3.48 \(\int \frac{1}{(3-2 x)^{21/2} (1+x+2 x^2)^{10}} \, dx\)

Optimal. Leaf size=648 \[ \text{result too large to display} \]

[Out]

4718120139975/(351733660450816*(3 - 2*x)^(19/2)) - 815900548375/(629418129227776*(3 - 2*x)^(17/2)) - 302950882
3715/(1555033025150976*(3 - 2*x)^(15/2)) - 13515743021825/(13476952884641792*(3 - 2*x)^(13/2)) - 5846828446875
/(14513641568075776*(3 - 2*x)^(11/2)) - 37283626871975/(261245548225363968*(3 - 2*x)^(9/2)) - 132355162272575/
(2844673747342852096*(3 - 2*x)^(7/2)) - 11557581705725/(812763927812243456*(3 - 2*x)^(5/2)) - 46601678385075/(
11378694989371408384*(3 - 2*x)^(3/2)) - 24229218097975/(22757389978742816768*Sqrt[3 - 2*x]) + x/(63*(3 - 2*x)^
(19/2)*(1 + x + 2*x^2)^9) + (53 + 173*x)/(7056*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + (8477 + 21409*x)/(691488*
(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + (5*(21409 + 47471*x))/(6453888*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + (41
*(47471 + 92875*x))/(90354432*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + (41*(3436375 + 5677637*x))/(5059848192*(3
- 2*x)^(19/2)*(1 + x + 2*x^2)^4) + (451*(811091 + 998691*x))/(10119696384*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3)
+ (451*(28962039 + 14627273*x))/(283351498752*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + (11275*(14627273 - 3505873
1*x))/(3966920982528*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932
869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 -
(11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2
*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 + (11275*(9756589235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sq
rt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/637206919404798869504 - (11275*(97565
89235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] -
2*x])/637206919404798869504

________________________________________________________________________________________

Rubi [A]  time = 1.1581, antiderivative size = 648, normalized size of antiderivative = 1., number of steps used = 29, 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} \[ \frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac{451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac{451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac{41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac{41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac{5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac{21409 x+8477}{691488 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac{173 x+53}{7056 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac{x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \sqrt{\frac{1}{2} \left (2 \sqrt{14}-7\right )} \log \left (-2 x-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right )}{637206919404798869504}-\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \sqrt{\frac{1}{2} \left (2 \sqrt{14}-7\right )} \log \left (-2 x+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}+\sqrt{14}+3\right )}{637206919404798869504}+\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{2 \sqrt{14}-7}}\right )}{318603459702399434752}-\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{2 \sqrt{3-2 x}+\sqrt{7+2 \sqrt{14}}}{\sqrt{2 \sqrt{14}-7}}\right )}{318603459702399434752} \]

Antiderivative was successfully verified.

[In]

Int[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]

[Out]

4718120139975/(351733660450816*(3 - 2*x)^(19/2)) - 815900548375/(629418129227776*(3 - 2*x)^(17/2)) - 302950882
3715/(1555033025150976*(3 - 2*x)^(15/2)) - 13515743021825/(13476952884641792*(3 - 2*x)^(13/2)) - 5846828446875
/(14513641568075776*(3 - 2*x)^(11/2)) - 37283626871975/(261245548225363968*(3 - 2*x)^(9/2)) - 132355162272575/
(2844673747342852096*(3 - 2*x)^(7/2)) - 11557581705725/(812763927812243456*(3 - 2*x)^(5/2)) - 46601678385075/(
11378694989371408384*(3 - 2*x)^(3/2)) - 24229218097975/(22757389978742816768*Sqrt[3 - 2*x]) + x/(63*(3 - 2*x)^
(19/2)*(1 + x + 2*x^2)^9) + (53 + 173*x)/(7056*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + (8477 + 21409*x)/(691488*
(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + (5*(21409 + 47471*x))/(6453888*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^6) + (41
*(47471 + 92875*x))/(90354432*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5) + (41*(3436375 + 5677637*x))/(5059848192*(3
- 2*x)^(19/2)*(1 + x + 2*x^2)^4) + (451*(811091 + 998691*x))/(10119696384*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3)
+ (451*(28962039 + 14627273*x))/(283351498752*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + (11275*(14627273 - 3505873
1*x))/(3966920982528*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932
869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] - 2*Sqrt[3 - 2*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 -
(11275*Sqrt[(7 + 2*Sqrt[14])/2]*(9756589235 + 2148932869*Sqrt[14])*ArcTan[(Sqrt[7 + 2*Sqrt[14]] + 2*Sqrt[3 - 2
*x])/Sqrt[-7 + 2*Sqrt[14]]])/318603459702399434752 + (11275*(9756589235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sq
rt[14])/2]*Log[3 + Sqrt[14] - Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] - 2*x])/637206919404798869504 - (11275*(97565
89235 - 2148932869*Sqrt[14])*Sqrt[(-7 + 2*Sqrt[14])/2]*Log[3 + Sqrt[14] + Sqrt[7 + 2*Sqrt[14]]*Sqrt[3 - 2*x] -
2*x])/637206919404798869504

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)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{\int \frac{1680-1484 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^9} \, dx}{1764}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{\int \frac{2534672-3322984 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^8} \, dx}{2765952}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{\int \frac{3218135760-5287166640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^7} \, dx}{3794886144}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{\int \frac{3218122918080-6729253503840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^6} \, dx}{4462786105344}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{\int \frac{2223971291223360-6819728658120000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^5} \, dx}{4373530383237120}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{\int \frac{602017891719552000-5205664113141824640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^4} \, dx}{3428847820457902080}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{\int \frac{-644013851165157876480-2602338158011857027840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^3} \, dx}{2016162518429246423040}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{\int \frac{-781280013553524600192000-460008659488539446208000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^2} \, dx}{790335707224264597831680}\\ &=\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-209865664941946247912832000+324150102079841867727744000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )} \, dx}{154905798615955861175009280}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-2327225523695253718758144000+1105437952711266214715136000 x}{(3-2 x)^{19/2} \left (1+x+2 x^2\right )} \, dx}{4337362361246764112900259840}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-20828680094984562179495424000-2676274378513417586741760000 x}{(3-2 x)^{17/2} \left (1+x+2 x^2\right )} \, dx}{121446146114909395161207275520}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-161276892002849662262479872000-99372366651018754238432256000 x}{(3-2 x)^{15/2} \left (1+x+2 x^2\right )} \, dx}{3400492091217463064513803714560}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-1091470402720759789622974464000-1241341767917511174480513024000 x}{(3-2 x)^{13/2} \left (1+x+2 x^2\right )} \, dx}{95213778554088965806386504007680}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-6249079685931055968022769664000-11813932218388106205374976000000 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )} \, dx}{2665985799514491042578822112215040}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-26364773050672235333432205312000-95879912054052861104340934656000 x}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )} \, dx}{74647602386405749192207019142021120}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{-19158360297272160458775773184000-680738564527006107959774429184000 x}{(3-2 x)^{7/2} \left (1+x+2 x^2\right )} \, dx}{2090132866819360977381796535976591360}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{1208210246675834932249342672896000-4161064828351125289593749667840000 x}{(3-2 x)^{5/2} \left (1+x+2 x^2\right )} \, dx}{58523720270942107366690303007344558080}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{17987811630108930037182240718848000-20133547983403412008565127315456000 x}{(3-2 x)^{3/2} \left (1+x+2 x^2\right )} \, dx}{1638664167586379006267328484205647626240}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\int \frac{184169589007678264314588180381696000-48850041379984751902661801017344000 x}{\sqrt{3-2 x} \left (1+x+2 x^2\right )} \, dx}{45882596692418612175485197557758133534720}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\operatorname{Subst}\left (\int \frac{-221789053875402272921190957711360000-48850041379984751902661801017344000 x^2}{28-14 x^2+2 x^4} \, dx,x,\sqrt{3-2 x}\right )}{22941298346209306087742598778879066767360}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\operatorname{Subst}\left (\int \frac{-221789053875402272921190957711360000 \sqrt{7+2 \sqrt{14}}-\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt{14}\right ) x}{\sqrt{14}-\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt{14 \left (7+2 \sqrt{14}\right )}}+\frac{\operatorname{Subst}\left (\int \frac{-221789053875402272921190957711360000 \sqrt{7+2 \sqrt{14}}+\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt{14}\right ) x}{\sqrt{14}+\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt{14 \left (7+2 \sqrt{14}\right )}}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{\left (11275 \left (9756589235-2148932869 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{-\sqrt{7+2 \sqrt{14}}+2 x}{\sqrt{14}-\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}-\frac{\left (11275 \left (9756589235-2148932869 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{\sqrt{7+2 \sqrt{14}}+2 x}{\sqrt{14}+\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}-\frac{\left (11275 \left (30085060166+9756589235 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{\sqrt{14}-\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{1274413838809597739008}-\frac{\left (11275 \left (30085060166+9756589235 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{\sqrt{14}+\sqrt{7+2 \sqrt{14}} x+x^2} \, dx,x,\sqrt{3-2 x}\right )}{1274413838809597739008}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \log \left (3+\sqrt{14}-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}-2 x\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}-\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \log \left (3+\sqrt{14}+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}-2 x\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}+\frac{\left (11275 \left (30085060166+9756589235 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{7-2 \sqrt{14}-x^2} \, dx,x,-\sqrt{7+2 \sqrt{14}}+2 \sqrt{3-2 x}\right )}{637206919404798869504}+\frac{\left (11275 \left (30085060166+9756589235 \sqrt{14}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{7-2 \sqrt{14}-x^2} \, dx,x,\sqrt{7+2 \sqrt{14}}+2 \sqrt{3-2 x}\right )}{637206919404798869504}\\ &=\frac{4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac{815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac{3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac{13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac{5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac{37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac{132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac{11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac{46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac{24229218097975}{22757389978742816768 \sqrt{3-2 x}}+\frac{x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac{53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac{8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac{5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac{41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac{41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac{451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac{451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac{11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{\sqrt{7+2 \sqrt{14}}-2 \sqrt{3-2 x}}{\sqrt{-7+2 \sqrt{14}}}\right )}{318603459702399434752}-\frac{11275 \sqrt{\frac{1}{2} \left (7+2 \sqrt{14}\right )} \left (9756589235+2148932869 \sqrt{14}\right ) \tan ^{-1}\left (\frac{\sqrt{7+2 \sqrt{14}}+2 \sqrt{3-2 x}}{\sqrt{-7+2 \sqrt{14}}}\right )}{318603459702399434752}+\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \log \left (3+\sqrt{14}-\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}-2 x\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}-\frac{11275 \left (9756589235-2148932869 \sqrt{14}\right ) \log \left (3+\sqrt{14}+\sqrt{7+2 \sqrt{14}} \sqrt{3-2 x}-2 x\right )}{91029559914971267072 \sqrt{14 \left (7+2 \sqrt{14}\right )}}\\ \end{align*}

Mathematica [C]  time = 6.08693, size = 610, normalized size = 0.94 \[ \frac{x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}+\frac{\frac{67816 x+20776}{1568 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac{\frac{117492592 x+46521776}{1372 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac{\frac{164128134240 x+74020332960}{1176 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac{\frac{184316990760000 x+94209549053760}{980 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac{1}{980} \left (\frac{157747397367934080 x+95476201213680000}{784 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac{1}{784} \left (\frac{89735798552133000960 x+72879297583985544960}{588 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac{1}{588} \left (\frac{18400346379541577848320 x+36432734212165998389760}{392 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac{1}{392} \left (\frac{6440121232839552246912000-15435719146659136558464000 x}{196 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac{1}{196} \left (\frac{39479926882545221954112000}{19 (3-2 x)^{19/2}}+\frac{1}{266} \left (-\frac{908021664138480966930240000}{17 (3-2 x)^{17/2}}+\frac{1}{238} \left (-\frac{19105520493023248582746201600}{(3-2 x)^{15/2}}+\frac{1}{210} \left (-\frac{26849557435537239465884310720000}{13 (3-2 x)^{13/2}}+\frac{1}{182} \left (-\frac{150994423858598796539274120000000}{(3-2 x)^{11/2}}+\frac{1}{154} \left (-\frac{8237718113587514139784976619840000}{(3-2 x)^{9/2}}+\frac{1}{126} \left (-\frac{338389312036560466460044072847040000}{(3-2 x)^{7/2}}+\frac{1}{98} \left (-\frac{10135305528576510550836394515648960000}{(3-2 x)^{5/2}}+\frac{1}{70} \left (-\frac{204334375738495648812805956791073600000}{(3-2 x)^{3/2}}+\frac{1}{42} \left (-\frac{2230994866519889796828561036406228800000}{\sqrt{3-2 x}}+\frac{1}{7} \left (\frac{\sqrt{\frac{1}{2} \left (7-i \sqrt{7}\right )} \left (-31233928131278457155599854509687203200000-71750597240923349846054347713013891200000 i \sqrt{7}\right ) \tanh ^{-1}\left (\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7-i \sqrt{7}}}\right )}{-14+2 i \sqrt{7}}+\frac{\sqrt{\frac{1}{2} \left (7+i \sqrt{7}\right )} \left (-31233928131278457155599854509687203200000+71750597240923349846054347713013891200000 i \sqrt{7}\right ) \tanh ^{-1}\left (\frac{\sqrt{2} \sqrt{3-2 x}}{\sqrt{7+i \sqrt{7}}}\right )}{-14-2 i \sqrt{7}}\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )}{1176}}{1372}}{1568}}{1764} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((3 - 2*x)^(21/2)*(1 + x + 2*x^2)^10),x]

[Out]

x/(63*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^9) + ((20776 + 67816*x)/(1568*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^8) + ((4
6521776 + 117492592*x)/(1372*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^7) + ((74020332960 + 164128134240*x)/(1176*(3 -
2*x)^(19/2)*(1 + x + 2*x^2)^6) + ((94209549053760 + 184316990760000*x)/(980*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^5
) + ((95476201213680000 + 157747397367934080*x)/(784*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^4) + ((72879297583985544
960 + 89735798552133000960*x)/(588*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^3) + ((36432734212165998389760 + 184003463
79541577848320*x)/(392*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)^2) + ((6440121232839552246912000 - 1543571914665913655
8464000*x)/(196*(3 - 2*x)^(19/2)*(1 + x + 2*x^2)) + (39479926882545221954112000/(19*(3 - 2*x)^(19/2)) + (-9080
21664138480966930240000/(17*(3 - 2*x)^(17/2)) + (-19105520493023248582746201600/(3 - 2*x)^(15/2) + (-268495574
35537239465884310720000/(13*(3 - 2*x)^(13/2)) + (-150994423858598796539274120000000/(3 - 2*x)^(11/2) + (-82377
18113587514139784976619840000/(3 - 2*x)^(9/2) + (-338389312036560466460044072847040000/(3 - 2*x)^(7/2) + (-101
35305528576510550836394515648960000/(3 - 2*x)^(5/2) + (-204334375738495648812805956791073600000/(3 - 2*x)^(3/2
) + (-2230994866519889796828561036406228800000/Sqrt[3 - 2*x] + ((Sqrt[(7 - I*Sqrt[7])/2]*(-3123392813127845715
5599854509687203200000 - (71750597240923349846054347713013891200000*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]*(-31233928131278457155599854509687203
200000 + (71750597240923349846054347713013891200000*I)*Sqrt[7])*ArcTanh[(Sqrt[2]*Sqrt[3 - 2*x])/Sqrt[7 + I*Sqr
t[7]]])/(-14 - (2*I)*Sqrt[7]))/7)/42)/70)/98)/126)/154)/182)/210)/238)/266)/196)/392)/588)/784)/980)/1176)/137
2)/1568)/1764

________________________________________________________________________________________

Maple [A]  time = 0.053, size = 719, normalized size = 1.1 \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)^(21/2)/(2*x^2+x+1)^10,x)

[Out]

1/5367029731/(3-2*x)^(19/2)+5/4802079233/(3-2*x)^(17/2)+73/23727920916/(3-2*x)^(15/2)+165/25705247659/(3-2*x)^
(13/2)+2365/221460595216/(3-2*x)^(11/2)+30349/1993145356944/(3-2*x)^(9/2)+854095/43406276662336/(3-2*x)^(7/2)+
75933/3100448333024/(3-2*x)^(5/2)+8519225/260437659974016/(3-2*x)^(3/2)+891605/12401793332096/(3-2*x)^(1/2)+1/
86812553324672*(-43462358811134257841/1179648*(3-2*x)^(27/2)+192384852501874197/65536*(3-2*x)^(29/2)-135284109
9712333/8192*(3-2*x)^(31/2)+4606702222670185/786432*(3-2*x)^(33/2)-25865320405815/262144*(3-2*x)^(35/2)+544765
170330150812273/1024*(3-2*x)^(1/2)-3476987783905860258979/1536*(3-2*x)^(3/2)+9364999706478908741137/2048*(3-2*
x)^(5/2)-23851905772903279054347/4096*(3-2*x)^(7/2)+192983613795383541041317/36864*(3-2*x)^(9/2)-5775842147534
8449750643/16384*(3-2*x)^(11/2)+60333035869584695411551/32768*(3-2*x)^(13/2)-149770885083493978040723/196608*(
3-2*x)^(15/2)+66256899944582155696811/262144*(3-2*x)^(17/2)-17729978841543630405471/262144*(3-2*x)^(19/2)+2869
878271121283060373/196608*(3-2*x)^(21/2)-165574989211387894481/65536*(3-2*x)^(23/2)+45406001689183688581/13107
2*(3-2*x)^(25/2))/((3-2*x)^2-7+14*x)^9+206922416016525/1274413838809597739008*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)-389615613935075/637206919404798869504*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)-206922416016525/637206919404798869504/(-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)[phone]
075/318603459702399434752/(-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))-110005543624625/318603459702399434752/(-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)-206922416016525/1274413838809597739008*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)[phone]/637206919404798869504*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)-206922416016525/637206919404798869504/(-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)+3
89615613935075/318603459702399434752/(-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))-110005543624625/318603459702399434752/(-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)

________________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{10}{\left (-2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3-2*x)^(21/2)/(2*x^2+x+1)^10,x, algorithm="maxima")

[Out]

integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)), x)

________________________________________________________________________________________

Fricas [B]  time = 3.68979, size = 11992, normalized size = 18.51 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3-2*x)^(21/2)/(2*x^2+x+1)^10,x, algorithm="fricas")

[Out]

1/1094755373086200603246995644663447631605361478665641987670016*(4732002380085251586622550100*4787936175075825
342943147314686^(1/4)*sqrt(1169607525756986)*sqrt(14)*sqrt(7)*(524288*x^28 - 5505024*x^27 + 24772608*x^26 - 64
684032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20 - 515594240*x
^19 + 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 248434368*x^13 + 18
6495624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 5497632*x^6 - 223
5114*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049)*sqrt(327571850528462403199*sqrt(14) + 122
6422380928157351936)*arctan(1/36562170851931970248855340113387035354417457241870626866024945379489008832725311
219252*4787936175075825342943147314686^(3/4)*sqrt(2776387167632535361)*sqrt(12865682783326846)*sqrt(1169607525
756986)*sqrt(4787936175075825342943147314686^(1/4)*sqrt(1169607525756986)*sqrt(-2*x + 3)*sqrt(3275718505284624
03199*sqrt(14) + 1226422380928157351936)*(2148932869*sqrt(14) - 9756589235) - 71440233164918992209696826631202
812*x + 28280279689505005187146*sqrt(22335021272086100802556094) + 107160349747378488314545239946804218)*(9756
589235*sqrt(14)*sqrt(7) - 30085060166*sqrt(7))*sqrt(327571850528462403199*sqrt(14) + 1226422380928157351936) -
1/1023573670806157676669100144258228441327447900096742*4787936175075825342943147314686^(3/4)*sqrt(11696075257
56986)*(9756589235*sqrt(14)*sqrt(7) - 30085060166*sqrt(7))*sqrt(-2*x + 3)*sqrt(327571850528462403199*sqrt(14)
+ 1226422380928157351936) + 2/7*sqrt(14)*sqrt(7) + sqrt(7)) + 4732002380085251586622550100*4787936175075825342
943147314686^(1/4)*sqrt(1169607525756986)*sqrt(14)*sqrt(7)*(524288*x^28 - 5505024*x^27 + 24772608*x^26 - 64684
032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20 - 515594240*x^19
+ 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 248434368*x^13 + 18649
5624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 5497632*x^6 - 223511
4*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049)*sqrt(327571850528462403199*sqrt(14) + 122642
2380928157351936)*arctan(1/39296670234816303076555330542603297083388480635973027797585697454399143598928370335
464344780800*4787936175075825342943147314686^(3/4)*sqrt(2776387167632535361)*sqrt(1169607525756986)*sqrt(-1486
2107440409842545228890767360000*4787936175075825342943147314686^(1/4)*sqrt(1169607525756986)*sqrt(-2*x + 3)*sq
rt(327571850528462403199*sqrt(14) + 1226422380928157351936)*(2148932869*sqrt(14) - 9756589235) - 1061752420864
956548109093061495542399038192585561809435358469816320000*x + 420304555190263689316852795001664341102416628348
354560000*sqrt(22335021272086100802556094) + 15926286312974348221636395922433135985572888783427141530377047244
80000)*(9756589235*sqrt(14)*sqrt(7) - 30085060166*sqrt(7))*sqrt(327571850528462403199*sqrt(14) + 1226422380928
157351936) - 1/1023573670806157676669100144258228441327447900096742*4787936175075825342943147314686^(3/4)*sqrt
(1169607525756986)*(9756589235*sqrt(14)*sqrt(7) - 30085060166*sqrt(7))*sqrt(-2*x + 3)*sqrt(3275718505284624031
99*sqrt(14) + 1226422380928157351936) - 2/7*sqrt(14)*sqrt(7) - sqrt(7)) + 271150425*47879361750758253429431473
14686^(1/4)*sqrt(1169607525756986)*(642998537252061761731821568*x^28 - 6751484641146648498184126464*x^27 + 303
81680885159918241828569088*x^26 - 79329944533473119853663485952*x^25 + 146844790944939604835504750592*x^24 - 2
37989833600419359560990457856*x^23 + 362048363881489025715123781632*x^22 - 474352077153419437787597242368*x^21
+ 550984441886077267281495195648*x^20 - 632336315413643784471854448640*x^19 + 662885025215707070319757885440*
x^18 - 609018199514371017360613048320*x^17 + 573612464628670331388690432000*x^16 - 505075664975624031448627937
280*x^15 + 372261773996761581935835217920*x^14 - 304685469106942025132773736448*x^13 + 22872240721876240451949
1928064*x^12 - 129043951976611196927641387008*x^11 + 102555257051181053298083889152*x^10 - 6106806763728381810
5902989312*x^9 + 23430879305087206538965155840*x^8 - 24573192412708929931548033024*x^7 + 674241892690682755903
8615552*x^6 - 2741193833525857491515080704*x^5 + 4017914249140640432768679936*x^4 + 90121441102219972323783475
2*x^3 + 1013866212399974688642564096*x^2 - 327571850528462403199*sqrt(14)*(524288*x^28 - 5505024*x^27 + 247726
08*x^26 - 64684032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20 -
515594240*x^19 + 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 2484343
68*x^13 + 186495624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 54976
32*x^6 - 2235114*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049) + 168977702066662448107094016
*x + 72419015171426763474468864)*sqrt(327571850528462403199*sqrt(14) + 1226422380928157351936)*log(14862107440
409842545228890767360000/2776387167632535361*4787936175075825342943147314686^(1/4)*sqrt(1169607525756986)*sqrt
(-2*x + 3)*sqrt(327571850528462403199*sqrt(14) + 1226422380928157351936)*(2148932869*sqrt(14) - 9756589235) -
382422319640069460132720868272698184789257093120000*x + 151385426388014656165701481356328960000*sqrt(223350212
72086100802556094) + 573633479460104190199081302409047277183885639680000) - 271150425*478793617507582534294314
7314686^(1/4)*sqrt(1169607525756986)*(642998537252061761731821568*x^28 - 6751484641146648498184126464*x^27 + 3
0381680885159918241828569088*x^26 - 79329944533473119853663485952*x^25 + 146844790944939604835504750592*x^24 -
237989833600419359560990457856*x^23 + 362048363881489025715123781632*x^22 - 474352077153419437787597242368*x^
21 + 550984441886077267281495195648*x^20 - 632336315413643784471854448640*x^19 + 66288502521570707031975788544
0*x^18 - 609018199514371017360613048320*x^17 + 573612464628670331388690432000*x^16 - 5050756649756240314486279
37280*x^15 + 372261773996761581935835217920*x^14 - 304685469106942025132773736448*x^13 + 228722407218762404519
491928064*x^12 - 129043951976611196927641387008*x^11 + 102555257051181053298083889152*x^10 - 61068067637283818
105902989312*x^9 + 23430879305087206538965155840*x^8 - 24573192412708929931548033024*x^7 + 6742418926906827559
038615552*x^6 - 2741193833525857491515080704*x^5 + 4017914249140640432768679936*x^4 + 901214411022199723237834
752*x^3 + 1013866212399974688642564096*x^2 - 327571850528462403199*sqrt(14)*(524288*x^28 - 5505024*x^27 + 2477
2608*x^26 - 64684032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20
- 515594240*x^19 + 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 24843
4368*x^13 + 186495624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 549
7632*x^6 - 2235114*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049) + 1689777020666624481070940
16*x + 72419015171426763474468864)*sqrt(327571850528462403199*sqrt(14) + 1226422380928157351936)*log(-14862107
440409842545228890767360000/2776387167632535361*4787936175075825342943147314686^(1/4)*sqrt(1169607525756986)*s
qrt(-2*x + 3)*sqrt(327571850528462403199*sqrt(14) + 1226422380928157351936)*(2148932869*sqrt(14) - 9756589235)
- 382422319640069460132720868272698184789257093120000*x + 151385426388014656165701481356328960000*sqrt(223350
21272086100802556094) + 573633479460104190199081302409047277183885639680000) + 1272935063665829315736416183610
522832*(240031204937714427494400*x^27 - 2621948941596237063782400*x^26 + 12365045055896811105484800*x^25 - 339
69890064381284111155200*x^24 + 65360120291258796757811200*x^23 - 106701725825102321939251200*x^22 + 1622903072
23249502039654400*x^21 - 216634228326470609547509760*x^20 + 253788172995391086570485760*x^19 - 287279159180291
305208156160*x^18 + 304010591010966811155955200*x^17 - 282644664539994827031006720*x^16 + 25881925681516324984
5447936*x^15 - 229408132984166521977166336*x^14 + 172649692294614969274168896*x^13 - 1333125413772463861158902
40*x^12 + 102031573634317834547976132*x^11 - 59791102681494117572149176*x^10 + 41613884937255303086792337*x^9
- 27246604251076689552043953*x^8 + 10718131725916893151555068*x^7 - 8685973988079840377705700*x^6 + 3673303058
277822225386926*x^5 - 809990362095044210054958*x^4 + 1362587089603925431664856*x^3 + 111926768697602999806116*
x^2 + 205702452014540322797289*x - 4884417100172357749737)*sqrt(-2*x + 3))/(524288*x^28 - 5505024*x^27 + 24772
608*x^26 - 64684032*x^25 + 119734272*x^24 - 194052096*x^23 + 295206912*x^22 - 386777088*x^21 + 449261568*x^20
- 515594240*x^19 + 540503040*x^18 - 496581120*x^17 + 467712000*x^16 - 411828480*x^15 + 303534720*x^14 - 248434
368*x^13 + 186495624*x^12 - 105219828*x^11 + 83621482*x^10 - 49793667*x^9 + 19105065*x^8 - 20036484*x^7 + 5497
632*x^6 - 2235114*x^5 + 3276126*x^4 + 734832*x^3 + 826686*x^2 + 137781*x + 59049)

________________________________________________________________________________________

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)**(21/2)/(2*x**2+x+1)**10,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 )}^{10}{\left (-2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3-2*x)^(21/2)/(2*x^2+x+1)^10,x, algorithm="giac")

[Out]

integrate(1/((2*x^2 + x + 1)^10*(-2*x + 3)^(21/2)), x)