
7092639503349451327418417311)*sqrt(12868460882463048970358421717432178503450051394)*sqrt(-41148303668605102441
456509058170322829014409271501775935163876370158714880*5795904991921858556653045419515717067178458593845454142
08024478076585205782332794174344701326^(1/4)*sqrt(12868460882463048970358421717432178503450051394)*sqrt(-2*x +
3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1414902237184872838557078903668
4124101210161640127797919744)*(8061110911143276053983022787*sqrt(14) - 30297118912219360725028693061) - 865682
03145318221187283609975727790977789396744211474536443644223954841516195622280522256097905125871171599697702873
04130190501793583932157415533491476293668491490879550259200*x + 3965593907324073569969746483230704022801033497
1057954913097176452275244656121253105297648773136457461603590116807858434249634034483200*sqrt(1667893719659639
59581098742817586289130679764812156476721038706576007991289033281726) + 12985230471797733178092541496359168646
66840951163172118046654663359322622742934334207833841468576888067573995465543095619528575269037589823612330023
7214440502737236319325388800)*(30297118912219360725028693061*sqrt(14)*sqrt(7) - 112855552756005864755762319018
*sqrt(7))*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1414902237184872838557078
9036684124101210161640127797919744) - 1/3316417226807754157604240694473580354307118412805780544574064399284894
7205475131833297639875732592434272266883677954804521721584006729715127306903510*579590499192185855665304541951
571706717845859384545414208024478076585205782332794174344701326^(3/4)*sqrt(12868460882463048970358421717432178
503450051394)*(30297118912219360725028693061*sqrt(14)*sqrt(7) - 112855552756005864755762319018*sqrt(7))*sqrt(-
2*x + 3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 14149022371848728385570789
036684124101210161640127797919744) - 2/7*sqrt(14)*sqrt(7) - sqrt(7)) + 131989413465*57959049919218585566530454
1951571706717845859384545414208024478076585205782332794174344701326^(1/4)*sqrt(1286846088246304897035842171743
2178503450051394)*(7778507309755217852827317402300628134029188898204494505702056024604672*x^58 - 1594593998499
81965982960006747162876747598372413192137366892148504395776*x^57 + 1514864298574828676838120064098047329102184
537925325304985475410791759872*x^56 - 892292019770295427942453647511410804824823331485283075985347101722463436
8*x^55 + 37049516473070962334132314494495535591639403546454145111565499223693590528*x^54 - 1180347160935271234
57170227067542059725196738523651032986322545956112826368*x^53 + 3091500883715018126702794566785458630846874314
24928239641662378993516544000*x^52 - 7029813219577723067338398307511579526660847075114275792779434714800806952
96*x^51 + 1434633067237123554683051124392269116634712360343909848074251531317913059328*x^50 - 2668269505590172
280049044367109090002286110479558215558121161934960041394176*x^49 + 457384120744655026269982119717501065035316
3360439432757916212490278077988864*x^48 - 73161742413508666198700167998340894258382768146404489814486698266055
66132224*x^47 + 11009607522130108303720327150964714549103431151620256934238701471906607923200*x^46 - 156437415
84311556183830093683288060491254305358060645835780583727821171458048*x^45 + 2110025352532224532336938735530842
3247443333718020271970799243119655863189504*x^44 - 27165127755860162519562776582318065307577993759440407412731
079664252858925056*x^43 + 33434860614488797445569848022836846490704329307177012620295046744354886516736*x^42 -
39423053452220154576417414767228020698502502067094287273232395028270405386240*x^41 + 447271210204836554576971
63684573632669291499878162600868891481089937948803072*x^40 - 4886724164180449109058887543828561168102105844573
2456635375173947494808682496*x^39 + 51418940512534773548948006303169583307602870096615653180441644588670698651
648*x^38 - 52321584373373921405102385656105852737472886187697968626781038013392969793536*x^37 + 51511663097513
038298418017302280041042555202201663326957909758403045704597504*x^36 - 489810603519174731161686619741905999571
94981022285273133557262743720935030784*x^35 + 4519962149033940434515349853481794660915616369562519347955038731
6578561556480*x^34 - 40488058273321419593059609736233623808382658876397516863365177557098594041856*x^33 + 3505
6083872074800487067567855249064178835868891722789291640219304625845567488*x^32 - 29549246430146582583344598166
261232974679787401051000932261220746996918255616*x^31 + 242338937838739945110707883369250065804077743121445205
88033549546084404035584*x^30 - 19178256794663007372927055945418126742331837591606363287110323072444760326144*x
^29 + 14841488064956066674396728991150443932171972367710399727450886674237452451840*x^28 - 1118495816568042648
3017504655762227434727279734038187934149692650461581017088*x^27 + 80897166364264609042152707250524108677377533
24963557154237119238802310692864*x^26 - 5778094322150667683524604055656091788176032034840667186889924766260787
150848*x^25 + 4001981217534875094193016454474000992606384388164616536275697009008293445632*x^24 - 263332969512
2681099815509968337451855552798186482448768403487600071757791232*x^23 + 17542366897322253251089903529813657607
14551507499414546495918038905132154880*x^22 - 1105270234651195608285450831265261372770545225432391865666772571
865191809024*x^21 + 657767960709374731018983428860987490965225871389829139166803055706072154112*x^20 - 4186845
08551704217004632820201538271464823125615024056822995425518287847424*x^19 + 2292254204254442941911476461763416
99520323501828496374466278758575222292480*x^18 - 1265190599528928078062208761554970753195041029849816038292222
51966222041088*x^17 + 78935884826693368065254828931908211891519394127734424705049022825815343104*x^16 - 324981
77952781175771570102356850846229225588393916533119446726744429559808*x^15 + 2049188594701091333375687670878228
9162249577789257433177529423102866358272*x^14 - 10709341936487878696123475460109781566666232126271592963297115
430325321728*x^13 + 2578142151849856182075133918988458447112007949561957497307465546935042048*x^12 - 340705360
6551726299099037573789747390828310557439249471191823118374010880*x^11 + 36149668743642480393069390477870078076
9490487415840984941622807133945856*x^10 - 37495307901989006080062610714625460487937855057716050197265913068965
0688*x^9 + 361092974099972372832558605269197722032357635208049111095191908288299008*x^8 + 14100218474776899700
9392595202128779106364989840476870319621019208253440*x^7 + 146999213652233656885845331514573869620245040110547
854481309077147222016*x^6 + 53140053722923555611929392435834198275650668430851979724323340159025152*x^5 + 2575
9965066905016287490162796639138798257488660077636512705521601478656*x^4 + 656150053590976829964372071235147875
0499548998321662130594802672074752*x^3 + 197886524098866028084493164340758882951573699949383461081430556776857
6*x^2 - 3781484028801678888003468129339153727662345024772741260943*sqrt(14)*(549755813888*x^58 - 1126999418470
4*x^57 + 107064944754688*x^56 - 630638638006272*x^55 + 2618521301286912*x^54 - 8342252417974272*x^53 + 2184957
2376576000*x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363618304*x^49 + 323261995581177
856*x^48 - 517079841212727296*x^47 + 778117896260812800*x^46 - 1105641165387988992*x^45 + 1491287028233404416*
x^44 - 1919929663119949824*x^43 + 2363050939901804544*x^42 - 2786274020645928960*x^41 + 3161145685194047488*x^
40 - 3453753931369283584*x^39 + 3634098467102523392*x^38 - 3697893960325791744*x^37 + 3640651752731836416*x^36
- 3461798212247617536*x^35 + 3194540251789393920*x^34 - 2861544579495297024*x^33 + 2477632938217930752*x^32 -
2088430257127768064*x^31 + 1712761005459316736*x^30 - 1355447485390974976*x^29 + 1048940886155151360*x^28 - 7
90511024135089152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 282845069599813728*x^24 - 1861138
97194906128*x^23 + 123982890381352520*x^22 - 78116367732251996*x^21 + 46488580159296898*x^20 - 295910556608299
71*x^19 + 16200795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441*x^16 - 2296849711499532*x^15 + 144
8289882400788*x^14 - 756896247319212*x^13 + 182213447974992*x^12 - 240797810407770*x^11 + 25549234281774*x^10
- 26500281727302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164*x^6 + 3755740313808*x^5 + 18206
18017974*x^4 + 463742325333*x^3 + 139858796529*x^2 + 19758444939*x + 3486784401) + 279562679474852283443466797
268108117189203842033755028120580564975616*x + 493345904955621676664941406943720206804477368294861814330436291
13344)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1414902237184872838557078903
6684124101210161640127797919744)*log(4114830366860510244145650905817032282901440927150177593516387637015871488
0/1634857335323112850812492677092639503349451327418417311*5795904991921858556653045419515717067178458593845454
14208024478076585205782332794174344701326^(1/4)*sqrt(12868460882463048970358421717432178503450051394)*sqrt(-2*
x + 3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1414902237184872838557078903
6684124101210161640127797919744)*(8061110911143276053983022787*sqrt(14) - 30297118912219360725028693061) - 529
51533613915553191922904161192663574869868505075814894398859634892573324132628969090213563223147240807581427299
25427200*x + 24256513529606021838214197524700823604475704121457581896019753481444860834611200*sqrt(16678937196
5963959581098742817586289130679764812156476721038706576007991289033281726) + 794273004208733297878843562417889
9536230480275761372234159828945233885998619894345363532034483472086121137214094888140800) - 131989413465*57959
0499192185855665304541951571706717845859384545414208024478076585205782332794174344701326^(1/4)*sqrt(1286846088
2463048970358421717432178503450051394)*(7778507309755217852827317402300628134029188898204494505702056024604672
*x^58 - 159459399849981965982960006747162876747598372413192137366892148504395776*x^57 + 1514864298574828676838
120064098047329102184537925325304985475410791759872*x^56 - 892292019770295427942453647511410804824823331485283
0759853471017224634368*x^55 + 37049516473070962334132314494495535591639403546454145111565499223693590528*x^54
- 118034716093527123457170227067542059725196738523651032986322545956112826368*x^53 + 3091500883715018126702794
56678545863084687431424928239641662378993516544000*x^52 - 7029813219577723067338398307511579526660847075114275
79277943471480080695296*x^51 + 1434633067237123554683051124392269116634712360343909848074251531317913059328*x^
50 - 2668269505590172280049044367109090002286110479558215558121161934960041394176*x^49 + 457384120744655026269
9821197175010650353163360439432757916212490278077988864*x^48 - 73161742413508666198700167998340894258382768146
40448981448669826605566132224*x^47 + 1100960752213010830372032715096471454910343115162025693423870147190660792
3200*x^46 - 15643741584311556183830093683288060491254305358060645835780583727821171458048*x^45 + 2110025352532
2245323369387355308423247443333718020271970799243119655863189504*x^44 - 27165127755860162519562776582318065307
577993759440407412731079664252858925056*x^43 + 334348606144887974455698480228368464907043293071770126202950467
44354886516736*x^42 - 39423053452220154576417414767228020698502502067094287273232395028270405386240*x^41 + 447
27121020483655457697163684573632669291499878162600868891481089937948803072*x^40 - 4886724164180449109058887543
8285611681021058445732456635375173947494808682496*x^39 + 51418940512534773548948006303169583307602870096615653
180441644588670698651648*x^38 - 52321584373373921405102385656105852737472886187697968626781038013392969793536*
x^37 + 51511663097513038298418017302280041042555202201663326957909758403045704597504*x^36 - 489810603519174731
16168661974190599957194981022285273133557262743720935030784*x^35 + 4519962149033940434515349853481794660915616
3695625193479550387316578561556480*x^34 - 40488058273321419593059609736233623808382658876397516863365177557098
594041856*x^33 + 35056083872074800487067567855249064178835868891722789291640219304625845567488*x^32 - 29549246
430146582583344598166261232974679787401051000932261220746996918255616*x^31 + 242338937838739945110707883369250
06580407774312144520588033549546084404035584*x^30 - 1917825679466300737292705594541812674233183759160636328711
0323072444760326144*x^29 + 14841488064956066674396728991150443932171972367710399727450886674237452451840*x^28
- 11184958165680426483017504655762227434727279734038187934149692650461581017088*x^27 + 80897166364264609042152
70725052410867737753324963557154237119238802310692864*x^26 - 5778094322150667683524604055656091788176032034840
667186889924766260787150848*x^25 + 400198121753487509419301645447400099260638438816461653627569700900829344563
2*x^24 - 2633329695122681099815509968337451855552798186482448768403487600071757791232*x^23 + 17542366897322253
25108990352981365760714551507499414546495918038905132154880*x^22 - 1105270234651195608285450831265261372770545
225432391865666772571865191809024*x^21 + 657767960709374731018983428860987490965225871389829139166803055706072
154112*x^20 - 418684508551704217004632820201538271464823125615024056822995425518287847424*x^19 + 2292254204254
44294191147646176341699520323501828496374466278758575222292480*x^18 - 1265190599528928078062208761554970753195
04102984981603829222251966222041088*x^17 + 7893588482669336806525482893190821189151939412773442470504902282581
5343104*x^16 - 32498177952781175771570102356850846229225588393916533119446726744429559808*x^15 + 2049188594701
0913333756876708782289162249577789257433177529423102866358272*x^14 - 10709341936487878696123475460109781566666
232126271592963297115430325321728*x^13 + 257814215184985618207513391898845844711200794956195749730746554693504
2048*x^12 - 3407053606551726299099037573789747390828310557439249471191823118374010880*x^11 + 36149668743642480
3930693904778700780769490487415840984941622807133945856*x^10 - 37495307901989006080062610714625460487937855057
7160501972659130689650688*x^9 + 361092974099972372832558605269197722032357635208049111095191908288299008*x^8 +
141002184747768997009392595202128779106364989840476870319621019208253440*x^7 + 146999213652233656885845331514
573869620245040110547854481309077147222016*x^6 + 5314005372292355561192939243583419827565066843085197972432334
0159025152*x^5 + 25759965066905016287490162796639138798257488660077636512705521601478656*x^4 + 656150053590976
8299643720712351478750499548998321662130594802672074752*x^3 + 197886524098866028084493164340758882951573699949
3834610814305567768576*x^2 - 3781484028801678888003468129339153727662345024772741260943*sqrt(14)*(549755813888
*x^58 - 11269994184704*x^57 + 107064944754688*x^56 - 630638638006272*x^55 + 2618521301286912*x^54 - 8342252417
974272*x^53 + 21849572376576000*x^52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363618304*x
^49 + 323261995581177856*x^48 - 517079841212727296*x^47 + 778117896260812800*x^46 - 1105641165387988992*x^45 +
1491287028233404416*x^44 - 1919929663119949824*x^43 + 2363050939901804544*x^42 - 2786274020645928960*x^41 + 3
161145685194047488*x^40 - 3453753931369283584*x^39 + 3634098467102523392*x^38 - 3697893960325791744*x^37 + 364
0651752731836416*x^36 - 3461798212247617536*x^35 + 3194540251789393920*x^34 - 2861544579495297024*x^33 + 24776
32938217930752*x^32 - 2088430257127768064*x^31 + 1712761005459316736*x^30 - 1355447485390974976*x^29 + 1048940
886155151360*x^28 - 790511024135089152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 282845069599
813728*x^24 - 186113897194906128*x^23 + 123982890381352520*x^22 - 78116367732251996*x^21 + 46488580159296898*x
^20 - 29591055660829971*x^19 + 16200795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441*x^16 - 229684
9711499532*x^15 + 1448289882400788*x^14 - 756896247319212*x^13 + 182213447974992*x^12 - 240797810407770*x^11 +
25549234281774*x^10 - 26500281727302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164*x^6 + 3755
740313808*x^5 + 1820618017974*x^4 + 463742325333*x^3 + 139858796529*x^2 + 19758444939*x + 3486784401) + 279562
679474852283443466797268108117189203842033755028120580564975616*x + 493345904955621676664941406943720206804477
36829486181433043629113344)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 1414902
2371848728385570789036684124101210161640127797919744)*log(-411483036686051024414565090581703228290144092715017
75935163876370158714880/1634857335323112850812492677092639503349451327418417311*579590499192185855665304541951
571706717845859384545414208024478076585205782332794174344701326^(1/4)*sqrt(12868460882463048970358421717432178
503450051394)*sqrt(-2*x + 3)*sqrt(3781484028801678888003468129339153727662345024772741260943*sqrt(14) + 141490
22371848728385570789036684124101210161640127797919744)*(8061110911143276053983022787*sqrt(14) - 30297118912219
360725028693061) - 5295153361391555319192290416119266357486986850507581489439885963489257332413262896909021356
322314724080758142729925427200*x + 242565135296060218382141975247008236044757041214575818960197534814448608346
11200*sqrt(166789371965963959581098742817586289130679764812156476721038706576007991289033281726) + 79427300420
87332978788435624178899536230480275761372234159828945233885998619894345363532034483472086121137214094888140800
) + 32596578204984962032912596746480962439109746225179791317800502510255796338156401518821079958557305776*(528
52595088141665875251392948545451373376947250790400*x^57 - 1098967795066273315162856093421299059440183747910041
600*x^56 + 10607209489316853390896228799650834948444579920210821120*x^55 - 63571167550234753994014104400074223
346580880315719352320*x^54 + 268751102085050752152483783816672599931031121283482910720*x^53 - 8709469732195211
14804962921504691759517713269107195904000*x^52 + 2313758021932448312425321649336084981029506072497608458240*x^
51 - 5316604047160267290459856323292969345744886768161070776320*x^50 + 109354424880090472643664483912756043687
54310437883074314240*x^49 - 20476557691160001147471559886237056465998405634456352194560*x^48 + 353027942391988
02111604239039735944127462536376667298856960*x^47 - 5671470898806852061310131397489198229777877710835380387840
0*x^46 + 85640241664030935730039797515882941408552267458802253561856*x^45 - 1220632507001743165534252209491650
95613494323059071276548096*x^44 + 165018067996212231343716673011244333927488403644331103092736*x^43 - 21276257
9742469905820226823821664465308559175943457404354560*x^42 + 26220732585283145852092858573622401829922651309656
3188826112*x^41 - 309440537906112411118620445892815079684504011563969741324288*x^40 + 351087306412578660000108
019219405351826065473130972707815424*x^39 - 383554582100586246362167645670892818138191443491318786949120*x^38
+ 403492607520849908998883514652547403915763268860927101370368*x^37 - 4100918333825403109806187469427332428400
05307528588546801664*x^36 + 403232407441991792232348027512081003879684846626157308542976*x^35 - 38299557981652
7529641915302665409995875084862589265975050240*x^34 + 35258725976686171315668012005219964863981639961010033885
1840*x^33 - 315079971582181801347294250924732868231627903206246048727040*x^32 + 272316634459399870536836933035
003973818695505518285221314560*x^31 - 228671395190671097020869564500875726797589816165421143277568*x^30 + 1868
86111688985929098566117844019918629526116042561389293568*x^29 - 1475750290559999948394062876488436939011818876
10273533861888*x^28 + 113537974641311616719165089124033846938888435216187251000320*x^27 - 85196415623233396170
197188512975026308393874494506050046976*x^26 + 61490717519886743793977904289150681209548071542812762022208*x^2
5 - 43499929568624033785147670292431465440609985987022819309056*x^24 + 300153071991834924184261152329177022613
64741866517547318384*x^23 - 19714530664252367893694794632442175393727220660187813722224*x^22 + 129086874190604
91715559483506875260114803121732707547895900*x^21 - 8152620728427620176711248504306621849196751343566681977176
*x^20 + 4826566229889649998651082918574281667310767186073269174097*x^19 - 298003128882125717162643727073135846
3613690258748044875631*x^18 + 1674381797717888336240082619136481913141447194739865411447*x^17 - 89389321151613
3869906083243128705875958804128593529339933*x^16 + 539470558336347193822687371553759571054898242285358894340*x
^15 - 242275403875001443743419975934494764357192021279244664252*x^14 + 130786287070310326986845647168054788265
093887227255620788*x^13 - 73538381632205950970872198730312615396368885742113789428*x^12 + 20332630553731386602
117293249018874668950007879116154590*x^11 - 18584188962732131818655387362586480212623851120277665058*x^10 + 45
78529043479744243222124864085177021652064523434159250*x^9 - 15899763973164591775427513408147196788369653864187
28758*x^8 + 2136884518140645208822032972708844209401147725933248644*x^7 + 527431838252429406648106098496733847
843023830337908772*x^6 + 591293371646480980468080856862103952285194702447206232*x^5 + 153671770129689537528196
360895808154174885919188027188*x^4 + 77286799075459568078148376312494588624748077088337625*x^3 + 1320315506476
3141960070155528810313105199695006969241*x^2 + 4110042898499321701713055782797445718557813264221007*x + 142488
114863139797187698618852924003909944526763627)*sqrt(-2*x + 3))/(549755813888*x^58 - 11269994184704*x^57 + 1070
64944754688*x^56 - 630638638006272*x^55 + 2618521301286912*x^54 - 8342252417974272*x^53 + 21849572376576000*x^
52 - 49684091485814784*x^51 + 101394501297242112*x^50 - 188583312363618304*x^49 + 323261995581177856*x^48 - 51
7079841212727296*x^47 + 778117896260812800*x^46 - 1105641165387988992*x^45 + 1491287028233404416*x^44 - 191992
9663119949824*x^43 + 2363050939901804544*x^42 - 2786274020645928960*x^41 + 3161145685194047488*x^40 - 34537539
31369283584*x^39 + 3634098467102523392*x^38 - 3697893960325791744*x^37 + 3640651752731836416*x^36 - 3461798212
247617536*x^35 + 3194540251789393920*x^34 - 2861544579495297024*x^33 + 2477632938217930752*x^32 - 208843025712
7768064*x^31 + 1712761005459316736*x^30 - 1355447485390974976*x^29 + 1048940886155151360*x^28 - 79051102413508
9152*x^27 + 571750925528393856*x^26 - 408374103192240192*x^25 + 282845069599813728*x^24 - 186113897194906128*x
^23 + 123982890381352520*x^22 - 78116367732251996*x^21 + 46488580159296898*x^20 - 29591055660829971*x^19 + 162
00795673453545*x^18 - 8941894120163277*x^17 + 5578893209169441*x^16 - 2296849711499532*x^15 + 1448289882400788
*x^14 - 756896247319212*x^13 + 182213447974992*x^12 - 240797810407770*x^11 + 25549234281774*x^10 - 26500281727
302*x^9 + 25520701332582*x^8 + 9965507230260*x^7 + 10389354811164*x^6 + 3755740313808*x^5 + 1820618017974*x^4
+ 463742325333*x^3 + 139858796529*x^2 + 19758444939*x + 3486784401)
________________________________________________________________________________________
giac [A] time = 6.84, size = 1382, normalized size = 1.31 \[ \text {result too large to display} \]
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, algorithm="giac")
[Out]
115/5820884187057104679865572244942878614409445376*sqrt(7)*(902844422048046918046098552144*14^(3/4)*sqrt(2)*(s
qrt(14) + 4)^(3/2) + 2708533266144140754138295656432*14^(3/4)*sqrt(2)*sqrt(sqrt(14) + 4)*(sqrt(14) - 4) - 1934
66661867438625295592546888*14^(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-8*sqrt(14) + 32) + 80611109111432760539830227
87*14^(3/4)*sqrt(7)*(-8*sqrt(14) + 32)^(3/2) + 27146218545348547209625708982656*14^(1/4)*sqrt(2)*sqrt(sqrt(14)
+ 4) - 1939015610382039086401836355904*14^(1/4)*sqrt(7)*sqrt(-8*sqrt(14) + 32))*arctan(1/28*14^(3/4)*(14^(1/4
)*sqrt(1/2)*sqrt(sqrt(14) + 4) + 2*sqrt(-2*x + 3))/sqrt(-1/8*sqrt(14) + 1/2)) + 115/58208841870571046798655722
44942878614409445376*sqrt(7)*(902844422048046918046098552144*14^(3/4)*sqrt(2)*(sqrt(14) + 4)^(3/2) + 270853326
6144140754138295656432*14^(3/4)*sqrt(2)*sqrt(sqrt(14) + 4)*(sqrt(14) - 4) - 193466661867438625295592546888*14^
(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-8*sqrt(14) + 32) + 8061110911143276053983022787*14^(3/4)*sqrt(7)*(-8*sqrt(1
4) + 32)^(3/2) + 27146218545348547209625708982656*14^(1/4)*sqrt(2)*sqrt(sqrt(14) + 4) - 1939015610382039086401
836355904*14^(1/4)*sqrt(7)*sqrt(-8*sqrt(14) + 32))*arctan(-1/28*14^(3/4)*(14^(1/4)*sqrt(1/2)*sqrt(sqrt(14) + 4
) - 2*sqrt(-2*x + 3))/sqrt(-1/8*sqrt(14) + 1/2)) - 115/11641768374114209359731144489885757228818890752*sqrt(7)
*(128977774578292416863728364592*14^(3/4)*sqrt(7)*sqrt(2)*(sqrt(14) + 4)^(3/2) + 38693332373487725059118509377
6*14^(3/4)*sqrt(7)*sqrt(2)*sqrt(sqrt(14) + 4)*(sqrt(14) - 4) + 1354266633072070377069147828216*14^(3/4)*(sqrt(
14) + 4)*sqrt(-8*sqrt(14) + 32) - 56427776378002932377881159509*14^(3/4)*(-8*sqrt(14) + 32)^(3/2) + 3878031220
764078172803672711808*14^(1/4)*sqrt(7)*sqrt(2)*sqrt(sqrt(14) + 4) + 13573109272674273604812854491328*14^(1/4)*
sqrt(-8*sqrt(14) + 32))*log(14^(1/4)*sqrt(1/2)*sqrt(-2*x + 3)*sqrt(sqrt(14) + 4) - 2*x + sqrt(14) + 3) + 115/1
1641768374114209359731144489885757228818890752*sqrt(7)*(128977774578292416863728364592*14^(3/4)*sqrt(7)*sqrt(2
)*(sqrt(14) + 4)^(3/2) + 386933323734877250591185093776*14^(3/4)*sqrt(7)*sqrt(2)*sqrt(sqrt(14) + 4)*(sqrt(14)
- 4) + 1354266633072070377069147828216*14^(3/4)*(sqrt(14) + 4)*sqrt(-8*sqrt(14) + 32) - 5642777637800293237788
1159509*14^(3/4)*(-8*sqrt(14) + 32)^(3/2) + 3878031220764078172803672711808*14^(1/4)*sqrt(7)*sqrt(2)*sqrt(sqrt
(14) + 4) + 13573109272674273604812854491328*14^(1/4)*sqrt(-8*sqrt(14) + 32))*log(-14^(1/4)*sqrt(1/2)*sqrt(-2*
x + 3)*sqrt(sqrt(14) + 4) - 2*x + sqrt(14) + 3) + 1/24112597431479447071556104988390860001680293888*(385912796
294138623132486146144809805*(2*x - 3)^37*sqrt(-2*x + 3) + 49944166626569370884317542782684785215*(2*x - 3)^36*
sqrt(-2*x + 3) + 3157104325190190818790417015768672100251*(2*x - 3)^35*sqrt(-2*x + 3) + 1298626635397428297270
10168448772257537793*(2*x - 3)^34*sqrt(-2*x + 3) + 3907056032933059027385185682832433217956200*(2*x - 3)^33*sq
rt(-2*x + 3) + 91626342308240062913659469031676941328847688*(2*x - 3)^32*sqrt(-2*x + 3) + 17430518397837166544
58570168808933730174627004*(2*x - 3)^31*sqrt(-2*x + 3) + 27638544507622729125093621837291437830917462708*(2*x
- 3)^30*sqrt(-2*x + 3) + 372498510070445411629537388290851713705080145718*(2*x - 3)^29*sqrt(-2*x + 3) + 432995
3516930687342337472014272666363969651587314*(2*x - 3)^28*sqrt(-2*x + 3) + 438994445601123086236053311571438967
25828415934650*(2*x - 3)^27*sqrt(-2*x + 3) + 391609357365773780316151578457972453648367489837454*(2*x - 3)^26*
sqrt(-2*x + 3) + 3095031701758849575040626937399363198202032753884252*(2*x - 3)^25*sqrt(-2*x + 3) + 2179071962
2224681379416567825910093368668334676797780*(2*x - 3)^24*sqrt(-2*x + 3) + 137261402924198725794062163116053277
099106968046586092*(2*x - 3)^23*sqrt(-2*x + 3) + 776171183055652545384871388553173912691352168500951876*(2*x -
3)^22*sqrt(-2*x + 3) + 3950095526376994607880784338655934603802167995433166405*(2*x - 3)^21*sqrt(-2*x + 3) +
18125803816832861597832766873339882118924015183338007655*(2*x - 3)^20*sqrt(-2*x + 3) + 75083414508694050144426
639977685085540038804754309758915*(2*x - 3)^19*sqrt(-2*x + 3) + 2809326520733483435177760906312718952356113432
84275820345*(2*x - 3)^18*sqrt(-2*x + 3) + 949449516366891514866641779309597536478490489987954462580*(2*x - 3)^
17*sqrt(-2*x + 3) + 2896666953760570249650513456393600983703549509654469117900*(2*x - 3)^16*sqrt(-2*x + 3) + 7
968283692957988567650795129108295704483768260379820818752*(2*x - 3)^15*sqrt(-2*x + 3) + 1972749457881227765860
6009712831861626922226523266435734336*(2*x - 3)^14*sqrt(-2*x + 3) + 438441033794236958424800303207601166664911
72278035172870400*(2*x - 3)^13*sqrt(-2*x + 3) + 87180772449453719112409715850861698835279004734515297162496*(2
*x - 3)^12*sqrt(-2*x + 3) + 154427451620079851403012035013949923367197814895239131529728*(2*x - 3)^11*sqrt(-2*
x + 3) + 242351725944359254347670713000225450988365795247877220072960*(2*x - 3)^10*sqrt(-2*x + 3) + 3346460914
32259174045261099248092390902126268663782608549888*(2*x - 3)^9*sqrt(-2*x + 3) + 403034519668261986708991686890
381317841470126237337802123264*(2*x - 3)^8*sqrt(-2*x + 3) + 41864679464547332971489609516908707261586337343463
4780753920*(2*x - 3)^7*sqrt(-2*x + 3) + 369621715112196031007775193340564258755874521674193323966464*(2*x - 3)
^6*sqrt(-2*x + 3) + 272008032423513780299697431707644217391623176190273099661312*(2*x - 3)^5*sqrt(-2*x + 3) +
162377109720555022535973021706211388170650620411678744248320*(2*x - 3)^4*sqrt(-2*x + 3) + 75556666748884291766
220892297166603376040200755275694800896*(2*x - 3)^3*sqrt(-2*x + 3) + 25715217479147156311480451271603595696519
278112265697558528*(2*x - 3)^2*sqrt(-2*x + 3) - 5695058898488457914056616763522088045930624578769252515840*(-2
*x + 3)^(3/2) + 616047393270423249767303997369406352855404127230297374720*sqrt(-2*x + 3))/((2*x - 3)^2 + 14*x
- 7)^19 + 1/43768013439874312895399492130064309616640*(991856055479912729664933375*(2*x - 3)^19 - 465215115289
202563341931875*(2*x - 3)^18 + 376870004361848629670138100*(2*x - 3)^17 - 347816399209073565143694750*(2*x - 3
)^16 + 333480450533749292133360000*(2*x - 3)^15 - 319778248261094005065228000*(2*x - 3)^14 + 30029231123186929
3365336000*(2*x - 3)^13 - 272225522279980529558298000*(2*x - 3)^12 + 235508819476507302437712000*(2*x - 3)^11
- 192403914635036320216640640*(2*x - 3)^10 + 146870291549367152461094400*(2*x - 3)^9 - 10354496371898148475125
1200*(2*x - 3)^8 + 66520770217483444975816704*(2*x - 3)^7 - 38308222816032989365145600*(2*x - 3)^6 + 193645363
10461049463275520*(2*x - 3)^5 - 8351885944887834417868800*(2*x - 3)^4 + 2950396963171184804659200*(2*x - 3)^3
- 800398003403553957642240*(2*x - 3)^2 + 296499732880545408614400*x - 458814330239510651535360)/((2*x - 3)^19*
sqrt(-2*x + 3))
________________________________________________________________________________________
maple [A] time = 0.10, size = 989, normalized size = 0.93 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(-2*x+3)^(41/2)/(2*x^2+x+1)^20,x)
[Out]
-7192279694031133468210490184035/1624130632549415368266063684414865684824064/(-7+2*14^(1/2))^(1/2)*(7+2*14^(1/
2))*14^(1/2)*arctan((2*(-2*x+3)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))-719227969403113346821049018
4035/1624130632549415368266063684414865684824064/(-7+2*14^(1/2))^(1/2)*(7+2*14^(1/2))*14^(1/2)*arctan((2*(-2*x
+3)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))-7192279694031133468210490184035/32482612650988307365321
27368829731369648128*(7+2*14^(1/2))^(1/2)*14^(1/2)*ln(-2*x+3+14^(1/2)-(-2*x+3)^(1/2)*(7+2*14^(1/2))^(1/2))+134
57531633280790190212932747565/812065316274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*(7+2*14^(1/2))*
arctan((2*(-2*x+3)^(1/2)-(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))-3484168674905226483378299702015/81206531
6274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*14^(1/2)*arctan((2*(-2*x+3)^(1/2)-(7+2*14^(1/2))^(1/2
))/(-7+2*14^(1/2))^(1/2))+7192279694031133468210490184035/3248261265098830736532127368829731369648128*(7+2*14^
(1/2))^(1/2)*14^(1/2)*ln(-2*x+3+14^(1/2)+(-2*x+3)^(1/2)*(7+2*14^(1/2))^(1/2))+13457531633280790190212932747565
/812065316274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*(7+2*14^(1/2))*arctan((2*(-2*x+3)^(1/2)+(7+2
*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))-3484168674905226483378299702015/8120653162747076841330318422074328424
12032/(-7+2*14^(1/2))^(1/2)*14^(1/2)*arctan((2*(-2*x+3)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))+683
151246370725/30145677658996078082575630336/(-2*x+3)^(1/2)+769045155125/100934188590388654294338048/(-2*x+3)^(9
/2)+838467657280275/105509871806486273289014706176/(-2*x+3)^(7/2)+9270470094105/1076631344964145645806272512/(
-2*x+3)^(5/2)+320421783064625/30145677658996078082575630336/(-2*x+3)^(3/2)+8192823353/186370221887015007929292
8/(-2*x+3)^(19/2)+8972680075/1667523037936450070946304/(-2*x+3)^(17/2)+102495360575/16479051198430800701116416
/(-2*x+3)^(15/2)+122484655975/17852305464966700759542784/(-2*x+3)^(13/2)+10815878546425/1480368099325700262983
624704/(-2*x+3)^(11/2)+1/3111898385606868039/(-2*x+3)^(39/2)+10/2952313853011644037/(-2*x+3)^(37/2)+143/781964
2097165976098/(-2*x+3)^(35/2)+355/5266289575642392066/(-2*x+3)^(33/2)+52865/277038748585308867472/(-2*x+3)^(31
/2)+14333/32395660116830472406/(-2*x+3)^(29/2)+1478345/1689042692987850837168/(-2*x+3)^(27/2)+475387/312785683
886639043920/(-2*x+3)^(25/2)+16575515/7006399319060714583808/(-2*x+3)^(23/2)+246866015/73567192850137503129984
/(-2*x+3)^(21/2)+13457531633280790190212932747565/1624130632549415368266063684414865684824064*(7+2*14^(1/2))^(
1/2)*ln(-2*x+3+14^(1/2)-(-2*x+3)^(1/2)*(7+2*14^(1/2))^(1/2))-13457531633280790190212932747565/1624130632549415
368266063684414865684824064*(7+2*14^(1/2))^(1/2)*ln(-2*x+3+14^(1/2)+(-2*x+3)^(1/2)*(7+2*14^(1/2))^(1/2))+1/301
45677658996078082575630336*(2672239984790337844292019294315182385216573077301785/117922622078976*(-2*x+3)^(41/
2)+1186323846453826237212517196312193819452761764018822545/3915399561216*(-2*x+3)^(21/2)-176509423589632626758
71173166229809316744939271143/51904512*(-2*x+3)^(11/2)+807597736492641378942268937217995835353849465/1048576*(
-2*x+3)^(1/2)-55066091420817590167865401986871791412011888132876913/5527622909952*(-2*x+3)^(31/2)+273748752892
8439357869138774910126923363791747141675/755914244096*(-2*x+3)^(33/2)-1166457217021587688420366823074349521448
8310113371105/9826885173248*(-2*x+3)^(35/2)+12646629333382722716904430763732665179119615389552413/25098715136*
(-2*x+3)^(17/2)-2593673203685044441695042001860835122939346700333136537/6199382638592*(-2*x+3)^(19/2)-75593011
6404682856570195190192032441294632160945523631/3915399561216*(-2*x+3)^(23/2)+853508502207214511987093866021124
087908041634697244059/7830799122432*(-2*x+3)^(25/2)-6886173809894005543994516442461871486007042005189775/12562
7793408*(-2*x+3)^(27/2)+136329987967245395141848253765147208279814148352958009/5527622909952*(-2*x+3)^(29/2)+1
808668971148992206490172102870787954874541181/334114095890432*(-2*x+3)^(57/2)-11968977253082880651292892111395
530933265219/25701084299264*(-2*x+3)^(59/2)+339556544641293541759958988614814460549873/9826885173248*(-2*x+3)^
(61/2)-64243396719140374998473027009027485263697/29480655519744*(-2*x+3)^(63/2)+129886852748727110357425618672
922324659/1133871366144*(-2*x+3)^(65/2)-503502693505289734438057515605193725/103079215104*(-2*x+3)^(67/2)+1338
83313322119397348791732981953297/824633720832*(-2*x+3)^(69/2)-3254850748003483429666738850178379/824633720832*
(-2*x+3)^(71/2)+360433340020130123942335063779145/5772436045824*(-2*x+3)^(73/2)-928342237074576734557978321305
/1924145348608*(-2*x+3)^(75/2)+13805722741822612586258592099428566280191230197271405/39307540692992*(-2*x+3)^(
37/2)-1006304725834560333245233940167063186576585913370455/10720238370816*(-2*x+3)^(39/2)-44796329357069082297
154473725670903546220392558695/9070970929152*(-2*x+3)^(43/2)+2860722331769322369839567258415059386301607579614
3/29480655519744*(-2*x+3)^(45/2)-5059022664167725408892162874688680417923742003781/29480655519744*(-2*x+3)^(47
/2)+73012476452577571533836489036461787385135079265/2680059592704*(-2*x+3)^(49/2)-1939242920901534821454026903
132433081580221023737/501171143835648*(-2*x+3)^(51/2)+490738543064879423955077165987434152441563270473/1002342
287671296*(-2*x+3)^(53/2)-55011835288361289002011693179378316699033102675/1002342287671296*(-2*x+3)^(55/2)-223
97546321209486953062074374795737299957063565/3145728*(-2*x+3)^(3/2)+404531566689883337048499233527781983599187
634017/12582912*(-2*x+3)^(5/2)-1188598027552254830082683218064697188605612952419/12582912*(-2*x+3)^(7/2)+38315
83379166294091823572953989993625772471445345/18874368*(-2*x+3)^(9/2)+99778501261680101871691304247745683309731
23412551261/21592276992*(-2*x+3)^(13/2)-1255696718499588580979726331572072320357969297077745/2399141888*(-2*x+
3)^(15/2))/(14*x+(-2*x+3)^2-7)^19
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{20} {\left (-2 \, x + 3\right )}^{\frac {41}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x, algorithm="maxima")
[Out]
integrate(1/((2*x^2 + x + 1)^20*(-2*x + 3)^(41/2)), x)
________________________________________________________________________________________
mupad [B] time = 0.97, size = 1017, normalized size = 0.96 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/((3 - 2*x)^(41/2)*(x + 2*x^2 + 1)^20),x)
[Out]
((64356352*(2*x - 3)^2)/38073 - (5767168*x)/1443 - (7517962240*(2*x - 3)^3)/5444439 + (1357449428992*(2*x - 3)
^4)/1181443263 - (34130408095744*(2*x - 3)^5)/34261854627 + (1965832636456960*(2*x - 3)^6)/2158496841501 - (95
52588571922432*(2*x - 3)^7)/10792484207505 + (69571472879183872*(2*x - 3)^8)/75547389452535 - (520483872994611
2*(2*x - 3)^9)/5036492630169 + (325082052781755904*(2*x - 3)^10)/257635969158645 - (461538785202937088*(2*x -
3)^11)/272428464995505 + (17726678744562203264*(2*x - 3)^12)/6992330601551295 - (1432471149647610304*(2*x - 3)
^13)/332968123883395 + (2043463601243388704*(2*x - 3)^14)/241114848329355 - (96972768477343976816*(2*x - 3)^15
)/4840844262612435 + (10833870670122545927656*(2*x - 3)^16)/181389282075536535 - (44340157049832305729324*(2*x
- 3)^17)/181389282075536535 + (691509778132186261807282*(2*x - 3)^18)/423241658176251915 - (13577358331537082
239703407*(2*x - 3)^19)/423241658176251915 + (5094959438589599396407530394650672614981*(2*x - 3)^20)/203594616
979243053623625646080 + (47475340273724148225749886260884632526403*(2*x - 3)^21)/20359461697924305362362564608
0 + (547362406727667345868176230754600752341499*(2*x - 3)^22)/518240843219891409223774371840 + (13632173991688
46741803250531443496167647559*(2*x - 3)^23)/438511482724523500112424468480 + (40035704814224807138997531075224
0020201388159*(2*x - 3)^24)/59856817391897457765345939947520 + (167803532186710618751778512174316524508553291*
(2*x - 3)^25)/14964204347974364441336484986880 + (51108771060698315319124863093548144195799415067*(2*x - 3)^26
)/3351981773946257634859372637061120 + (393987083187206735082003889381221664346090053*(2*x - 3)^27)/2280259710
1675222005846072360960 + (194509919512254900809288150922829785396777195281*(2*x - 3)^28)/116889620835048984189
96786631802880 + (39904941217415859849678112809547525787872838871677*(2*x - 3)^29)/288717363462570990949220629
8055311360 + (298202908298252068565416529654031351573999658954519*(2*x - 3)^30)/297834753887704811716038123378
33738240 + (17278370717837126498790206579435572552986029824411*(2*x - 3)^31)/270758867170640737923671021253033
9840 + (136589909140623157483229616961110867609087469195457*(2*x - 3)^32)/379062414038897033093139429754247577
60 + (12124448510282132213121066777925721516746772830847*(2*x - 3)^33)/6689336718333477054584813466251427840 +
(5268103225464003924284598756770514565895682824129*(2*x - 3)^34)/6458669934942667500978440588104826880 + (617
17610092862026266313005902016039510287732711413*(2*x - 3)^35)/187301428113337357528374777055039979520 + (23627
9120368028123256783334911177879141056326577387*(2*x - 3)^36)/1972268029364372858760322438733412433920 + (10069
18289966448819369741773577875830109223667348001*(2*x - 3)^37)/25639484381736847163884191703534361640960 + (834
3152514122341340412513706840068954518337251868859*(2*x - 3)^38)/717905562688631720588757367698962125946880 + (
6690164526112934310361705118130577674249448391954923*(2*x - 3)^39)/2153716688065895161766272103096886377840640
+ (305581065207833944849384015433140408874881230574613*(2*x - 3)^40)/4074599139584125981719974249102217471590
40 + (731867339371195846981841457176808134814103613309*(2*x - 3)^41)/4477581472070468111780191482529909309440
+ (9815653611211549232290414629069353244130713267641*(2*x - 3)^42)/305594935468809448628998068682666310369280
+ (11199801517259481678687287141859390404145132617*(2*x - 3)^43)/1971580228831028700832245604404298776576 + (1
365647472724278381706307194167071805455474221*(2*x - 3)^44)/1514223059760507936375862611533082132480 + (403050
1165904934786218654181916754194500565501*(2*x - 3)^45)/31462190241690553789142923150742928752640 + (1428009628
445556490988667295522054915842433631*(2*x - 3)^46)/88094132676733550609600184822080200507392 + (16008905392663
3694221849846408842457682603621*(2*x - 3)^47)/88094132676733550609600184822080200507392 + (2100199814096720892
415827167854475800682460389*(2*x - 3)^48)/11716519646005562231076824581336666667483136 + (73152102949146076476
2993572365861799703833*(2*x - 3)^49)/47435302210548834943630868750350877196288 + (1452782501142468088174528794
40670605483477*(2*x - 3)^50)/126959191210586587643247325184762641907712 + (30541762468911990334017682046220545
95917*(2*x - 3)^51)/42319730403528862547749108394920880635904 + (43226241215596960235839037876452347793*(2*x -
3)^52)/11393773570180847609009375337094083248128 + (167572141694212657464927107565976575*(2*x - 3)^53)/103579
7597289167964455397757917643931648 + (935756145095208333386444273642906999*(2*x - 3)^54)/174013996344580218028
506823330164180516864 + (3250015519725523200399609528788299*(2*x - 3)^55)/248591423349400311469295461900234543
59552 + (359910711199433658030176367535945*(2*x - 3)^56)/174013996344580218028506823330164180516864 + (9270277
54781476746208047620505*(2*x - 3)^57)/58004665448193406009502274443388060172288 + 79953920/10101)/(59763039589
48914397184*(3 - 2*x)^(39/2) - 56774887610014686773248*(3 - 2*x)^(41/2) + 263597692475068188590080*(3 - 2*x)^(
43/2) - 796876101097706139353088*(3 - 2*x)^(45/2) + 1763207861643670399942656*(3 - 2*x)^(47/2) - 3043249843014
358669590528*(3 - 2*x)^(49/2) + 4264137522753475514499072*(3 - 2*x)^(51/2) - 4984324075408572529754112*(3 - 2*
x)^(53/2) + 4956568063057422401458176*(3 - 2*x)^(55/2) - 4255315771373708518529024*(3 - 2*x)^(57/2) + 31897796
13484873345291264*(3 - 2*x)^(59/2) - 2106235539086912777861632*(3 - 2*x)^(61/2) + 1233708448609783150169088*(3
- 2*x)^(63/2) - 644615788666077029453568*(3 - 2*x)^(65/2) + 301787157080763250721664*(3 - 2*x)^(67/2) - 12703
7834354660188150464*(3 - 2*x)^(69/2) + 48214067552985728953272*(3 - 2*x)^(71/2) - 16530947936007918636468*(3 -
2*x)^(73/2) + 5127550624086495626518*(3 - 2*x)^(75/2) - 1440010379792375040419*(3 - 2*x)^(77/2) + 36625361600
6178259037*(3 - 2*x)^(79/2) - 84341571102081217533*(3 - 2*x)^(81/2) + 17570724326889842913*(3 - 2*x)^(83/2) -
3306899061710229804*(3 - 2*x)^(85/2) + 561126236614140036*(3 - 2*x)^(87/2) - 85611621840452988*(3 - 2*x)^(89/2
) + 11703514272799272*(3 - 2*x)^(91/2) - 1427192816292922*(3 - 2*x)^(93/2) + 154386157043846*(3 - 2*x)^(95/2)
- 14711313018374*(3 - 2*x)^(97/2) + 1223975378934*(3 - 2*x)^(99/2) - 87916389372*(3 - 2*x)^(101/2) + 537238018
8*(3 - 2*x)^(103/2) - 273870408*(3 - 2*x)^(105/2) + 11333994*(3 - 2*x)^(107/2) - 365883*(3 - 2*x)^(109/2) + 86
45*(3 - 2*x)^(111/2) - 133*(3 - 2*x)^(113/2) + (3 - 2*x)^(115/2)) - (atan(((3 - 2*x)^(1/2)*(- 7^(1/2)*81742866
76615564254062463385463197516747256637092086555i - 26470388201611752216024276905374076093636415173409188826601
)^(1/2)*12432068249297696284897249001366340523282983937937427139335625i)/(546445444973747744833043391094451536
0385310133698367639025956899464609704986819634313026095523633767314455423557204931772416*((7^(1/2)*37665585007
3799072335964720186587398406296145585988886284558062903152597529420137587598125i)/2732227224868738724165216955
472257680192655066849183819512978449732304852493409817156513047761816883657227711778602465886208 + 77752097412
3765253499790235238946338576340593433713638916736753944556393731049211251145625/390318174981248389166459565067
465382884665009549883402787568349961757836070487116736644721108830983379603958825514637983744)) + (12432068249
297696284897249001366340523282983937937427139335625*7^(1/2)*(3 - 2*x)^(1/2)*(- 7^(1/2)*81742866766155642540624
63385463197516747256637092086555i - 26470388201611752216024276905374076093636415173409188826601)^(1/2))/(54644
54449737477448330433910944515360385310133698367639025956899464609704986819634313026095523633767314455423557204
931772416*((7^(1/2)*376655850073799072335964720186587398406296145585988886284558062903152597529420137587598125
i)/27322272248687387241652169554722576801926550668491838195129784497323048524934098171565130477618168836572277
11778602465886208 + 777520974123765253499790235238946338576340593433713638916736753944556393731049211251145625
/3903181749812483891664595650674653828846650095498834027875683499617578360704871167366447211088309833796039588
25514637983744)))*(- 7^(1/2)*8174286676615564254062463385463197516747256637092086555i - 2647038820161175221602
4276905374076093636415173409188826601)^(1/2)*115i)/812065316274707684133031842207432842412032 + (atan(((3 - 2*
x)^(1/2)*(7^(1/2)*8174286676615564254062463385463197516747256637092086555i - 264703882016117522160242769053740
76093636415173409188826601)^(1/2)*12432068249297696284897249001366340523282983937937427139335625i)/(5464454449
73747744833043391094451536038531013369836763902595689946460970498681963431302609552363376731445542355720493177
2416*((7^(1/2)*376655850073799072335964720186587398406296145585988886284558062903152597529420137587598125i)/27
32227224868738724165216955472257680192655066849183819512978449732304852493409817156513047761816883657227711778
602465886208 - 777520974123765253499790235238946338576340593433713638916736753944556393731049211251145625/3903
18174981248389166459565067465382884665009549883402787568349961757836070487116736644721108830983379603958825514
637983744)) - (12432068249297696284897249001366340523282983937937427139335625*7^(1/2)*(3 - 2*x)^(1/2)*(7^(1/2)
*8174286676615564254062463385463197516747256637092086555i - 26470388201611752216024276905374076093636415173409
188826601)^(1/2))/(5464454449737477448330433910944515360385310133698367639025956899464609704986819634313026095
523633767314455423557204931772416*((7^(1/2)*376655850073799072335964720186587398406296145585988886284558062903
152597529420137587598125i)/27322272248687387241652169554722576801926550668491838195129784497323048524934098171
56513047761816883657227711778602465886208 - 777520974123765253499790235238946338576340593433713638916736753944
556393731049211251145625/3903181749812483891664595650674653828846650095498834027875683499617578360704871167366
44721108830983379603958825514637983744)))*(7^(1/2)*8174286676615564254062463385463197516747256637092086555i -
26470388201611752216024276905374076093636415173409188826601)^(1/2)*115i)/8120653162747076841330318422074328424
12032
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
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
________________________________________________________________________________________