3.1.48 \(\int \frac {1}{(3-2 x)^{21/2} (1+x+2 x^2)^{10}} \, dx\) [48]

Optimal. Leaf size=648 \[ \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 ) \sqrt {\frac {1}{2} \left (-7+2 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{637206919404798869504}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (-7+2 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{637206919404798869504} \]

[Out]

4718120139975/351733660450816/(3-2*x)^(19/2)-815900548375/629418129227776/(3-2*x)^(17/2)-3029508823715/1555033
025150976/(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)-11
557581705725/812763927812243456/(3-2*x)^(5/2)-46601678385075/11378694989371408384/(3-2*x)^(3/2)+1/63*x/(3-2*x)
^(19/2)/(2*x^2+x+1)^9+1/7056*(53+173*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^8+1/691488*(8477+21409*x)/(3-2*x)^(19/2)/(2
*x^2+x+1)^7+5/6453888*(21409+47471*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^6+41/90354432*(47471+92875*x)/(3-2*x)^(19/2)/
(2*x^2+x+1)^5+41/5059848192*(3436375+5677637*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^4+451/10119696384*(811091+998691*x)
/(3-2*x)^(19/2)/(2*x^2+x+1)^3+451/283351498752*(28962039+14627273*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^2+11275/396692
0982528*(14627273-35058731*x)/(3-2*x)^(19/2)/(2*x^2+x+1)-24229218097975/22757389978742816768/(3-2*x)^(1/2)+112
75/1274413838809597739008*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(9756589235-2148932869*14^(1/2
))*(-14+4*14^(1/2))^(1/2)-11275/1274413838809597739008*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(
9756589235-2148932869*14^(1/2))*(-14+4*14^(1/2))^(1/2)+11275/637206919404798869504*arctan((-2*(3-2*x)^(1/2)+(7
+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(9756589235+2148932869*14^(1/2))*(14+4*14^(1/2))^(1/2)-11275/637206
919404798869504*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(9756589235+2148932869*14
^(1/2))*(14+4*14^(1/2))^(1/2)

________________________________________________________________________________________

Rubi [A]
time = 0.71, antiderivative size = 648, normalized size of antiderivative = 1.00, number of steps used = 29, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used = {754, 836, 842, 840, 1183, 648, 632, 210, 642} \begin {gather*} \frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \text {ArcTan}\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 ) \text {ArcTan}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752}+\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} \end {gather*}

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 210

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(-(Rt[-a, 2]*Rt[-b, 2])^(-1))*ArcTan[Rt[-b, 2]*(x/Rt[-a, 2])
], x] /; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 632

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 642

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[d*(Log[RemoveContent[a + b*x +
c*x^2, x]]/b), x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 648

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 754

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 836

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 840

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 842

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 1183

Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[a/c, 2]}, With[{r =
Rt[2*q - b/c, 2]}, Dist[1/(2*c*q*r), Int[(d*r - (d - e*q)*x)/(q - r*x + x^2), x], x] + Dist[1/(2*c*q*r), Int[(
d*r + (d - e*q)*x)/(q + r*x + x^2), x], x]]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2
- b*d*e + a*e^2, 0] && NegQ[b^2 - 4*a*c]

Rubi steps

\begin {align*} \int \frac {1}{(3-2 x)^{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 {\text {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 {\text {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 {\text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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 ) \text {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*}

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Mathematica [C] Result contains complex when optimal does not.
time = 7.15, size = 253, normalized size = 0.39 \begin {gather*} \frac {\frac {14 \left (-4884417100172357749737+205702452014540322797289 x+111926768697602999806116 x^2+1362587089603925431664856 x^3-809990362095044210054958 x^4+3673303058277822225386926 x^5-8685973988079840377705700 x^6+10718131725916893151555068 x^7-27246604251076689552043953 x^8+41613884937255303086792337 x^9-59791102681494117572149176 x^{10}+102031573634317834547976132 x^{11}-133312541377246386115890240 x^{12}+172649692294614969274168896 x^{13}-229408132984166521977166336 x^{14}+258819256815163249845447936 x^{15}-282644664539994827031006720 x^{16}+304010591010966811155955200 x^{17}-287279159180291305208156160 x^{18}+253788172995391086570485760 x^{19}-216634228326470609547509760 x^{20}+162290307223249502039654400 x^{21}-106701725825102321939251200 x^{22}+65360120291258796757811200 x^{23}-33969890064381284111155200 x^{24}+12365045055896811105484800 x^{25}-2621948941596237063782400 x^{26}+240031204937714427494400 x^{27}\right )}{(3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}-426093525 \sqrt {2293002953699236822393+30540258843957888971 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1-\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )-426093525 \sqrt {2293002953699236822393-30540258843957888971 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1+\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )}{12040343345613377038712832} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((14*(-4884417100172357749737 + 205702452014540322797289*x + 111926768697602999806116*x^2 + 136258708960392543
1664856*x^3 - 809990362095044210054958*x^4 + 3673303058277822225386926*x^5 - 8685973988079840377705700*x^6 + 1
0718131725916893151555068*x^7 - 27246604251076689552043953*x^8 + 41613884937255303086792337*x^9 - 597911026814
94117572149176*x^10 + 102031573634317834547976132*x^11 - 133312541377246386115890240*x^12 + 172649692294614969
274168896*x^13 - 229408132984166521977166336*x^14 + 258819256815163249845447936*x^15 - 28264466453999482703100
6720*x^16 + 304010591010966811155955200*x^17 - 287279159180291305208156160*x^18 + 253788172995391086570485760*
x^19 - 216634228326470609547509760*x^20 + 162290307223249502039654400*x^21 - 106701725825102321939251200*x^22
+ 65360120291258796757811200*x^23 - 33969890064381284111155200*x^24 + 12365045055896811105484800*x^25 - 262194
8941596237063782400*x^26 + 240031204937714427494400*x^27))/((3 - 2*x)^(19/2)*(1 + x + 2*x^2)^9) - 426093525*Sq
rt[2293002953699236822393 + (30540258843957888971*I)*Sqrt[7]]*ArcTan[(Sqrt[-1 - I/Sqrt[7]]*Sqrt[3 - 2*x])/2] -
426093525*Sqrt[2293002953699236822393 - (30540258843957888971*I)*Sqrt[7]]*ArcTan[(Sqrt[-1 + I/Sqrt[7]]*Sqrt[3
- 2*x])/2])/12040343345613377038712832

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Maple [A]
time = 0.91, size = 550, normalized size = 0.85 Too large to display

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,method=_RETURNVERBOSE)

[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*(-165574989211387894481/65536*(3-2*x)^(23/2)+45406001689183688581/131072*(3-2*x)^(25/2)-4346235
8811134257841/1179648*(3-2*x)^(27/2)+192384852501874197/65536*(3-2*x)^(29/2)-1352841099712333/8192*(3-2*x)^(31
/2)+4606702222670185/786432*(3-2*x)^(33/2)-25865320405815/262144*(3-2*x)^(35/2)+544765170330150812273/1024*(3-
2*x)^(1/2)-3476987783905860258979/1536*(3-2*x)^(3/2)+9364999706478908741137/2048*(3-2*x)^(5/2)-238519057729032
79054347/4096*(3-2*x)^(7/2)+192983613795383541041317/36864*(3-2*x)^(9/2)-57758421475348449750643/16384*(3-2*x)
^(11/2)+60333035869584695411551/32768*(3-2*x)^(13/2)-149770885083493978040723/196608*(3-2*x)^(15/2)[phone]
4582155696811/262144*(3-2*x)^(17/2)-17729978841543630405471/262144*(3-2*x)^(19/2)+2869878271121283060373/19660
8*(3-2*x)^(21/2))/((3-2*x)^2-7+14*x)^9+11275/1274413838809597739008*(18352320711*(7+2*14^(1/2))^(1/2)*14^(1/2)
-69111417106*(7+2*14^(1/2))^(1/2))*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))+11275/318603459702399
434752*(-9756589235*14^(1/2)-1/2*(18352320711*(7+2*14^(1/2))^(1/2)*14^(1/2)-69111417106*(7+2*14^(1/2))^(1/2))*
(7+2*14^(1/2))^(1/2))/(-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
))-11275/1274413838809597739008*(18352320711*(7+2*14^(1/2))^(1/2)*14^(1/2)-69111417106*(7+2*14^(1/2))^(1/2))*l
n(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))-11275/318603459702399434752*(9756589235*14^(1/2)+1/2*(183
52320711*(7+2*14^(1/2))^(1/2)*14^(1/2)-69111417106*(7+2*14^(1/2))^(1/2))*(7+2*14^(1/2))^(1/2))/(-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))

________________________________________________________________________________________

Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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] Leaf count of result is larger than twice the leaf count of optimal. 1563 vs. \(2 (491) = 982\).
time = 1.73, size = 1563, normalized size = 2.41 \begin {gather*} \text {Too large to display} \end {gather*}

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*47...

________________________________________________________________________________________

Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

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 [B] Leaf count of result is larger than twice the leaf count of optimal. 1000 vs. \(2 (491) = 982\).
time = 1.75, size = 1000, normalized size = 1.54 \begin {gather*} -\frac {11275}{142734349946674946768896} \, \sqrt {7} {\left (6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 15042530083 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} - 45127590249 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} - 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {2 \, \sqrt {14} + 8}\right )} \arctan \left (\frac {14^{\frac {3}{4}} {\left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {\sqrt {14} + 4} + 2 \, \sqrt {-2 \, x + 3}\right )}}{28 \, \sqrt {-\frac {1}{8} \, \sqrt {14} + \frac {1}{2}}}\right ) - \frac {11275}{142734349946674946768896} \, \sqrt {7} {\left (6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 15042530083 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} - 45127590249 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} - 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {2 \, \sqrt {14} + 8}\right )} \arctan \left (-\frac {14^{\frac {3}{4}} {\left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {\sqrt {14} + 4} - 2 \, \sqrt {-2 \, x + 3}\right )}}{28 \, \sqrt {-\frac {1}{8} \, \sqrt {14} + \frac {1}{2}}}\right ) - \frac {11275}{285468699893349893537792} \, \sqrt {7} {\left (2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 45127590249 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 15042530083 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} + 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {-2 \, \sqrt {14} + 8}\right )} \log \left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {-2 \, x + 3} \sqrt {\sqrt {14} + 4} - 2 \, x + \sqrt {14} + 3\right ) + \frac {11275}{285468699893349893537792} \, \sqrt {7} {\left (2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 45127590249 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 15042530083 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} + 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {-2 \, \sqrt {14} + 8}\right )} \log \left (-14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {-2 \, x + 3} \sqrt {\sqrt {14} + 4} - 2 \, x + \sqrt {14} + 3\right ) + \frac {232787883652335 \, {\left (2 \, x - 3\right )}^{17} \sqrt {-2 \, x + 3} + 13820106668010555 \, {\left (2 \, x - 3\right )}^{16} \sqrt {-2 \, x + 3} + 389618236717151904 \, {\left (2 \, x - 3\right )}^{15} \sqrt {-2 \, x + 3} + 6925854690067471092 \, {\left (2 \, x - 3\right )}^{14} \sqrt {-2 \, x + 3} + 86924717622268515682 \, {\left (2 \, x - 3\right )}^{13} \sqrt {-2 \, x + 3} + 817308030405306394458 \, {\left (2 \, x - 3\right )}^{12} \sqrt {-2 \, x + 3} + 5960699611609964201316 \, {\left (2 \, x - 3\right )}^{11} \sqrt {-2 \, x + 3} + 34438539253455396724476 \, {\left (2 \, x - 3\right )}^{10} \sqrt {-2 \, x + 3} + 159569809573892673649239 \, {\left (2 \, x - 3\right )}^{9} \sqrt {-2 \, x + 3} + 596312099501239401271299 \, {\left (2 \, x - 3\right )}^{8} \sqrt {-2 \, x + 3} + 1797250621001927736488676 \, {\left (2 \, x - 3\right )}^{7} \sqrt {-2 \, x + 3} + 4343978582610098069631672 \, {\left (2 \, x - 3\right )}^{6} \sqrt {-2 \, x + 3} + 8317212692450176764092592 \, {\left (2 \, x - 3\right )}^{5} \sqrt {-2 \, x + 3} + 12350951282904546626644288 \, {\left (2 \, x - 3\right )}^{4} \sqrt {-2 \, x + 3} + 13738697725192288735303872 \, {\left (2 \, x - 3\right )}^{3} \sqrt {-2 \, x + 3} + 10788479661863702869789824 \, {\left (2 \, x - 3\right )}^{2} \sqrt {-2 \, x + 3} - 5340653236079401357791744 \, {\left (-2 \, x + 3\right )}^{\frac {3}{2}} + 1255138952440667471476992 \, \sqrt {-2 \, x + 3}}{204816509808685350912 \, {\left ({\left (2 \, x - 3\right )}^{2} + 14 \, x - 7\right )}^{9}} + \frac {235862511885 \, {\left (2 \, x - 3\right )}^{9} - 107316677325 \, {\left (2 \, x - 3\right )}^{8} + 80348352084 \, {\left (2 \, x - 3\right )}^{7} - 64554208290 \, {\left (2 \, x - 3\right )}^{6} + 49954696792 \, {\left (2 \, x - 3\right )}^{5} - 35035280280 \, {\left (2 \, x - 3\right )}^{4} + 21058773120 \, {\left (2 \, x - 3\right )}^{3} - 10093321056 \, {\left (2 \, x - 3\right )}^{2} + 6831901440 \, x - 10859127552}{3280733202692679552 \, {\left (2 \, x - 3\right )}^{9} \sqrt {-2 \, x + 3}} \end {gather*}

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]

-11275/142734349946674946768896*sqrt(7)*(6446798607*14^(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-2*sqrt(14) + 8) + 21
48932869*14^(3/4)*sqrt(7)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) - 15042530083*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sq
rt(14) + 4) - 45127590249*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 78052713880*14^(1/4)*sqrt(7)*sqrt(-2*
sqrt(14) + 8) - 546368997160*14^(1/4)*sqrt(2*sqrt(14) + 8))*arctan(1/28*14^(3/4)*(14^(1/4)*sqrt(1/2)*sqrt(sqrt
(14) + 4) + 2*sqrt(-2*x + 3))/sqrt(-1/8*sqrt(14) + 1/2)) - 11275/142734349946674946768896*sqrt(7)*(6446798607*
14^(3/4)*sqrt(7)*(sqrt(14) + 4)*sqrt(-2*sqrt(14) + 8) + 2148932869*14^(3/4)*sqrt(7)*(sqrt(14) - 4)*sqrt(-2*sqr
t(14) + 8) - 15042530083*14^(3/4)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4) - 45127590249*14^(3/4)*sqrt(2*sqrt(14) +
8)*(sqrt(14) - 4) + 78052713880*14^(1/4)*sqrt(7)*sqrt(-2*sqrt(14) + 8) - 546368997160*14^(1/4)*sqrt(2*sqrt(14
) + 8))*arctan(-1/28*14^(3/4)*(14^(1/4)*sqrt(1/2)*sqrt(sqrt(14) + 4) - 2*sqrt(-2*x + 3))/sqrt(-1/8*sqrt(14) +
1/2)) - 11275/285468699893349893537792*sqrt(7)*(2148932869*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) + 4
) + 6446798607*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 45127590249*14^(3/4)*(sqrt(14) + 4)*sqrt
(-2*sqrt(14) + 8) + 15042530083*14^(3/4)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) + 78052713880*14^(1/4)*sqrt(7)*s
qrt(2*sqrt(14) + 8) + 546368997160*14^(1/4)*sqrt(-2*sqrt(14) + 8))*log(14^(1/4)*sqrt(1/2)*sqrt(-2*x + 3)*sqrt(
sqrt(14) + 4) - 2*x + sqrt(14) + 3) + 11275/285468699893349893537792*sqrt(7)*(2148932869*14^(3/4)*sqrt(7)*sqrt
(2*sqrt(14) + 8)*(sqrt(14) + 4) + 6446798607*14^(3/4)*sqrt(7)*sqrt(2*sqrt(14) + 8)*(sqrt(14) - 4) + 4512759024
9*14^(3/4)*(sqrt(14) + 4)*sqrt(-2*sqrt(14) + 8) + 15042530083*14^(3/4)*(sqrt(14) - 4)*sqrt(-2*sqrt(14) + 8) +
78052713880*14^(1/4)*sqrt(7)*sqrt(2*sqrt(14) + 8) + 546368997160*14^(1/4)*sqrt(-2*sqrt(14) + 8))*log(-14^(1/4)
*sqrt(1/2)*sqrt(-2*x + 3)*sqrt(sqrt(14) + 4) - 2*x + sqrt(14) + 3) + 1/204816509808685350912*(232787883652335*
(2*x - 3)^17*sqrt(-2*x + 3) + 13820106668010555*(2*x - 3)^16*sqrt(-2*x + 3) + 389618236717151904*(2*x - 3)^15*
sqrt(-2*x + 3) + 6925854690067471092*(2*x - 3)^14*sqrt(-2*x + 3) + 86924717622268515682*(2*x - 3)^13*sqrt(-2*x
+ 3) + 817308030405306394458*(2*x - 3)^12*sqrt(-2*x + 3) + 5960699611609964201316*(2*x - 3)^11*sqrt(-2*x + 3)
+ 34438539253455396724476*(2*x - 3)^10*sqrt(-2*x + 3) + 159569809573892673649239*(2*x - 3)^9*sqrt(-2*x + 3) +
596312099501239401271299*(2*x - 3)^8*sqrt(-2*x + 3) + 1797250621001927736488676*(2*x - 3)^7*sqrt(-2*x + 3) +
4343978582610098069631672*(2*x - 3)^6*sqrt(-2*x + 3) + 8317212692450176764092592*(2*x - 3)^5*sqrt(-2*x + 3) +
12350951282904546626644288*(2*x - 3)^4*sqrt(-2*x + 3) + 13738697725192288735303872*(2*x - 3)^3*sqrt(-2*x + 3)
+ 10788479661863702869789824*(2*x - 3)^2*sqrt(-2*x + 3) - 5340653236079401357791744*(-2*x + 3)^(3/2) + 1255138
952440667471476992*sqrt(-2*x + 3))/((2*x - 3)^2 + 14*x - 7)^9 + 1/3280733202692679552*(235862511885*(2*x - 3)^
9 - 107316677325*(2*x - 3)^8 + 80348352084*(2*x - 3)^7 - 64554208290*(2*x - 3)^6 + 49954696792*(2*x - 3)^5 - 3
5035280280*(2*x - 3)^4 + 21058773120*(2*x - 3)^3 - 10093321056*(2*x - 3)^2 + 6831901440*x - 10859127552)/((2*x
- 3)^9*sqrt(-2*x + 3))

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Mupad [B]
time = 0.56, size = 567, normalized size = 0.88 \begin {gather*} \frac {\frac {184192\,{\left (2\,x-3\right )}^2}{47481}-\frac {18944\,x}{2261}-\frac {15552\,{\left (2\,x-3\right )}^3}{4199}+\frac {5666272\,{\left (2\,x-3\right )}^4}{1440257}-\frac {63490768\,{\left (2\,x-3\right )}^5}{12962313}+\frac {533495672\,{\left (2\,x-3\right )}^6}{70572593}-\frac {1111521492\,{\left (2\,x-3\right )}^7}{70572593}+\frac {78007323158\,{\left (2\,x-3\right )}^8}{1482024453}-\frac {250239440467\,{\left (2\,x-3\right )}^9}{494008151}+\frac {1118693654785651073\,{\left (2\,x-3\right )}^{10}}{453254454575104}+\frac {1624300450152249301\,{\left (2\,x-3\right )}^{11}}{97125954551808}+\frac {35048653520674948897\,{\left (2\,x-3\right )}^{12}}{906508909150208}+\frac {95527511967437577915\,{\left (2\,x-3\right )}^{13}}{1813017818300416}+\frac {5640662999731415610547\,{\left (2\,x-3\right )}^{14}}{114220122552926208}+\frac {1737142288764447500149\,{\left (2\,x-3\right )}^{15}}{50764498912411648}+\frac {12971210667229097601055\,{\left (2\,x-3\right )}^{16}}{710702984773763072}+\frac {32723441206946795665235\,{\left (2\,x-3\right )}^{17}}{4264217908642578432}+\frac {102645797034777710681325\,{\left (2\,x-3\right )}^{18}}{39799367147330732032}+\frac {1460931787430200665315\,{\left (2\,x-3\right )}^{19}}{2094703534070038528}+\frac {687618468821894139745\,{\left (2\,x-3\right )}^{20}}{4528256169239642112}+\frac {39968995676603847725\,{\left (2\,x-3\right )}^{21}}{1509418723079880704}+\frac {5940132943613849875\,{\left (2\,x-3\right )}^{22}}{1625527855624486912}+\frac {5717978503620010375\,{\left (2\,x-3\right )}^{23}}{14629750700620382208}+\frac {178056995818325525\,{\left (2\,x-3\right )}^{24}}{5689347494685704192}+\frac {179665281323275\,{\left (2\,x-3\right )}^{25}}{101595490976530432}+\frac {1433237383402275\,{\left (2\,x-3\right )}^{26}}{22757389978742816768}+\frac {24229218097975\,{\left (2\,x-3\right )}^{27}}{22757389978742816768}+\frac {37120}{2261}}{20661046784\,{\left (3-2\,x\right )}^{19/2}-92974710528\,{\left (3-2\,x\right )}^{21/2}[phone]\,{\left (3-2\,x\right )}^{23/2}-270069397248\,{\left (3-2\,x\right )}^{25/2}[phone]\,{\left (3-2\,x\right )}^{27/2}-187609683744\,{\left (3-2\,x\right )}^{29/2}[phone]\,{\left (3-2\,x\right )}^{31/2}-47554666992\,{\left (3-2\,x\right )}^{33/2}[phone]\,{\left (3-2\,x\right )}^{35/2}-5111496103\,{\left (3-2\,x\right )}^{37/2}[phone]\,{\left (3-2\,x\right )}^{39/2}-242625852\,{\left (3-2\,x\right )}^{41/2}[phone]\,{\left (3-2\,x\right )}^{43/2}-4883634\,{\left (3-2\,x\right )}^{45/2}+482454\,{\left (3-2\,x\right )}^{47/2}-35868\,{\left (3-2\,x\right )}^{49/2}+1890\,{\left (3-2\,x\right )}^{51/2}-63\,{\left (3-2\,x\right )}^{53/2}+{\left (3-2\,x\right )}^{55/2}}-\frac {\mathrm {atan}\left (\frac {\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}\,43774618035829144330316520640625{}\mathrm {i}}{330008698047761583560870082619263806430093600589158123831296\,\left (\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}+\frac {43774618035829144330316520640625\,\sqrt {7}\,\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}}{330008698047761583560870082619263806430093600589158123831296\,\left (\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}\right )\,\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,11275{}\mathrm {i}}{318603459702399434752}+\frac {\mathrm {atan}\left (\frac {\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}\,43774618035829144330316520640625{}\mathrm {i}}{330008698047761583560870082619263806430093600589158123831296\,\left (-\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}-\frac {43774618035829144330316520640625\,\sqrt {7}\,\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}}{330008698047761583560870082619263806430093600589158123831296\,\left (-\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}\right )\,\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,11275{}\mathrm {i}}{318603459702399434752} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((184192*(2*x - 3)^2)/47481 - (18944*x)/2261 - (15552*(2*x - 3)^3)/4199 + (5666272*(2*x - 3)^4)/1440257 - (634
90768*(2*x - 3)^5)/12962313 + (533495672*(2*x - 3)^6)/70572593 - (1111521492*(2*x - 3)^7)/70572593 + (78007323
158*(2*x - 3)^8)/1482024453 - (250239440467*(2*x - 3)^9)/494008151 + (1118693654785651073*(2*x - 3)^10)/453254
454575104 + (1624300450152249301*(2*x - 3)^11)/97125954551808 + (35048653520674948897*(2*x - 3)^12)/9065089091
50208 + (95527511967437577915*(2*x - 3)^13)/1813017818300416 + (5640662999731415610547*(2*x - 3)^14)/114220122
552926208 + (1737142288764447500149*(2*x - 3)^15)/50764498912411648 + (12971210667229097601055*(2*x - 3)^16)/7
10702984773763072 + (32723441206946795665235*(2*x - 3)^17)/4264217908642578432 + (102645797034777710681325*(2*
x - 3)^18)/39799367147330732032 + (1460931787430200665315*(2*x - 3)^19)/2094703534070038528 + (687618468821894
139745*(2*x - 3)^20)/4528256169239642112 + (39968995676603847725*(2*x - 3)^21)/1509418723079880704 + (59401329
43613849875*(2*x - 3)^22)/1625527855624486912 + (5717978503620010375*(2*x - 3)^23)/14629750700620382208 + (178
056995818325525*(2*x - 3)^24)/5689347494685704192 + (179665281323275*(2*x - 3)^25)/101595490976530432 + (14332
37383402275*(2*x - 3)^26)/22757389978742816768 + (24229218097975*(2*x - 3)^27)/22757389978742816768 + 37120/22
61)/(20661046784*(3 - 2*x)^(19/2) - 92974710528*(3 - 2*x)^(21/2) + 199231522560*(3 - 2*x)^(23/2) - 27006939724
8*(3 - 2*x)^(25/2) + 259475340096*(3 - 2*x)^(27/2) - 187609683744*(3 - 2*x)^(29/2) + 105782451264*(3 - 2*x)^(3
1/2) - 47554666992*(3 - 2*x)^(33/2) + 17278167438*(3 - 2*x)^(35/2) - 5111496103*(3 - 2*x)^(37/2) + 1234154817*
(3 - 2*x)^(39/2) - 242625852*(3 - 2*x)^(41/2) + 38550456*(3 - 2*x)^(43/2) - 4883634*(3 - 2*x)^(45/2) + 482454*
(3 - 2*x)^(47/2) - 35868*(3 - 2*x)^(49/2) + 1890*(3 - 2*x)^(51/2) - 63*(3 - 2*x)^(53/2) + (3 - 2*x)^(55/2)) -
(atan(((- 7^(1/2)*30540258843957888971i - 2293002953699236822393)^(1/2)*(3 - 2*x)^(1/2)*4377461803582914433031
6520640625i)/(330008698047761583560870082619263806430093600589158123831296*((7^(1/2)*4270909670946074738724274
49424977178671875i)/165004349023880791780435041309631903215046800294579061915648 + 803365829195061345550676106
938401175484375/23572049860554398825776434472804557602149542899225580273664)) + (43774618035829144330316520640
625*7^(1/2)*(- 7^(1/2)*30540258843957888971i - 2293002953699236822393)^(1/2)*(3 - 2*x)^(1/2))/(330008698047761
583560870082619263806430093600589158123831296*((7^(1/2)*427090967094607473872427449424977178671875i)/165004349
023880791780435041309631903215046800294579061915648 + 803365829195061345550676106938401175484375/2357204986055
4398825776434472804557602149542899225580273664)))*(- 7^(1/2)*30540258843957888971i - 2293002953699236822393)^(
1/2)*11275i)/318603459702399434752 + (atan(((7^(1/2)*30540258843957888971i - 2293002953699236822393)^(1/2)*(3
- 2*x)^(1/2)*43774618035829144330316520640625i)/(330008698047761583560870082619263806430093600589158123831296*
((7^(1/2)*427090967094607473872427449424977178671875i)/1650043490238807917804350413096319032150468002945790619
15648 - 803365829195061345550676106938401175484375/23572049860554398825776434472804557602149542899225580273664
)) - (43774618035829144330316520640625*7^(1/2)*(7^(1/2)*30540258843957888971i - 2293002953699236822393)^(1/2)*
(3 - 2*x)^(1/2))/(330008698047761583560870082619263806430093600589158123831296*((7^(1/2)*427090967094607473872
427449424977178671875i)/165004349023880791780435041309631903215046800294579061915648 - 80336582919506134555067
6106938401175484375/23572049860554398825776434472804557602149542899225580273664)))*(7^(1/2)*305402588439578889
71i - 2293002953699236822393)^(1/2)*11275i)/318603459702399434752

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