3.51 \(\int \frac{1}{(3-2 x+x^2)^{21/2} (1+x+2 x^2)^{10}} \, dx\)
Optimal. Leaf size=638 \[ \text{result too large to display} \]
[Out]
(37358055634422583 - 14024622879097678*x)/(1840124479200000000*(3 - 2*x + x^2)^(19/2)) + (476849951294984711 -
125181871472148210*x)/(104273720488000000000*(3 - 2*x + x^2)^(17/2)) + (7851758375483333511 + 194216499620458
4234*x)/(15641058073200000000000*(3 - 2*x + x^2)^(15/2)) - (11*(7502325106308201089 - 7813986379726516886*x))/
(406667509903200000000000*(3 - 2*x + x^2)^(13/2)) - (3*(69053268515296359011 - 44840736195018286006*x))/(11470
10925368000000000000*(3 - 2*x + x^2)^(11/2)) - (838519439380295335657 - 466189390555853643870*x)/(938463484392
0000000000000*(3 - 2*x + x^2)^(9/2)) - (1117646664729238460189 - 568839749685437871554*x)/(3128211614640000000
0000000*(3 - 2*x + x^2)^(7/2)) - (6551405511565449301689 - 3127298559983309301910*x)/(521368602440000000000000
000*(3 - 2*x + x^2)^(5/2)) - (4179039782398459850819 - 1886993445589652402694*x)/(1042737204880000000000000000
*(3 - 2*x + x^2)^(3/2)) - (12105495874518671061833 - 5117656435043679338190*x)/(10427372048800000000000000000*
Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(630*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^9) + (887 + 2218*x)/(88200*(3 -
2*x + x^2)^(19/2)*(1 + x + 2*x^2)^8) + (14453 + 29371*x)/(1080450*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^7) +
(8837931 + 17459234*x)/(605052000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^6) + (447940041 + 813432205*x)/(26471
025000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^5) + (592729157441 + 911061463974*x)/(29647548000000*(3 - 2*x +
x^2)^(19/2)*(1 + x + 2*x^2)^4) + (277010166219 + 310705340015*x)/(12353145000000*(3 - 2*x + x^2)^(19/2)*(1 + x
+ 2*x^2)^3) + (5488221294349 + 1384103301166*x)/(276710448000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^2) -
(37857197792117 + 146548895467025*x)/(2421216420000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)) + (Sqrt[(810422
25921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7
*(81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2]))]*(2729445895
23248381749 + 191941026386645109841*Sqrt[2] + (656826642296538601431 + 464885615909893491590*Sqrt[2])*x))/Sqrt
[3 - 2*x + x^2]])/32282885600000000000000000 - (Sqrt[(-81042225921274689605478944797800854846405 + 57305922523
001707126026363878666500308992*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-81042225921274689605478944797800854846405 + 5
7305922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 - 191941026386645109841*Sqrt[2] + (
656826642296538601431 - 464885615909893491590*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000
________________________________________________________________________________________
Rubi [A] time = 1.39713, antiderivative size = 638, normalized size of antiderivative = 1.,
number of steps used = 24, number of rules used = 6, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.261, Rules used
= {974, 1060, 1035, 1029, 206, 204} \[ -\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{x^2-2 x+3}}-\frac{146548895467025 x+37857197792117}{2421216420000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (x^2-2 x+3\right )^{3/2}}+\frac{1384103301166 x+5488221294349}{276710448000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^2}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (x^2-2 x+3\right )^{5/2}}+\frac{310705340015 x+277010166219}{12353145000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^3}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (x^2-2 x+3\right )^{7/2}}+\frac{911061463974 x+592729157441}{29647548000000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^4}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (x^2-2 x+3\right )^{9/2}}+\frac{813432205 x+447940041}{26471025000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^5}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (x^2-2 x+3\right )^{11/2}}+\frac{17459234 x+8837931}{605052000 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^6}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (x^2-2 x+3\right )^{13/2}}+\frac{29371 x+14453}{1080450 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^7}+\frac{1942164996204584234 x+7851758375483333511}{15641058073200000000000 \left (x^2-2 x+3\right )^{15/2}}+\frac{2218 x+887}{88200 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^8}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (x^2-2 x+3\right )^{17/2}}-\frac{1-10 x}{630 \left (x^2-2 x+3\right )^{19/2} \left (2 x^2+x+1\right )^9}+\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (x^2-2 x+3\right )^{19/2}}+\frac{\sqrt{\frac{1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )}} \left (\left (656826642296538601431+464885615909893491590 \sqrt{2}\right ) x+191941026386645109841 \sqrt{2}+272944589523248381749\right )}{\sqrt{x^2-2 x+3}}\right )}{32282885600000000000000000}-\frac{\sqrt{\frac{1}{70} \left (57305922523001707126026363878666500308992 \sqrt{2}-81042225921274689605478944797800854846405\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (57305922523001707126026363878666500308992 \sqrt{2}-81042225921274689605478944797800854846405\right )}} \left (\left (656826642296538601431-464885615909893491590 \sqrt{2}\right ) x-191941026386645109841 \sqrt{2}+272944589523248381749\right )}{\sqrt{x^2-2 x+3}}\right )}{32282885600000000000000000} \]
Antiderivative was successfully verified.
[In]
Int[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]
[Out]
(37358055634422583 - 14024622879097678*x)/(1840124479200000000*(3 - 2*x + x^2)^(19/2)) + (476849951294984711 -
125181871472148210*x)/(104273720488000000000*(3 - 2*x + x^2)^(17/2)) + (7851758375483333511 + 194216499620458
4234*x)/(15641058073200000000000*(3 - 2*x + x^2)^(15/2)) - (11*(7502325106308201089 - 7813986379726516886*x))/
(406667509903200000000000*(3 - 2*x + x^2)^(13/2)) - (3*(69053268515296359011 - 44840736195018286006*x))/(11470
10925368000000000000*(3 - 2*x + x^2)^(11/2)) - (838519439380295335657 - 466189390555853643870*x)/(938463484392
0000000000000*(3 - 2*x + x^2)^(9/2)) - (1117646664729238460189 - 568839749685437871554*x)/(3128211614640000000
0000000*(3 - 2*x + x^2)^(7/2)) - (6551405511565449301689 - 3127298559983309301910*x)/(521368602440000000000000
000*(3 - 2*x + x^2)^(5/2)) - (4179039782398459850819 - 1886993445589652402694*x)/(1042737204880000000000000000
*(3 - 2*x + x^2)^(3/2)) - (12105495874518671061833 - 5117656435043679338190*x)/(10427372048800000000000000000*
Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(630*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^9) + (887 + 2218*x)/(88200*(3 -
2*x + x^2)^(19/2)*(1 + x + 2*x^2)^8) + (14453 + 29371*x)/(1080450*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^7) +
(8837931 + 17459234*x)/(605052000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^6) + (447940041 + 813432205*x)/(26471
025000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^5) + (592729157441 + 911061463974*x)/(29647548000000*(3 - 2*x +
x^2)^(19/2)*(1 + x + 2*x^2)^4) + (277010166219 + 310705340015*x)/(12353145000000*(3 - 2*x + x^2)^(19/2)*(1 + x
+ 2*x^2)^3) + (5488221294349 + 1384103301166*x)/(276710448000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)^2) -
(37857197792117 + 146548895467025*x)/(2421216420000000*(3 - 2*x + x^2)^(19/2)*(1 + x + 2*x^2)) + (Sqrt[(810422
25921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2])/70]*ArcTan[(Sqrt[5/(7
*(81042225921274689605478944797800854846405 + 57305922523001707126026363878666500308992*Sqrt[2]))]*(2729445895
23248381749 + 191941026386645109841*Sqrt[2] + (656826642296538601431 + 464885615909893491590*Sqrt[2])*x))/Sqrt
[3 - 2*x + x^2]])/32282885600000000000000000 - (Sqrt[(-81042225921274689605478944797800854846405 + 57305922523
001707126026363878666500308992*Sqrt[2])/70]*ArcTanh[(Sqrt[5/(7*(-81042225921274689605478944797800854846405 + 5
7305922523001707126026363878666500308992*Sqrt[2]))]*(272944589523248381749 - 191941026386645109841*Sqrt[2] + (
656826642296538601431 - 464885615909893491590*Sqrt[2])*x))/Sqrt[3 - 2*x + x^2]])/32282885600000000000000000
Rule 974
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((d_.) + (e_.)*(x_) + (f_.)*(x_)^2)^(q_), x_Symbol] :> Simp[((2*a
*c^2*e - b^2*c*e + b^3*f + b*c*(c*d - 3*a*f) + c*(2*c^2*d + b^2*f - c*(b*e + 2*a*f))*x)*(a + b*x + c*x^2)^(p +
1)*(d + e*x + f*x^2)^(q + 1))/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)), x] - Dist[1/
((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)), Int[(a + b*x + c*x^2)^(p + 1)*(d + e*x + f*
x^2)^q*Simp[2*c*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1) - (2*c^2*d + b^2*f - c*(b*e + 2*a*f))*(a*f*(
p + 1) - c*d*(p + 2)) - e*(b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f))*(p + q + 2) + (2*f*(2*a*c^2*e - b^
2*c*e + b^3*f + b*c*(c*d - 3*a*f))*(p + q + 2) - (2*c^2*d + b^2*f - c*(b*e + 2*a*f))*(b*f*(p + 1) - c*e*(2*p +
q + 4)))*x + c*f*(2*c^2*d + b^2*f - c*(b*e + 2*a*f))*(2*p + 2*q + 5)*x^2, x], x], x] /; FreeQ[{a, b, c, d, e,
f, q}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0] && LtQ[p, -1] && NeQ[(c*d - a*f)^2 - (b*d - a*e)*(c*e
- b*f), 0] && !( !IntegerQ[p] && ILtQ[q, -1]) && !IGtQ[q, 0]
Rule 1060
Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((A_.) + (B_.)*(x_) + (C_.)*(x_)^2)*((d_) + (e_.)*(x_) + (f_.)*(x_
)^2)^(q_), x_Symbol] :> Simp[((a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^(q + 1)*((A*c - a*C)*(2*a*c*e - b*(c
*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) + c*(A*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) - B*(b
*c*d - 2*a*c*e + a*b*f) + C*(b^2*d - a*b*e - 2*a*(c*d - a*f)))*x))/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)
*(c*e - b*f))*(p + 1)), x] + Dist[1/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)), Int[(a
+ b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^q*Simp[(b*B - 2*A*c - 2*a*C)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f)
)*(p + 1) + (b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*e + a*B*f) + 2*(A*c*(c*d - a*f) - a*(c*C*d - B*c*e - a*C
*f)))*(a*f*(p + 1) - c*d*(p + 2)) - e*((A*c - a*C)*(2*a*c*e - b*(c*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f -
c*(b*e + 2*a*f)))*(p + q + 2) - (2*f*((A*c - a*C)*(2*a*c*e - b*(c*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f - c
*(b*e + 2*a*f)))*(p + q + 2) - (b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*e + a*B*f) + 2*(A*c*(c*d - a*f) - a*(
c*C*d - B*c*e - a*C*f)))*(b*f*(p + 1) - c*e*(2*p + q + 4)))*x - c*f*(b^2*(C*d + A*f) - b*(B*c*d + A*c*e + a*C*
e + a*B*f) + 2*(A*c*(c*d - a*f) - a*(c*C*d - B*c*e - a*C*f)))*(2*p + 2*q + 5)*x^2, x], x], x] /; FreeQ[{a, b,
c, d, e, f, A, B, C, q}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0] && LtQ[p, -1] && NeQ[(c*d - a*f)^2 -
(b*d - a*e)*(c*e - b*f), 0] && !( !IntegerQ[p] && ILtQ[q, -1]) && !IGtQ[q, 0]
Rule 1035
Int[((g_.) + (h_.)*(x_))/(((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*Sqrt[(d_.) + (e_.)*(x_) + (f_.)*(x_)^2]), x_Symb
ol] :> With[{q = Rt[(c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f), 2]}, Dist[1/(2*q), Int[Simp[h*(b*d - a*e) - g*(c*
d - a*f - q) - (g*(c*e - b*f) - h*(c*d - a*f + q))*x, x]/((a + b*x + c*x^2)*Sqrt[d + e*x + f*x^2]), x], x] - D
ist[1/(2*q), Int[Simp[h*(b*d - a*e) - g*(c*d - a*f + q) - (g*(c*e - b*f) - h*(c*d - a*f - q))*x, x]/((a + b*x
+ c*x^2)*Sqrt[d + e*x + f*x^2]), x], x]] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e
^2 - 4*d*f, 0] && NeQ[b*d - a*e, 0] && NegQ[b^2 - 4*a*c]
Rule 1029
Int[((g_.) + (h_.)*(x_))/(((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*Sqrt[(d_.) + (e_.)*(x_) + (f_.)*(x_)^2]), x_Symb
ol] :> Dist[-2*g*(g*b - 2*a*h), Subst[Int[1/Simp[g*(g*b - 2*a*h)*(b^2 - 4*a*c) - (b*d - a*e)*x^2, x], x], x, S
imp[g*b - 2*a*h - (b*h - 2*g*c)*x, x]/Sqrt[d + e*x + f*x^2]], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && NeQ[
b^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0] && NeQ[b*d - a*e, 0] && EqQ[h^2*(b*d - a*e) - 2*g*h*(c*d - a*f) + g^2*(
c*e - b*f), 0]
Rule 206
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 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])
Rubi steps
\begin{align*} \int \frac{1}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}-\frac{\int \frac{-2960+3060 x-1800 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^9} \, dx}{3150}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}-\frac{\int \frac{-8066100+8650900 x-7541200 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^8} \, dx}{8820000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}-\frac{\int \frac{-18577805000+18950890000 x-18797440000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^7} \, dx}{21609000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}-\frac{\int \frac{-34422218025000+37067282625000 x-39283276500000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^6} \, dx}{45378900000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}-\frac{\int \frac{-47542711206750000+57420932725500000 x-68328305220000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^5} \, dx}{79413075000000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}-\frac{\int \frac{-40751213836916250000+59562989955686250000 x-88828492737465000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^4} \, dx}{111178305000000000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}-\frac{\int \frac{-7802817431641312500000+24109394856584625000000 x-70467971115402000000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^3} \, dx}{116737220250000000000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{\int \frac{16833881379064542187500000-26649709913445904687500000 x-8992346134762856250000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )^2} \, dx}{81716054175000000000000000}\\ &=-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{-6456478383150221671875000000-27827888668333982156250000000 x+34622176554084656250000000000 x^2}{\left (3-2 x+x^2\right )^{21/2} \left (1+x+2 x^2\right )} \, dx}{28600618961250000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{4967712444964210062187500000000-37459045941891614735625000000000 x+29819854396681437847500000000000 x^2}{\left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )} \, dx}{108682352052750000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{14762203931705757912393750000000000-35273795655183209407237500000000000 x+14195624224941607014000000000000000 x^2}{\left (3-2 x+x^2\right )^{17/2} \left (1+x+2 x^2\right )} \, dx}{369519996979350000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{17682321750123664132939125000000000000-22751442786535433811492750000000000000 x-3854226434967997412373000000000000000 x^2}{\left (3-2 x+x^2\right )^{15/2} \left (1+x+2 x^2\right )} \, dx}{1108559990938050000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{13399310005134207269200312500000000000000-7942120150303904451111225000000000000000 x-14620749915106285745394600000000000000000 x^2}{\left (3-2 x+x^2\right )^{13/2} \left (1+x+2 x^2\right )} \, dx}{2882255976438930000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{6370652021675523452523402750000000000000000+1397569502668803779552737500000000000000000 x-14873447992206590376760170000000000000000000 x^2}{\left (3-2 x+x^2\right )^{11/2} \left (1+x+2 x^2\right )} \, dx}{6340963148165646000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{1329917982742483936025158935000000000000000000+3615108788879230023346255290000000000000000000 x-9071784474158200631669632800000000000000000000 x^2}{\left (3-2 x+x^2\right )^{9/2} \left (1+x+2 x^2\right )} \, dx}{11413733666698162800000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{-420915070441561410503321633100000000000000000000+2181291929685915536692331929800000000000000000000 x-3486830438264921097598322474400000000000000000000 x^2}{\left (3-2 x+x^2\right )^{7/2} \left (1+x+2 x^2\right )} \, dx}{15979227133377427920000000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{-379110186022081999740742476990000000000000000000000+666051943754340912077121512700000000000000000000000 x-766779031495028265360690083040000000000000000000000 x^2}{\left (3-2 x+x^2\right )^{5/2} \left (1+x+2 x^2\right )} \, dx}{15979227133377427920000000000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{-96896452988962143502089877773000000000000000000000000+91746249937845836577877948114800000000000000000000000 x-69400489538857249491540692270400000000000000000000000 x^2}{\left (3-2 x+x^2\right )^{3/2} \left (1+x+2 x^2\right )} \, dx}{9587536280026456752000000000000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{3-2 x+x^2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{-6260702387317500351852137783268000000000000000000000000+2570011459509637702693150504488000000000000000000000000 x}{\sqrt{3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{1917507256005291350400000000000000000000000000000000000000000}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{3-2 x+x^2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\int \frac{296985108420000000000000000000000000 \left (148672670724261260159-105404315061877410477 \sqrt{2}\right )-296985108420000000000000000000000000 \left (62135959399493560795-43268355662383849682 \sqrt{2}\right ) x}{\sqrt{3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{19175072560052913504000000000000000000000000000000000000000000 \sqrt{2}}+\frac{\int \frac{296985108420000000000000000000000000 \left (148672670724261260159+105404315061877410477 \sqrt{2}\right )-296985108420000000000000000000000000 \left (62135959399493560795+43268355662383849682 \sqrt{2}\right ) x}{\sqrt{3-2 x+x^2} \left (1+x+2 x^2\right )} \, dx}{19175072560052913504000000000000000000000000000000000000000000 \sqrt{2}}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{3-2 x+x^2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}-\frac{\left (3788075362500000 \left (114611845046003414252052727757333000617984-81042225921274689605478944797800854846405 \sqrt{2}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{-617401082362674084274800000000000000000000000000000000000000000000000000 \left (81042225921274689605478944797800854846405-57305922523001707126026363878666500308992 \sqrt{2}\right )-5 x^2} \, dx,x,\frac{296985108420000000000000000000000000 \left (272944589523248381749-191941026386645109841 \sqrt{2}\right )+296985108420000000000000000000000000 \left (656826642296538601431-464885615909893491590 \sqrt{2}\right ) x}{\sqrt{3-2 x+x^2}}\right )}{823543}-\frac{\left (3788075362500000 \left (114611845046003414252052727757333000617984+81042225921274689605478944797800854846405 \sqrt{2}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{-617401082362674084274800000000000000000000000000000000000000000000000000 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )-5 x^2} \, dx,x,\frac{296985108420000000000000000000000000 \left (272944589523248381749+191941026386645109841 \sqrt{2}\right )+296985108420000000000000000000000000 \left (656826642296538601431+464885615909893491590 \sqrt{2}\right ) x}{\sqrt{3-2 x+x^2}}\right )}{823543}\\ &=\frac{37358055634422583-14024622879097678 x}{1840124479200000000 \left (3-2 x+x^2\right )^{19/2}}+\frac{476849951294984711-125181871472148210 x}{104273720488000000000 \left (3-2 x+x^2\right )^{17/2}}+\frac{7851758375483333511+1942164996204584234 x}{15641058073200000000000 \left (3-2 x+x^2\right )^{15/2}}-\frac{11 (7502325106308201089-7813986379726516886 x)}{406667509903200000000000 \left (3-2 x+x^2\right )^{13/2}}-\frac{3 (69053268515296359011-44840736195018286006 x)}{1147010925368000000000000 \left (3-2 x+x^2\right )^{11/2}}-\frac{838519439380295335657-466189390555853643870 x}{9384634843920000000000000 \left (3-2 x+x^2\right )^{9/2}}-\frac{1117646664729238460189-568839749685437871554 x}{31282116146400000000000000 \left (3-2 x+x^2\right )^{7/2}}-\frac{6551405511565449301689-3127298559983309301910 x}{521368602440000000000000000 \left (3-2 x+x^2\right )^{5/2}}-\frac{4179039782398459850819-1886993445589652402694 x}{1042737204880000000000000000 \left (3-2 x+x^2\right )^{3/2}}-\frac{12105495874518671061833-5117656435043679338190 x}{10427372048800000000000000000 \sqrt{3-2 x+x^2}}-\frac{1-10 x}{630 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^9}+\frac{887+2218 x}{88200 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^8}+\frac{14453+29371 x}{1080450 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^7}+\frac{8837931+17459234 x}{605052000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^6}+\frac{447940041+813432205 x}{26471025000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^5}+\frac{592729157441+911061463974 x}{29647548000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^4}+\frac{277010166219+310705340015 x}{12353145000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^3}+\frac{5488221294349+1384103301166 x}{276710448000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )^2}-\frac{37857197792117+146548895467025 x}{2421216420000000 \left (3-2 x+x^2\right )^{19/2} \left (1+x+2 x^2\right )}+\frac{\sqrt{\frac{1}{70} \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )}} \left (272944589523248381749+191941026386645109841 \sqrt{2}+\left (656826642296538601431+464885615909893491590 \sqrt{2}\right ) x\right )}{\sqrt{3-2 x+x^2}}\right )}{32282885600000000000000000}-\frac{\sqrt{\frac{1}{70} \left (-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{5}{7 \left (-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992 \sqrt{2}\right )}} \left (272944589523248381749-191941026386645109841 \sqrt{2}+\left (656826642296538601431-464885615909893491590 \sqrt{2}\right ) x\right )}{\sqrt{3-2 x+x^2}}\right )}{32282885600000000000000000}\\ \end{align*}
Mathematica [C] time = 11.5202, size = 1431, normalized size = 2.24 \[ \text{result too large to display} \]
Warning: Unable to verify antiderivative.
[In]
Integrate[1/((3 - 2*x + x^2)^(21/2)*(1 + x + 2*x^2)^10),x]
[Out]
Sqrt[3 - 2*x + x^2]*((1 - x)/(11875000000*(3 - 2*x + x^2)^10) + (265 - 113*x)/(403750000000*(3 - 2*x + x^2)^9)
+ (82361 - 4841*x)/(60562500000000*(3 - 2*x + x^2)^8) + (1062937 + 1642511*x)/(1574625000000000*(3 - 2*x + x^
2)^7) + (7*(-678331 + 833371*x))/(2220625000000000*(3 - 2*x + x^2)^6) + (7*(-73161291 + 43964675*x))/(90843750
000000000*(3 - 2*x + x^2)^5) + (-1340879383 + 430593031*x)/(181687500000000000*(3 - 2*x + x^2)^4) - (11*(16261
25723 + 112950205*x))/(3028125000000000000*(3 - 2*x + x^2)^3) - (11*(3311570647 + 15286717673*x))/(36337500000
000000000*(3 - 2*x + x^2)^2) - (11*(-411521923277 + 484788625685*x))/(363375000000000000000*(3 - 2*x + x^2)) +
(251943 + 221770*x)/(6300000000000*(1 + x + 2*x^2)^9) - (73*(-888423 + 1604678*x))/(882000000000000*(1 + x +
2*x^2)^8) + (-2596903794 - 4965311863*x)/(10804500000000000*(1 + x + 2*x^2)^7) + (-539608494637 - 334647150510
*x)/(1210104000000000000*(1 + x + 2*x^2)^6) + (-40800462989458 + 56711874696335*x)/(264710250000000000000*(1 +
x + 2*x^2)^5) + (42018358198215561 + 129196597088670934*x)/(296475480000000000000000*(1 + x + 2*x^2)^4) + (62
819559864314747 + 169630389653846945*x)/(370594350000000000000000*(1 + x + 2*x^2)^3) + (1082422109196374795 +
4797048907791526114*x)/(8301313440000000000000000*(1 + x + 2*x^2)^2) + (65571203144429922747 + 367152793968978
953465*x)/(363182463000000000000000000*(1 + x + 2*x^2))) + ((232442807954946745795*I + 21634177831191924841*Sq
rt[7])*ArcTan[(-135063738860435016899586558948733259113515 + (188630894626466690216855285995045889396405*I)*Sq
rt[7] - 1506241361872688008559268776761430483700000*x - (105711500937472192718115651350352447938680*I)*Sqrt[7]
*x + 491153540508443587025809789813541985707360*x^2 - (460764064177139993399975100872663310399420*I)*Sqrt[7]*x
^2 - 180084985147246689199448745264977678818020*x^3 + (197868296377913870863837680953446009396860*I)*Sqrt[7]*x
^3 - 176004816500761880926774485599831047775825*x^4 - (207342833228459577163557043035558264835165*I)*Sqrt[7]*x
^4 + (186244248199755548159585682605666126004224*I)*Sqrt[10*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (114611845
046003414252052727757333000617984*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2] + (3008560932457589624116
38410362999126622208*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x^2*Sqrt[3 - 2*x + x^2] - (143264806307504267815065909696666
250772480*I)*Sqrt[10*(-5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*x + x^2])/(2368773290838836979864678493023884746594823*I
+ 423642940259238735473942663180025956729505*Sqrt[7] + (1890613486065620301760074218556745311646936*I)*x + 61
50574559311228258394328777942059796320*Sqrt[7]*x + (2511300259855822962340893027852239157667820*I)*x^2 - 20278
67550801106189867763431094227596320*Sqrt[7]*x^2 - (3134217746230760357128318797499380812303788*I)*x^3 + 634304
31602720043279192866968369397935660*Sqrt[7]*x^3 + (944749064886626467328385369190460703669697*I)*x^4 + 1638131
7765107264789462917221030750634835*Sqrt[7]*x^4)])/(16141442800000000000000000*Sqrt[70*(-5 + I*Sqrt[7])]) - ((I
/16141442800000000000000000)*(-232442807954946745795*I + 21634177831191924841*Sqrt[7])*ArcTan[(35*(43624942906
63946676585186218212607628595*I + 12104084007406821013541218948000741620843*Sqrt[7] - (40919031596617332707196
094500783237405000*I)*x + 175730701694606521668409393655487422752*Sqrt[7]*x + (2648728832926512757773396585336
4310310620*I)*x^2 - 57939072880031605424793240888406502752*Sqrt[7]*x^2 - (152388941497528256839248140210078630
70620*I)*x^3 + 1812298045792001236548367627667697083876*Sqrt[7]*x^3 - (795837271959975808913244203765619963595
*I)*x^4 + 468037650431636136841797634886592875281*Sqrt[7]*x^4))/(135063738860435016899586558948733259113515 +
(188630894626466690216855285995045889396405*I)*Sqrt[7] + 1506241361872688008559268776761430483700000*x - (1057
11500937472192718115651350352447938680*I)*Sqrt[7]*x - 491153540508443587025809789813541985707360*x^2 - (460764
064177139993399975100872663310399420*I)*Sqrt[7]*x^2 + 180084985147246689199448745264977678818020*x^3 + (197868
296377913870863837680953446009396860*I)*Sqrt[7]*x^3 + 176004816500761880926774485599831047775825*x^4 - (207342
833228459577163557043035558264835165*I)*Sqrt[7]*x^4 - (14326480630750426781506590969666625077248*I)*Sqrt[70*(5
+ I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - (14326480630750426781506590969666625077248*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^
2*Sqrt[3 - 2*x + x^2] + (28652961261500853563013181939333250154496*I)*Sqrt[70*(5 + I*Sqrt[7])]*x^3*Sqrt[3 - 2*
x + x^2])])/Sqrt[70*(5 + I*Sqrt[7])] - ((-232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(-I + Sq
rt[7] - (4*I)*x)^2*(I + Sqrt[7] + (4*I)*x)^2])/(32282885600000000000000000*Sqrt[70*(5 + I*Sqrt[7])]) + ((I/322
82885600000000000000000)*(232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(-I + Sqrt[7] - (4*I)*x)
^2*(I + Sqrt[7] + (4*I)*x)^2])/Sqrt[70*(-5 + I*Sqrt[7])] - ((I/32282885600000000000000000)*(232442807954946745
795*I + 21634177831191924841*Sqrt[7])*Log[(1 + x + 2*x^2)*(-13*I + 15*Sqrt[7] + (22*I)*x - 10*Sqrt[7]*x + (9*I
)*x^2 + 5*Sqrt[7]*x^2 + I*Sqrt[70*(-5 + I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] - I*Sqrt[70*(-5 + I*Sqrt[7])]*x*Sqrt[3
- 2*x + x^2])])/Sqrt[70*(-5 + I*Sqrt[7])] + ((-232442807954946745795*I + 21634177831191924841*Sqrt[7])*Log[(1
+ x + 2*x^2)*(-163*I + 15*Sqrt[7] + (122*I)*x - 10*Sqrt[7]*x - (41*I)*x^2 + 5*Sqrt[7]*x^2 - (13*I)*Sqrt[10*(5
+ I*Sqrt[7])]*Sqrt[3 - 2*x + x^2] + (5*I)*Sqrt[10*(5 + I*Sqrt[7])]*x*Sqrt[3 - 2*x + x^2])])/(3228288560000000
0000000000*Sqrt[70*(5 + I*Sqrt[7])])
________________________________________________________________________________________
Maple [B] time = 3.525, size = 86793, normalized size = 136. \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x)
[Out]
result too large to display
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (2 \, x^{2} + x + 1\right )}^{10}{\left (x^{2} - 2 \, x + 3\right )}^{\frac{21}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x, algorithm="maxima")
[Out]
integrate(1/((2*x^2 + x + 1)^10*(x^2 - 2*x + 3)^(21/2)), x)
________________________________________________________________________________________
Fricas [B] time = 6.01536, size = 30714, normalized size = 48.14 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x, algorithm="fricas")
[Out]
1/143446642399233767656421653603627286364552203186085711012681333261811289872032000000000000000000*(3604596077
6272236628083717974972055111190660172853358396135728761934386631817942748278579200*x^38 - 55871239203221966773
5297628612066854223455232679227055140103795809982992793178112598317977600*x^37 + 48121357636323435898491763496
58769357343953133075923345884119789718240615347695356895190323200*x^36 - 2871060775830083647426868136706524189
6063360827677699962522107958880738952242991399003888332800*x^35 + 13150918214713222130798493456693867156629022
4808133871438501689421822367827858786874250861388800*x^34 - 48615412586213217241775435956082154303807288316753
4048023582332295256693402493082467454965081600*x^33 + 15012511859003801791455877071511298942846464125440398838
21859865409233818038611634065993336166400*x^32 - 3960120768072419508193345390732915044310906172694579718477009
206696968949880161377086262197766400*x^31 + 909142000002142860704234021157216421398787616081889741815089464543
5329015717575267031369642428000*x^30 - 18424764929872158270698990044243761821209838303936935404825000845297214
002673057816247491027262800*x^29 + 334130737566736389253336251690111704455988115162219751155902004112933894344
16479555356860509015600*x^28 - 5481653256044929545971751700338269967324241093611430434462984210365662293449024
7108012261346586400*x^27 + 82245983094063518667736627604663547588572840238581597325736701493749880383650749401
133206999014400*x^26 - 113722848067639694402592735862649094093874045443618754295078471234595964240139128161766
283626302000*x^25 + 146086574413322248286514192550522624098477614094095488624493581512454991258074867544318895
241990800*x^24 - 175027094081001021682973752997412023251736305226127144272811232619626419165679723993392477178
363200*x^23 + 196887291605784159433455654443374481739030277196290989156609388218395099469530751149958413044135
200*x^22 - 208068683375682167383215047521697995267539026087882795784482813901791360434798005710722616487282000
*x^21 + 208171444918478482519618165392015730347012009814583465001141378703189206795143605224483243158516400*x^
20 - 196227556184540408353167422341576855508320001795821851558311176995574081069015969836642878534431200*x^19
+ 176534941677723459681422280024952573032106299529482816321219585323399086976471958310981405494523200*x^18 - 1
49136255738011380556954829398929258737007615204074730330565887220730783382923822619571340737358000*x^17 + 1218
90814483587724389011961696733756253105383654426234336150913799569962877883235263704480534144400*x^16 - 9198318
6053222129635537069278588580392985745730700928388526309371776740142438834607398588992195200*x^15 + 69317814132
471559316390137037592557060398996838342232414889371690271398098098738643314402130954400*x^14 - 457430708411325
00247970739727093296878765897323708593659902862883667237249390700654758574610918000*x^13 + 3299696552167639492
9803121509049143329451789049169789455644615129199190308917673348518481311574800*x^12 - 17770083757788737971933
739892049927033484890029804651938270182161740937851280707834822272274354400*x^11 + 135442252674514597019603692
38256374351899362683978498551483729852256655264147093337392596228028800*x^10 - 4813759732728488651728668551069
958186240925466978671799825767568732599092879797201593187475517200*x^9 + 5091181133639025216832620106123280320
347641869015804163342220634415255665812683873707564839486000*x^8 - 4642131185030564007583489945718840607733994
62026537769017971996084095803827142837363184426478400*x^7 + 17712338832647821260422671418114138499869713982650
32235916172889879027134542752439323372429279200*x^6 + 23911503454316320991841103252166564975049644786785360906
9487786445410804754998849116452338787600*x^5 + 79817891129994413353362937273464455099835468*126493875280426512
3815574105117799608149057272418^(1/4)*sqrt(1590558865810545927822094)*sqrt(35)*sqrt(2)*(512*x^38 - 7936*x^37 +
68352*x^36 - 407808*x^35 + 1867968*x^34 - 6905376*x^33 + 21323904*x^32 - 56249904*x^31 + 129135330*x^30 - 261
706983*x^29 + 474602241*x^28 - 778618854*x^27 + 1168229184*x^26 - 1615329345*x^25 + 2075026563*x^24 - 24861002
52*x^23 + 2796604422*x^22 - 2955425895*x^21 + 2956885529*x^20 - 2787233482*x^19 + 2507517852*x^18 - 2118344505
*x^17 + 1731347859*x^16 - 1306537272*x^15 + 984596334*x^14 - 649738605*x^13 + 468691803*x^12 - 252407834*x^11
+ 192383368*x^10 - 68375067*x^9 + 72315585*x^8 - 6593724*x^7 + 25158762*x^6 + 3396411*x^5 + 6720651*x^4 + 1325
322*x^3 + 1023516*x^2 + 137781*x + 59049)*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 11461184504
6003414252052727757333000617984)*arctan(1/54206850781156887023310518673090274966005685838243268724684064391985
05135017594564915473395777024743167351056637371274953501437271981836435236061968*sqrt(795279432905272963911047
)*(9939513250523192816422116593216797292815016511001378462170679301990*sqrt(1100522448786287362112823964249088
8848098)*sqrt(2888868076710542715672947094311)*sqrt(7)*(10*sqrt(2) + 9) + sqrt(1590558865810545927822094)*(5*1
264938752804265123815574105117799608149057272418^(3/4)*sqrt(2888868076710542715672947094311)*sqrt(35)*(3406136
97110906370000*sqrt(2) - 483753219647003202703) + 5566956030336910747377329*1264938752804265123815574105117799
608149057272418^(1/4)*sqrt(2888868076710542715672947094311)*sqrt(35)*(43734782664604992355*sqrt(2) - 662698265
80994560232))*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 114611845046003414252052727757333000617
984) + 147461812540444568715696613114138557910359478676937042172325597372869522935182724790786*sqrt(2888868076
710542715672947094311)*sqrt(7)*(125*sqrt(2) + 172))*sqrt(51917987317349015737304218750129712563906438262855815
11813805064*x^2 + sqrt(1590558865810545927822094)*(1264938752804265123815574105117799608149057272418^(1/4)*sqr
t(35)*sqrt(7)*sqrt(x^2 - 2*x + 3)*(43268355662383849682*sqrt(2) - 62135959399493560795) - 12649387528042651238
15574105117799608149057272418^(1/4)*sqrt(35)*sqrt(7)*(sqrt(2)*(43268355662383849682*x - 105404315061877410477)
- 62135959399493560795*x + 148672670724261260159))*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 1
14611845046003414252052727757333000617984) - 1297949682933725393432605468753242814097660956571395377953451266*
sqrt(x^2 - 2*x + 3)*(4*x + 1) - 3893849048801176180297816406259728442292982869714186133860353798*x + 874869761
17927258982681475740074062806745190*sqrt(11005224487862873621128239642490888848098) + 908564778053607775402823
8281272699698683626695999767645674158862) + 5/35309486994022006419332*sqrt(11005224487862873621128239642490888
848098)*sqrt(7)*(sqrt(2)*(10*x - 19) + 9*x - 29) + 1/701918227692516147086715878423299535653311118502220320740
26984349485892917146977000414136*sqrt(1590558865810545927822094)*(5*126493875280426512381557410511779960814905
7272418^(3/4)*sqrt(35)*(sqrt(2)*(340613697110906370000*x + 143139522536096832703) - 483753219647003202703*x -
197474174574809537297) + 5566956030336910747377329*1264938752804265123815574105117799608149057272418^(1/4)*sqr
t(35)*(sqrt(2)*(43734782664604992355*x + 22535043916389567877) - 66269826580994560232*x - 21199738748215424478
) - (5*1264938752804265123815574105117799608149057272418^(3/4)*sqrt(35)*(340613697110906370000*sqrt(2) - 48375
3219647003202703) + 5566956030336910747377329*1264938752804265123815574105117799608149057272418^(1/4)*sqrt(35)
*(43734782664604992355*sqrt(2) - 66269826580994560232))*sqrt(x^2 - 2*x + 3))*sqrt(8104222592127468960547894479
7800854846405*sqrt(2) + 114611845046003414252052727757333000617984) - 1/35309486994022006419332*sqrt(x^2 - 2*x
+ 3)*(5*sqrt(11005224487862873621128239642490888848098)*sqrt(7)*(10*sqrt(2) + 9) + 74179594525256316007*sqrt(
7)*(125*sqrt(2) + 172)) + 1/476*sqrt(7)*(25*sqrt(2)*(5*x - 1) + 172*x - 82)) + 7981789112999441335336293727346
4455099835468*1264938752804265123815574105117799608149057272418^(1/4)*sqrt(1590558865810545927822094)*sqrt(35)
*sqrt(2)*(512*x^38 - 7936*x^37 + 68352*x^36 - 407808*x^35 + 1867968*x^34 - 6905376*x^33 + 21323904*x^32 - 5624
9904*x^31 + 129135330*x^30 - 261706983*x^29 + 474602241*x^28 - 778618854*x^27 + 1168229184*x^26 - 1615329345*x
^25 + 2075026563*x^24 - 2486100252*x^23 + 2796604422*x^22 - 2955425895*x^21 + 2956885529*x^20 - 2787233482*x^1
9 + 2507517852*x^18 - 2118344505*x^17 + 1731347859*x^16 - 1306537272*x^15 + 984596334*x^14 - 649738605*x^13 +
468691803*x^12 - 252407834*x^11 + 192383368*x^10 - 68375067*x^9 + 72315585*x^8 - 6593724*x^7 + 25158762*x^6 +
3396411*x^5 + 6720651*x^4 + 1325322*x^3 + 1023516*x^2 + 137781*x + 59049)*sqrt(8104222592127468960547894479780
0854846405*sqrt(2) + 114611845046003414252052727757333000617984)*arctan(-1/54206850781156887023310518673090274
96600568583824326872468406439198505135017594564915473395777024743167351056637371274953501437271981836435236061
968*sqrt(795279432905272963911047)*(9939513250523192816422116593216797292815016511001378462170679301990*sqrt(1
1005224487862873621128239642490888848098)*sqrt(2888868076710542715672947094311)*sqrt(7)*(10*sqrt(2) + 9) - sqr
t(1590558865810545927822094)*(5*1264938752804265123815574105117799608149057272418^(3/4)*sqrt(28888680767105427
15672947094311)*sqrt(35)*(340613697110906370000*sqrt(2) - 483753219647003202703) + 5566956030336910747377329*1
264938752804265123815574105117799608149057272418^(1/4)*sqrt(2888868076710542715672947094311)*sqrt(35)*(4373478
2664604992355*sqrt(2) - 66269826580994560232))*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 114611
845046003414252052727757333000617984) + 1474618125404445687156966131141385579103594786769370421723255973728695
22935182724790786*sqrt(2888868076710542715672947094311)*sqrt(7)*(125*sqrt(2) + 172))*sqrt(51917987317349015737
30421875012971256390643826285581511813805064*x^2 - sqrt(1590558865810545927822094)*(12649387528042651238155741
05117799608149057272418^(1/4)*sqrt(35)*sqrt(7)*sqrt(x^2 - 2*x + 3)*(43268355662383849682*sqrt(2) - 62135959399
493560795) - 1264938752804265123815574105117799608149057272418^(1/4)*sqrt(35)*sqrt(7)*(sqrt(2)*(43268355662383
849682*x - 105404315061877410477) - 62135959399493560795*x + 148672670724261260159))*sqrt(81042225921274689605
478944797800854846405*sqrt(2) + 114611845046003414252052727757333000617984) - 12979496829337253934326054687532
42814097660956571395377953451266*sqrt(x^2 - 2*x + 3)*(4*x + 1) - 389384904880117618029781640625972844229298286
9714186133860353798*x + 87486976117927258982681475740074062806745190*sqrt(110052244878628736211282396424908888
48098) + 9085647780536077754028238281272699698683626695999767645674158862) - 5/35309486994022006419332*sqrt(11
005224487862873621128239642490888848098)*sqrt(7)*(sqrt(2)*(10*x - 19) + 9*x - 29) + 1/701918227692516147086715
87842329953565331111850222032074026984349485892917146977000414136*sqrt(1590558865810545927822094)*(5*126493875
2804265123815574105117799608149057272418^(3/4)*sqrt(35)*(sqrt(2)*(340613697110906370000*x + 143139522536096832
703) - 483753219647003202703*x - 197474174574809537297) + 5566956030336910747377329*12649387528042651238155741
05117799608149057272418^(1/4)*sqrt(35)*(sqrt(2)*(43734782664604992355*x + 22535043916389567877) - 662698265809
94560232*x - 21199738748215424478) - (5*1264938752804265123815574105117799608149057272418^(3/4)*sqrt(35)*(3406
13697110906370000*sqrt(2) - 483753219647003202703) + 5566956030336910747377329*1264938752804265123815574105117
799608149057272418^(1/4)*sqrt(35)*(43734782664604992355*sqrt(2) - 66269826580994560232))*sqrt(x^2 - 2*x + 3))*
sqrt(81042225921274689605478944797800854846405*sqrt(2) + 114611845046003414252052727757333000617984) + 1/35309
486994022006419332*sqrt(x^2 - 2*x + 3)*(5*sqrt(11005224487862873621128239642490888848098)*sqrt(7)*(10*sqrt(2)
+ 9) + 74179594525256316007*sqrt(7)*(125*sqrt(2) + 172)) - 1/476*sqrt(7)*(25*sqrt(2)*(5*x - 1) + 172*x - 82))
+ 24453*1264938752804265123815574105117799608149057272418^(1/4)*sqrt(1590558865810545927822094)*sqrt(35)*sqrt(
7)*(58681264663553748097050996611754496316407808*x^38 - 909559602285083095504290447482194692904321024*x^37 + 7
833948832584425370956308047669225258240442368*x^36 - 46739627304520560359301118801262456316018819072*x^35 + 21
4091258966892905713578429763409810498374336512*x^34 - 791437884096390872694182856990021126475411881984*x^33 +
2443971981023852389183004169635504201209831489536*x^32 - 6446905281100567635350197739288116580793540673536*x^3
1 + 14800438431924516080565532176343356954693567774720*x^30 - 299947201830530497516039209382919757180697281822
72*x^29 + 54395038503977968497675563443793146276549591302144*x^28 - 892389434445447556850205620339886110375559
93870336*x^27 + 133892902214827011092889528472923281328218944045056*x^26 - 18513587658740219001153199763371603
4835132689940480*x^25 + 237822622904897041561702187373073394318812215508992*x^24 - 284936536851054039764888677
994792967684286178131968*x^23 + 320523992669231941724388481023319612454782787125248*x^22 - 3387268147226859567
38928688519407226164440916295680*x^21 + 338894106068517834886487069250634573161464946753536*x^20 - 31944997194
6016546489637350034669310345971696140288*x^19 + 287391247503511322489973442496808422958321912250368*x^18 - 242
787372161112804792074580815007335314268010577920*x^17 + 198432972536437767771981576557768362169992275296256*x^
16 - 149744647365292015359562891324224536622995129499648*x^15 + 1128464024652710230240544677245701140256867808
70656*x^14 - 74467740316666419201365857719494322341993062072320*x^13 + 537176322997679581699504894236525505310
43035185152*x^12 - 28928927558805352147965359067020100302706002886656*x^11 + 220494127626442517733091046795428
09356433843290112*x^10 - 7836592584014101531712860147940403658565697404928*x^9 + 82882226224310888136345304586
17273979494874480640*x^8 - 755718873364113816635702120278992782166815932416*x^7 + 2883492131893278950354802589
097534717293712375808*x^6 + 389268931244541502203228657135011133961927655424*x^5 + 770266211020267891996472416
855047787936254787584*x^4 + 151897599700059336983359025256804087045027790848*x^3 + 117307057194105230541603999
703274443460516511744*x^2 - 81042225921274689605478944797800854846405*sqrt(2)*(512*x^38 - 7936*x^37 + 68352*x^
36 - 407808*x^35 + 1867968*x^34 - 6905376*x^33 + 21323904*x^32 - 56249904*x^31 + 129135330*x^30 - 261706983*x^
29 + 474602241*x^28 - 778618854*x^27 + 1168229184*x^26 - 1615329345*x^25 + 2075026563*x^24 - 2486100252*x^23 +
2796604422*x^22 - 2955425895*x^21 + 2956885529*x^20 - 2787233482*x^19 + 2507517852*x^18 - 2118344505*x^17 + 1
731347859*x^16 - 1306537272*x^15 + 984596334*x^14 - 649738605*x^13 + 468691803*x^12 - 252407834*x^11 + 1923833
68*x^10 - 68375067*x^9 + 72315585*x^8 - 6593724*x^7 + 25158762*x^6 + 3396411*x^5 + 6720651*x^4 + 1325322*x^3 +
1023516*x^2 + 137781*x + 59049) + 15791334622283396419062076883133098158146453504*x + 67677148381214556081694
61521342756353491337216)*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 1146118450460034142520527277
57333000617984)*log(5149263009740846168871608737947327093513510106682349523414420454231938660554455908352*x^2
+ 16517307604525632141069927349727551216675979497245715202048/16653749577489013357854121082231147111*sqrt(1590
558865810545927822094)*(1264938752804265123815574105117799608149057272418^(1/4)*sqrt(35)*sqrt(7)*sqrt(x^2 - 2*
x + 3)*(43268355662383849682*sqrt(2) - 62135959399493560795) - 12649387528042651238155741051177996081490572724
18^(1/4)*sqrt(35)*sqrt(7)*(sqrt(2)*(43268355662383849682*x - 105404315061877410477) - 62135959399493560795*x +
148672670724261260159))*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 1146118450460034142520527277
57333000617984) - 1287315752435211542217902184486831773378377526670587380853605113557984665138613977088*sqrt(x
^2 - 2*x + 3)*(4*x + 1) - 386194725730563462665370655346049532013513258001176214256081534067395399541584193126
4*x + 86770206865778458070361238647050247531051756333085943213766737920*sqrt(110052244878628736211282396424908
88848098) + 9011210267046480795525315291407822413648642686694111665975235794905892655970297839616) - 24453*126
4938752804265123815574105117799608149057272418^(1/4)*sqrt(1590558865810545927822094)*sqrt(35)*sqrt(7)*(5868126
4663553748097050996611754496316407808*x^38 - 909559602285083095504290447482194692904321024*x^37 + 783394883258
4425370956308047669225258240442368*x^36 - 46739627304520560359301118801262456316018819072*x^35 + 2140912589668
92905713578429763409810498374336512*x^34 - 791437884096390872694182856990021126475411881984*x^33 + 24439719810
23852389183004169635504201209831489536*x^32 - 6446905281100567635350197739288116580793540673536*x^31 + 1480043
8431924516080565532176343356954693567774720*x^30 - 29994720183053049751603920938291975718069728182272*x^29 + 5
4395038503977968497675563443793146276549591302144*x^28 - 89238943444544755685020562033988611037555993870336*x^
27 + 133892902214827011092889528472923281328218944045056*x^26 - 1851358765874021900115319976337160348351326899
40480*x^25 + 237822622904897041561702187373073394318812215508992*x^24 - 28493653685105403976488867799479296768
4286178131968*x^23 + 320523992669231941724388481023319612454782787125248*x^22 - 338726814722685956738928688519
407226164440916295680*x^21 + 338894106068517834886487069250634573161464946753536*x^20 - 3194499719460165464896
37350034669310345971696140288*x^19 + 287391247503511322489973442496808422958321912250368*x^18 - 24278737216111
2804792074580815007335314268010577920*x^17 + 198432972536437767771981576557768362169992275296256*x^16 - 149744
647365292015359562891324224536622995129499648*x^15 + 112846402465271023024054467724570114025686780870656*x^14
- 74467740316666419201365857719494322341993062072320*x^13 + 53717632299767958169950489423652550531043035185152
*x^12 - 28928927558805352147965359067020100302706002886656*x^11 + 22049412762644251773309104679542809356433843
290112*x^10 - 7836592584014101531712860147940403658565697404928*x^9 + 8288222622431088813634530458617273979494
874480640*x^8 - 755718873364113816635702120278992782166815932416*x^7 + 288349213189327895035480258909753471729
3712375808*x^6 + 389268931244541502203228657135011133961927655424*x^5 + 77026621102026789199647241685504778793
6254787584*x^4 + 151897599700059336983359025256804087045027790848*x^3 + 11730705719410523054160399970327444346
0516511744*x^2 - 81042225921274689605478944797800854846405*sqrt(2)*(512*x^38 - 7936*x^37 + 68352*x^36 - 407808
*x^35 + 1867968*x^34 - 6905376*x^33 + 21323904*x^32 - 56249904*x^31 + 129135330*x^30 - 261706983*x^29 + 474602
241*x^28 - 778618854*x^27 + 1168229184*x^26 - 1615329345*x^25 + 2075026563*x^24 - 2486100252*x^23 + 2796604422
*x^22 - 2955425895*x^21 + 2956885529*x^20 - 2787233482*x^19 + 2507517852*x^18 - 2118344505*x^17 + 1731347859*x
^16 - 1306537272*x^15 + 984596334*x^14 - 649738605*x^13 + 468691803*x^12 - 252407834*x^11 + 192383368*x^10 - 6
8375067*x^9 + 72315585*x^8 - 6593724*x^7 + 25158762*x^6 + 3396411*x^5 + 6720651*x^4 + 1325322*x^3 + 1023516*x^
2 + 137781*x + 59049) + 15791334622283396419062076883133098158146453504*x + 6767714838121455608169461521342756
353491337216)*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 114611845046003414252052727757333000617
984)*log(5149263009740846168871608737947327093513510106682349523414420454231938660554455908352*x^2 - 165173076
04525632141069927349727551216675979497245715202048/16653749577489013357854121082231147111*sqrt(159055886581054
5927822094)*(1264938752804265123815574105117799608149057272418^(1/4)*sqrt(35)*sqrt(7)*sqrt(x^2 - 2*x + 3)*(432
68355662383849682*sqrt(2) - 62135959399493560795) - 1264938752804265123815574105117799608149057272418^(1/4)*sq
rt(35)*sqrt(7)*(sqrt(2)*(43268355662383849682*x - 105404315061877410477) - 62135959399493560795*x + 1486726707
24261260159))*sqrt(81042225921274689605478944797800854846405*sqrt(2) + 114611845046003414252052727757333000617
984) - 1287315752435211542217902184486831773378377526670587380853605113557984665138613977088*sqrt(x^2 - 2*x +
3)*(4*x + 1) - 3861947257305634626653706553460495320135132580011762142560815340673953995415841931264*x + 86770
206865778458070361238647050247531051756333085943213766737920*sqrt(11005224487862873621128239642490888848098) +
9011210267046480795525315291407822413648642686694111665975235794905892655970297839616) + 47314906706448199876
3217709555105306943512932580756046793648401639888862209988063963205432771600*x^4 + 933056734920520960789163462
38331863328268414300012419250553508426219541327449647498113404575200*x^3 + 72057846855248153407479950560295894
451534022924762066351912610467773507163772995097552926305600*x^2 + 1068899738886597382826851562502670552786309
0230587961936087245720*(3372249001933422237824271360*x^37 - 53502205399640031394796147712*x^36 + 4691493940829
89701729494575872*x^35 - 2847499220912667753383035299072*x^34 + 13254252261100740556512388253568*x^33 - 497700
80058525077628064229832576*x^32 + 156010734937008739388220889457760*x^31 - 417516398850754397130111919794336*x
^30 + 971538171913365251873706873353652*x^29 - 1993653213575521837888601204380228*x^28 + 365555347185295760625
7345414140031*x^27 - 6054769996581738503753686155104785*x^26 + 9155494158513869230271529746307221*x^25 - 12740
106677685048178693605103009787*x^24 + 16442770202470076313197215936814318*x^23 - 19772569734288744720189854470
201506*x^22 + 22286437617621909921609206629636086*x^21 - 23584986647560742443188031208946882*x^20 + 2357939721
1179175240196614296051673*x^19 - 22218747553941794885903840542461607*x^18 + 1991229545408024658363639161381197
9*x^17 - 16801760806053390242995145349148613*x^16 + 13613407965006475288139078599341572*x^15 - 102793056507331
78669223634020962076*x^14 + 7606288378303449524327938977040824*x^13 - 5069838234992751929471190426115248*x^12
+ 3507425970596197680016078213030977*x^11 - 1974814483061344405275851094534735*x^10 + 135700238843005588183329
3557852283*x^9 - 566969010759169461615951049236597*x^8 + 458426000073846882432457044306894*x^7 - 9470455766525
3489332536549937026*x^6 + 135183920426913231415208872303230*x^5 - 1023095318901774638403186272874*x^4 + 293980
41153524973343917601742151*x^3 + 1933957195570062708781629134823*x^2 + 3397462350398947848063583843461*x - 800
38710871555316861345369643)*sqrt(x^2 - 2*x + 3) + 970009476897571295869922411388598579155265693217950893198823
6024507972118200210878516740079600*x + 41571834724181626965853817630939939106654243995055038279949582962177023
36371518947935745748400)/(512*x^38 - 7936*x^37 + 68352*x^36 - 407808*x^35 + 1867968*x^34 - 6905376*x^33 + 2132
3904*x^32 - 56249904*x^31 + 129135330*x^30 - 261706983*x^29 + 474602241*x^28 - 778618854*x^27 + 1168229184*x^2
6 - 1615329345*x^25 + 2075026563*x^24 - 2486100252*x^23 + 2796604422*x^22 - 2955425895*x^21 + 2956885529*x^20
- 2787233482*x^19 + 2507517852*x^18 - 2118344505*x^17 + 1731347859*x^16 - 1306537272*x^15 + 984596334*x^14 - 6
49738605*x^13 + 468691803*x^12 - 252407834*x^11 + 192383368*x^10 - 68375067*x^9 + 72315585*x^8 - 6593724*x^7 +
25158762*x^6 + 3396411*x^5 + 6720651*x^4 + 1325322*x^3 + 1023516*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/(x**2-2*x+3)**(21/2)/(2*x**2+x+1)**10,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [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/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x, algorithm="giac")
[Out]
Timed out