Integrand size = 42, antiderivative size = 374 \[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=-\frac {\sqrt {1-6 b} f \left (f-6 b f+2 \sqrt {1-6 b} (6 e+f)\right ) \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right ) \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )}{54 \sqrt {2} \sqrt {-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3}}+\frac {(1-6 b)^{3/2} f^2 \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right ) \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )^2}{162 \sqrt {2} \sqrt {-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3}}-\frac {\sqrt {1-6 b} \left (18 e^2+6 \left (1-\sqrt {1-6 b}\right ) e f+\left (1-\sqrt {1-6 b}-3 b\right ) f^2\right ) \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right ) \sqrt {2+\frac {1-6 x}{\sqrt {1-6 b}}} \text {arctanh}\left (\frac {\sqrt {2+\frac {1-6 x}{\sqrt {1-6 b}}}}{\sqrt {3}}\right )}{27 \sqrt {6} \sqrt {-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3}} \] Output:
-1/108*(1-6*b)^(1/2)*f*(f-6*b*f+2*(1-6*b)^(1/2)*(6*e+f))*(1-(1-6*x)/(1-6*b )^(1/2))*(2+(1-6*x)/(1-6*b)^(1/2))*2^(1/2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1- 6*x)-(1-6*x)^3)^(1/2)+1/324*(1-6*b)^(3/2)*f^2*(1-(1-6*x)/(1-6*b)^(1/2))*(2 +(1-6*x)/(1-6*b)^(1/2))^2*2^(1/2)/(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6 *x)^3)^(1/2)-1/162*(1-6*b)^(1/2)*(18*e^2+6*(1-(1-6*b)^(1/2))*e*f+(1-(1-6*b )^(1/2)-3*b)*f^2)*(1-(1-6*x)/(1-6*b)^(1/2))*(2+(1-6*x)/(1-6*b)^(1/2))^(1/2 )*arctanh(1/3*(2+(1-6*x)/(1-6*b)^(1/2))^(1/2)*3^(1/2))*6^(1/2)/(-2*(1-6*b) ^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(1/2)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 17.49 (sec) , antiderivative size = 1754, normalized size of antiderivative = 4.69 \[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx =\text {Too large to display} \] Input:
Integrate[(e + f*x)^2/Sqrt[1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 1 08*x^3],x]
Output:
(((1 - Sqrt[1 - 6*b] - 54*x^2 + 108*x^3 + b*(-9 + 6*Sqrt[1 - 6*b] + 54*x)) *(6*e^2*(1 - Sqrt[1 - 6*b] - 6*b + 6*Sqrt[1 - 6*b]*x) + 12*e*f*((1 + Sqrt[ 1 - 6*b])*x - b*(Sqrt[1 - 6*b] + 6*x)) - f^2*(-6*b^2 - 2*(1 + Sqrt[1 - 6*b ])*x + b*(1 + Sqrt[1 - 6*b] + 6*(2 + Sqrt[1 - 6*b])*x))))/((1 - 6*b)*(b + 2*x*(-1 + 3*x))) + ((1 - Sqrt[1 - 6*b] - 54*x^2 + 108*x^3 + b*(-9 + 6*Sqrt [1 - 6*b] + 54*x))*(-6*e^2*(-1 + Sqrt[1 - 6*b] + 6*x) - 12*e*f*(-b + x + S qrt[1 - 6*b]*x) + f^2*(b*(1 + 5*Sqrt[1 - 6*b] + 6*x) + 2*x*(-1 - 5*Sqrt[1 - 6*b] + 12*Sqrt[1 - 6*b]*x))))/(Sqrt[1 - 6*b]*(b + 2*x*(-1 + 3*x))) + 216 *(EllipticF[ArcSin[Sqrt[(-x + Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6* b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 3])/(-Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 2] + Root[1 - Sqrt [1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 3]) ]], (Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 2] - Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54* b*#1 - 54*#1^2 + 108*#1^3 & , 3])/(Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 1] - Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*#1^3 & , 3])]*(6*e^2 - b*f^2 + 2*f*(6*e + f)*Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 5 4*b*#1 - 54*#1^2 + 108*#1^3 & , 1]) - 2*f*(6*e + f)*EllipticE[ArcSin[Sqrt[ (-x + Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#...
Time = 1.65 (sec) , antiderivative size = 349, normalized size of antiderivative = 0.93, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2489, 27, 99, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {(e+f x)^2}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}} \, dx\) |
| \(\Big \downarrow \) 2489 |
| \(\displaystyle -\frac {157464 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \int -\frac {(e+f x)^2}{157464 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}dx}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \int \frac {(e+f x)^2}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}dx}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\) |
| \(\Big \downarrow \) 99 |
| \(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \int \left (-\frac {\sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} f^2}{36 (6 b-1)^2}+\frac {\left (6 b f-f-\sqrt {1-6 b} (12 e+2 f)\right ) f}{36 (1-6 b)^{3/2} \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}+\frac {18 \sqrt {1-6 b} e^2-6 \left (-6 b-\sqrt {1-6 b}+1\right ) f e-\left (-3 \left (2-\sqrt {1-6 b}\right ) b-\sqrt {1-6 b}+1\right ) f^2}{18 \sqrt {1-6 b} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}\right )dx}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \left (-\frac {\arctan \left (\frac {\sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{\sqrt {3} (1-6 b)^{3/4}}\right ) \left (18 \sqrt {1-6 b} e^2-6 \left (-6 b-\sqrt {1-6 b}+1\right ) e f-\left (-3 \left (2-\sqrt {1-6 b}\right ) b-\sqrt {1-6 b}+1\right ) f^2\right )}{54 \sqrt {3} (1-6 b)^{9/4}}-\frac {f \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \left (2 \sqrt {1-6 b} (6 e+f)-6 b f+f\right )}{108 (1-6 b)^{5/2}}-\frac {f^2 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}}{324 (1-6 b)^3}\right )}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\) |
Input:
Int[(e + f*x)^2/Sqrt[1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108*x^3 ],x]
Output:
(((1 - Sqrt[1 - 6*b])*(1 - 6*b) - 6*(1 - 6*b)*x)*Sqrt[-((1 + 2*Sqrt[1 - 6* b])*(1 - 6*b)) + 6*(1 - 6*b)*x]*(-1/108*(f*(f - 6*b*f + 2*Sqrt[1 - 6*b]*(6 *e + f))*Sqrt[-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x])/(1 - 6* b)^(5/2) - (f^2*(-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^(3/2) )/(324*(1 - 6*b)^3) - ((18*Sqrt[1 - 6*b]*e^2 - 6*(1 - Sqrt[1 - 6*b] - 6*b) *e*f - (1 - Sqrt[1 - 6*b] - 3*(2 - Sqrt[1 - 6*b])*b)*f^2)*ArcTan[Sqrt[-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x]/(Sqrt[3]*(1 - 6*b)^(3/4))] )/(54*Sqrt[3]*(1 - 6*b)^(9/4))))/Sqrt[1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108*x^3]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] && (IntegerQ[p] | | (GtQ[m, 0] && GeQ[n, -1]))
Int[((e_.) + (f_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2 + (d_.)*( x_)^3)^(p_), x_Symbol] :> Simp[(a + b*x + c*x^2 + d*x^3)^p/((c^3 - 4*b*c*d + 9*a*d^2 + d*(c^2 - 3*b*d)*x)^p*(b*c - 9*a*d + 2*(c^2 - 3*b*d)*x)^(2*p)) Int[(e + f*x)^m*(c^3 - 4*b*c*d + 9*a*d^2 + d*(c^2 - 3*b*d)*x)^p*(b*c - 9*a *d + 2*(c^2 - 3*b*d)*x)^(2*p), x], x] /; FreeQ[{a, b, c, d, e, f, m, p}, x] && NeQ[c^2 - 3*b*d, 0] && EqQ[b^2*c^2 - 4*a*c^3 - 4*b^3*d + 18*a*b*c*d - 2 7*a^2*d^2, 0] && !IntegerQ[p]
\[\int \frac {\left (f x +e \right )^{2}}{\sqrt {1-\left (1-6 b \right )^{\frac {3}{2}}-9 b +54 b x -54 x^{2}+108 x^{3}}}d x\]
Input:
int((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x)
Output:
int((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x)
Leaf count of result is larger than twice the leaf count of optimal. 915 vs. \(2 (310) = 620\).
Time = 0.21 (sec) , antiderivative size = 2078, normalized size of antiderivative = 5.56 \[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {Too large to display} \] Input:
integrate((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, a lgorithm="fricas")
Output:
[1/162*(3*sqrt(1/6)*(6*x^2 + b - 2*x)*sqrt((216*(6*b - 1)*e^3*f + 108*(6*b - 1)*e^2*f^2 - 12*(18*b^2 - 15*b + 2)*e*f^3 - 2*(18*b^2 - 9*b + 1)*f^4 - (108*(3*b - 1)*e^2*f^2 + 12*(9*b - 2)*e*f^3 - (9*b^2 - 12*b + 2)*f^4 - 324 *e^4 - 216*e^3*f)*sqrt(-6*b + 1))/(6*b - 1))*log((972*(5*b^2 - b)*e^4 + 64 8*(5*b^2 - b)*e^3*f + 108*(15*b^3 + 2*b^2 - b)*e^2*f^2 + 108*(5*b^3 - b^2) *e*f^3 + 27*(5*b^4 - b^3)*f^4 - 972*(b^2*f^4 + 4*(3*b + 1)*e^2*f^2 + 4*b*e *f^3 + 36*e^4 + 24*e^3*f)*x^4 + 648*(b^2*f^4 + 4*(3*b + 1)*e^2*f^2 + 4*b*e *f^3 + 36*e^4 + 24*e^3*f)*x^3 + 54*(36*(12*b - 5)*e^4 + 24*(12*b - 5)*e^3* f + 4*(36*b^2 - 3*b - 5)*e^2*f^2 + 4*(12*b^2 - 5*b)*e*f^3 + (12*b^3 - 5*b^ 2)*f^4)*x^2 + 2*sqrt(1/6)*(18*(6*b - 1)*e^2 - 6*(18*b^2 - 15*b + 2)*e*f - 2*(18*b^2 - 9*b + 1)*f^2 + 18*(6*(6*b - 1)*e*f + (6*b - 1)*f^2)*x^2 - 6*(1 8*(6*b - 1)*e^2 + 12*(6*b - 1)*e*f - (18*b^2 - 15*b + 2)*f^2)*x + (18*(3*b - 1)*e^2 + 6*(9*b - 2)*e*f - (9*b^2 - 12*b + 2)*f^2 + 18*((3*b - 1)*f^2 - 18*e^2 - 6*e*f)*x^2 - 6*(12*(3*b - 1)*e*f + (9*b - 2)*f^2 - 18*e^2)*x)*sq rt(-6*b + 1))*sqrt(108*x^3 + 54*b*x - 54*x^2 + (6*b - 1)*sqrt(-6*b + 1) - 9*b + 1)*sqrt((216*(6*b - 1)*e^3*f + 108*(6*b - 1)*e^2*f^2 - 12*(18*b^2 - 15*b + 2)*e*f^3 - 2*(18*b^2 - 9*b + 1)*f^4 - (108*(3*b - 1)*e^2*f^2 + 12*( 9*b - 2)*e*f^3 - (9*b^2 - 12*b + 2)*f^4 - 324*e^4 - 216*e^3*f)*sqrt(-6*b + 1))/(6*b - 1)) - 54*(36*(4*b - 1)*e^4 + 24*(4*b - 1)*e^3*f + 4*(12*b^2 + b - 1)*e^2*f^2 + 4*(4*b^2 - b)*e*f^3 + (4*b^3 - b^2)*f^4)*x - 27*(b^3*f...
\[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int \frac {\left (e + f x\right )^{2}}{\sqrt {54 b x + 6 b \sqrt {1 - 6 b} - 9 b + 108 x^{3} - 54 x^{2} - \sqrt {1 - 6 b} + 1}}\, dx \] Input:
integrate((f*x+e)**2/(1-(1-6*b)**(3/2)-9*b+54*b*x-54*x**2+108*x**3)**(1/2) ,x)
Output:
Integral((e + f*x)**2/sqrt(54*b*x + 6*b*sqrt(1 - 6*b) - 9*b + 108*x**3 - 5 4*x**2 - sqrt(1 - 6*b) + 1), x)
\[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int { \frac {{\left (f x + e\right )}^{2}}{\sqrt {108 \, x^{3} + 54 \, b x - 54 \, x^{2} - {\left (-6 \, b + 1\right )}^{\frac {3}{2}} - 9 \, b + 1}} \,d x } \] Input:
integrate((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, a lgorithm="maxima")
Output:
integrate((f*x + e)^2/sqrt(108*x^3 + 54*b*x - 54*x^2 - (-6*b + 1)^(3/2) - 9*b + 1), x)
Exception generated. \[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, a lgorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value
Timed out. \[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int \frac {{\left (e+f\,x\right )}^2}{\sqrt {54\,b\,x-9\,b-{\left (1-6\,b\right )}^{3/2}-54\,x^2+108\,x^3+1}} \,d x \] Input:
int((e + f*x)^2/(54*b*x - 9*b - (1 - 6*b)^(3/2) - 54*x^2 + 108*x^3 + 1)^(1 /2),x)
Output:
int((e + f*x)^2/(54*b*x - 9*b - (1 - 6*b)^(3/2) - 54*x^2 + 108*x^3 + 1)^(1 /2), x)
\[ \int \frac {(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {too large to display} \] Input:
int((f*x+e)^2/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x)
Output:
( - 36*sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x **3 - 54*x**2 + 1)*sqrt( - 6*b + 1)*b*e*f - 6*sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x**3 - 54*x**2 + 1)*sqrt( - 6*b + 1) *b*f**2 + 6*sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x**3 - 54*x**2 + 1)*sqrt( - 6*b + 1)*e*f + sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x**3 - 54*x**2 + 1)*sqrt( - 6*b + 1 )*f**2 - 141087744*sqrt( - 6*b + 1)*int(sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x**3 - 54*x**2 + 1)/(23079168*sqrt( - 6*b + 1)*b**8 + 311568768*sqrt( - 6*b + 1)*b**7*x**2 - 103856256*sqrt( - 6*b + 1)*b**7*x - 4588992*sqrt( - 6*b + 1)*b**7 + 1246275072*sqrt( - 6*b + 1)*b **6*x**4 - 830850048*sqrt( - 6*b + 1)*b**6*x**3 + 80850960*sqrt( - 6*b + 1 )*b**6*x**2 + 19208016*sqrt( - 6*b + 1)*b**6*x - 2027100*sqrt( - 6*b + 1)* b**6 + 1246275072*sqrt( - 6*b + 1)*b**5*x**6 - 1246275072*sqrt( - 6*b + 1) *b**5*x**5 + 219547584*sqrt( - 6*b + 1)*b**5*x**4 + 84426624*sqrt( - 6*b + 1)*b**5*x**3 - 49449528*sqrt( - 6*b + 1)*b**5*x**2 + 9228456*sqrt( - 6*b + 1)*b**5*x + 814462*sqrt( - 6*b + 1)*b**5 - 92021184*sqrt( - 6*b + 1)*b** 4*x**6 + 92021184*sqrt( - 6*b + 1)*b**4*x**5 - 143971344*sqrt( - 6*b + 1)* b**4*x**4 + 78939936*sqrt( - 6*b + 1)*b**4*x**3 - 2013408*sqrt( - 6*b + 1) *b**4*x**2 - 3525072*sqrt( - 6*b + 1)*b**4*x - 111254*sqrt( - 6*b + 1)*b** 4 - 120966048*sqrt( - 6*b + 1)*b**3*x**6 + 120966048*sqrt( - 6*b + 1)*b...