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]

-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

________________________________________________________________________________________

Rubi [A]  time = 2.48972, 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, 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 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 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 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 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]

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 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 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 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]

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}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{\int \frac{13067712-15937544 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{18}} \, dx}{13138272}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{\int \frac{44452059120-61847262960 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{17}} \, dx}{43776722304}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{\int \frac{140862854522880-213162453016800 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{16}} \, dx}{137283801145344}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{\int \frac{411257135544050880-672058124080956480 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{15}} \, dx}{403614375367311360}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{\int \frac{1093943980547175340800-1945933258510113828480 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{14}} \, dx}{1107517846007902371840}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{\int \frac{2613748771210815258935040-5150741239627162779559680 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{13}} \, dx}{2821955471628135243448320}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{\int \frac{5495319948977447333781657600-12350104150638064023941414400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{12}} \, dx}{6637239269269374092590448640}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{\int \frac{9830189811300874808578976332800-26468403751104415156166363366400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{11}} \, dx}{14309887864544770543625007267840}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{\int \frac{13994744255814899394658210554777600-49726828476855245625643612682496000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^{10}} \, dx}{28047380214507750265505014244966400}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{\int \frac{13068536369629429401640635068702208000-79426075962231715392089154535476326400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^9} \, dx}{49475578698391671468350845128120729600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{\int \frac{-621663169952319046771764500985957580800-101974001645639894672727830234002797158400 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^8} \, dx}{77577707399078140862374125160893304012800}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{\int \frac{-30781058646716715966024014766066735728640000-91664914528219083487057714121148102617088000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^7} \, dx}{106436614551535209263177299720745613105561600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{\int \frac{-64412327323696265886549616069250637895016448000-25707788838506946427978270639018495010476032000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^6} \, dx}{125169458712605406093496504471596841012140441600}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}+\frac{\int \frac{-67430989462987479984124242299597562667894677504000+82287258915490697105406527276587259062086377472000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^5} \, dx}{122666069538353297971626574382164904191897632768000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}+\frac{\int \frac{-12641043879585143204616228153551645061449995714560000+161124734478367517548652018811830529223223793500160000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^4} \, dx}{96170198518068985609755234315617284886447744090112000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}+\frac{\int \frac{68068541213694880932350653701675675390158594756935680000+127875080054950933515108749931588600071440916461486080000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^3} \, dx}{56548076728624563538536077777582963513231273524985856000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{\int \frac{85414151041513293818778811305636762456175069081725173760000-5205061494636461860243311207210532946592052023002726400000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )^2} \, dx}{22166846077620828907106142488812521697186659221794455552000}\\ &=\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{6724421340577980732010378947094366406252347332593730846720000-101043150693578590411737736011809849211032817167024064430080000 x}{(3-2 x)^{41/2} \left (1+x+2 x^2\right )} \, dx}{4344701831213682465792803927807254252648585207471713288192000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{255881672111781026679558503600374629672084412994797975633920000-579361218799159619542384900282481629641187513671769463193600000 x}{(3-2 x)^{39/2} \left (1+x+2 x^2\right )} \, dx}{121651651273983109042198509978603119074160385809207972069376000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{3205775814492567452521237829367960296659050331301922731458560000-2452640624347833610536075387293391259158787430051424876625920000 x}{(3-2 x)^{37/2} \left (1+x+2 x^2\right )} \, dx}{3406246235671527053181558279400887334076490802657823217942528000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{30551487764636206841242053409530464891589977510518231604920320000-1892740488116731853131501006288506368316523255100858333921280000 x}{(3-2 x)^{35/2} \left (1+x+2 x^2\right )} \, dx}{95374894598802757489083631823224845354141742474419050102390784000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{248197383093323118436199429288820731869352866594347569507205120000+110849508129844436246179207600390821356460770511467776416153600000 x}{(3-2 x)^{33/2} \left (1+x+2 x^2\right )} \, dx}{2670497048766477209694341691050295669915968789283733402866941952000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{1763880048486896074997237019109784212241901391731845003225333760000+1657886581152359091221872962757627855616176089446196936525742080000 x}{(3-2 x)^{31/2} \left (1+x+2 x^2\right )} \, dx}{74773917365461361871441567349408278757647126099944535280274374656000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{10795267225590450417534150227363017986702858954962366152751185920000+17002839680861738847320185852984903982664662103604561632055787520000 x}{(3-2 x)^{29/2} \left (1+x+2 x^2\right )} \, dx}{2093669686232918132400363885783431805214119530798446987847682490368000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{52356458443000125645632830112934335928293547432489805957897912320000+145198106987532234754057716027361495842799408441476834403339468800000 x}{(3-2 x)^{27/2} \left (1+x+2 x^2\right )} \, dx}{58622751214521707707210188801936090545995346862356515659735109730304000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{128455453568936535656947208848751695740749562576964778856504360960000+1080614475697193911106877616615906318769970640378820230251628462080000 x}{(3-2 x)^{25/2} \left (1+x+2 x^2\right )} \, dx}{1641437034006607815801885286454210535287869712145982438472583072448512000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{11155168222970774232376891145}{1685166332532616560247354224017408 (3-2 x)^{23/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-1133585322842895536958177562441799071613944780141922229651222036480000+6997508668458909609269054535090444695582822092580780496935788216320000 x}{(3-2 x)^{23/2} \left (1+x+2 x^2\right )} \, dx}{45960236952185018842452788020717894988060351940087508277232326028558336000}\\ &=-\frac{13056959628363355534285785425}{106924014357253562723941220352 (3-2 x)^{39/2}}-\frac{3948194343291401740321996415}{202881463139404195937734623232 (3-2 x)^{37/2}}-\frac{304688229262620222736480811}{537361713180043545997243056128 (3-2 x)^{35/2}}+\frac{2124315846756567455653862925}{1688851098565851144562763890688 (3-2 x)^{33/2}}+\frac{47657515074514118796095929535}{66632852434325399703658138959872 (3-2 x)^{31/2}}+\frac{34911619993974714062172751985}{124667917457770102671360389021696 (3-2 x)^{29/2}}+\frac{149066309808794760843017404825}{1624981820656451683095663001731072 (3-2 x)^{27/2}}+\frac{15848613964169066543734380171}{601845118761648771516912222863360 (3-2 x)^{25/2}}+\frac{11155168222970774232376891145}{1685166332532616560247354224017408 (3-2 x)^{23/2}}+\frac{14011818498091020272474956375}{10110997995195699361484125344104448 (3-2 x)^{21/2}}+\frac{x}{133 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{19}}+\frac{113+373 x}{33516 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{18}}+\frac{40657+107329 x}{7976808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{17}}+\frac{5 (751303+1831285 x)}{595601664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{16}}+\frac{184959785+429411497 x}{25015269888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{15}}+\frac{41652915209+92630823167 x}{4902992898048 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{14}}+\frac{2871555518177+6100156355517 x}{297448235814912 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{13}}+\frac{77559130805859+156274047129113 x}{7138757659557888 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{12}}+\frac{5 (2656658801194921+5020880176134289 x)}{1099368679571914752 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{11}}+\frac{45187921585208601+78752911037377255 x}{3420258114223734784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^{10}}+\frac{6063974149878048635+9477172618423641847 x}{430952522392190582784 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^9}+\frac{691833601144925854831+919498192874055581221 x}{48266682507925345271808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^8}+\frac{23 (919498192874055581221+908287136092467468517 x)}{1576711628592227945545728 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^7}+\frac{115 (908287136092467468517+298281884944522225747 x)}{10187982830903626725064704 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^6}+\frac{23 (2599313568802265110081-10426142448623187379187 x)}{20375965661807253450129408 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^5}-\frac{23 (10426142448623187379187+27513723463194262383705 x)}{20018492580021161284337664 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^4}-\frac{115 (26513224428169016478843+30673415406553789342019 x)}{76434244396444433994743808 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^3}-\frac{115 (88411609113007981044643-5712269536245152162963 x)}{125891696652967303050166272 (3-2 x)^{39/2} \left (1+x+2 x^2\right )^2}+\frac{115 (28561347681225760814815+965934812839019490346107 x)}{195831528126838026966925312 (3-2 x)^{39/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-23063699919660983514203529569715281964077202426296938831081352724480000+37450710719381875507781616960775471887041153434916994063009841152000000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )} \, dx}{1286886634661180527588678064580101059665689854322450231762505128799633408000}\\ \end{align*}

Mathematica [C]  time = 6.17009, 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

________________________________________________________________________________________

Maple [A]  time = 0.08, size = 989, normalized size = 0.9 \begin{align*} \text{result too large to display} \end{align*}

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)+13457531633280790190212932747565/812065316274707684133031842
207432842412032/(-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))-3484168674905226483378299702015/812065316274707684133031842207432842412032/(-7+2*14^(1/2))^(1/2)*a
rctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*14^(1/2)-7192279694031133468210490184035/3
248261265098830736532127368829731369648128*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))-348416867490522648337
8299702015/812065316274707684133031842207432842412032/(-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))*14^(1/2)-13457531633280790190212932747565/162413063254941536826606368441486
5684824064*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)+134575316332807901902129
32747565/1624130632549415368266063684414865684824064*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]/30145677658996078082575630336/(3-2*x)^(1/2)+10/2952313853011644037/(3-2*x)^(
37/2)+143/7819642097165976098/(3-2*x)^(35/2)+355/5266289575642392066/(3-2*x)^(33/2)+52865/27703874858530886747
2/(3-2*x)^(31/2)+14333/32395660116830472406/(3-2*x)^(29/2)+1478345/1689042692987850837168/(3-2*x)^(27/2)+47538
7/312785683886639043920/(3-2*x)^(25/2)[phone]/7006399319060714583808/(3-2*x)^(23/2)[phone]/73567192850137
503129984/(3-2*x)^(21/2)+1/3111898385606868039/(3-2*x)^(39/2)[phone]/1667523037936450070946304/(3-2*x)^(17
/2)[phone]/16479051198430800701116416/(3-2*x)^(15/2)[phone]/17852305464966700759542784/(3-2*x)^(13
/2)[phone]/1480368099325700262983624704/(3-2*x)^(11/2)[phone]/30145677658996078082575630336/(
3-2*x)^(3/2)[phone]/1863702218870150079292928/(3-2*x)^(19/2)[phone]/100934188590388654294338048/(3-2
*x)^(9/2)[phone]/105509871806486273289014706176/(3-2*x)^(7/2)[phone]/1076631344964145645806272
512/(3-2*x)^(5/2)-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)-71922796940
31133468210490184035/1624130632549415368266063684414865684824064/(-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)+1/30145677658996078082575630336*(8075977
36492641378942268937217995835353849465/1048576*(3-2*x)^(1/2)+490738543064879423955077165987434152441563270473/
1002342287671296*(3-2*x)^(53/2)-55011835288361289002011693179378316699033102675/1002342287671296*(3-2*x)^(55/2
)+1808668971148992206490172102870787954874541181/334114095890432*(3-2*x)^(57/2)-119689772530828806512928921113
95530933265219/25701084299264*(3-2*x)^(59/2)+339556544641293541759958988614814460549873/9826885173248*(3-2*x)^
(61/2)-64243396719140374998473027009027485263697/29480655519744*(3-2*x)^(63/2)+1298868527487271103574256186729
22324659/1133871366144*(3-2*x)^(65/2)-503502693505289734438057515605193725/103079215104*(3-2*x)^(67/2)+1338833
13322119397348791732981953297/824633720832*(3-2*x)^(69/2)-3254850748003483429666738850178379/824633720832*(3-2
*x)^(71/2)+360433340020130123942335063779145/5772436045824*(3-2*x)^(73/2)-928342237074576734557978321305/19241
45348608*(3-2*x)^(75/2)-44796329357069082297154473725670903546220392558695/9070970929152*(3-2*x)^(43/2)+286072
23317693223698395672584150593863016075796143/29480655519744*(3-2*x)^(45/2)-50590226641677254088921628746886804
17923742003781/29480655519744*(3-2*x)^(47/2)+73012476452577571533836489036461787385135079265/2680059592704*(3-
2*x)^(49/2)-1939242920901534821454026903132433081580221023737/501171143835648*(3-2*x)^(51/2)-10063047258345603
33245233940167063186576585913370455/10720238370816*(3-2*x)^(39/2)+13805722741822612586258592099428566280191230
197271405/39307540692992*(3-2*x)^(37/2)-22397546321209486953062074374795737299957063565/3145728*(3-2*x)^(3/2)+
404531566689883337048499233527781983599187634017/12582912*(3-2*x)^(5/2)-11885980275522548300826832180646971886
05612952419/12582912*(3-2*x)^(7/2)+3831583379166294091823572953989993625772471445345/18874368*(3-2*x)^(9/2)+99
77850126168010187169130424774568330973123412551261/21592276992*(3-2*x)^(13/2)-12556967184995885809797263315720
72320357969297077745/2399141888*(3-2*x)^(15/2)+2672239984790337844292019294315182385216573077301785/1179226220
78976*(3-2*x)^(41/2)+1186323846453826237212517196312193819452761764018822545/3915399561216*(3-2*x)^(21/2)-1765
0942358963262675871173166229809316744939271143/51904512*(3-2*x)^(11/2)-688617380989400554399451644246187148600
7042005189775/125627793408*(3-2*x)^(27/2)+136329987967245395141848253765147208279814148352958009/5527622909952
*(3-2*x)^(29/2)-55066091420817590167865401986871791412011888132876913/5527622909952*(3-2*x)^(31/2)[phone]
28439357869138774910126923363791747141675/755914244096*(3-2*x)^(33/2)-1166457217021587688420366823074349521448
8310113371105/9826885173248*(3-2*x)^(35/2)+12646629333382722716904430763732665179119615389552413/25098715136*(
3-2*x)^(17/2)-2593673203685044441695042001860835122939346700333136537/6199382638592*(3-2*x)^(19/2)-75593011640
4682856570195190192032441294632160945523631/3915399561216*(3-2*x)^(23/2)+8535085022072145119870938660211240879
08041634697244059/7830799122432*(3-2*x)^(25/2))/((3-2*x)^2-7+14*x)^19

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

Fricas [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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]

Timed out

________________________________________________________________________________________

Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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

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]

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