\(\int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [156]

Optimal result

Integrand size = 40, antiderivative size = 224 \[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=-\frac {(1-6 b) f \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right ) \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )}{9 \sqrt {2} \sqrt {-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3}}+\frac {(1-6 b) \left (f-\frac {6 e+f}{\sqrt {1-6 b}}\right ) \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right ) \sqrt {2+\frac {1-6 x}{\sqrt {1-6 b}}} \text {arctanh}\left (\frac {\sqrt {2+\frac {1-6 x}{\sqrt {1-6 b}}}}{\sqrt {3}}\right )}{9 \sqrt {6} \sqrt {-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3}} \] Output:

-1/18*(1-6*b)*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)+1/54*(1-6*b)*(f-(6* 
e+f)/(1-6*b)^(1/2))*(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)
                                                                                    
                                                                                    
 

Mathematica [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.

Time = 11.91 (sec) , antiderivative size = 1497, normalized size of antiderivative = 6.68 \[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx =\text {Too large to display} \] Input:

Integrate[(e + f*x)/Sqrt[1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108 
*x^3],x]
 

Output:

(2*(x - Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1 
^2 + 108*#1^3 & , 2])*(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])*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 & , 1])/(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])]*(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] - Ro 
ot[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54*b*#1 - 54*#1^2 + 108*# 
1^3 & , 3])]*(e + f*Root[1 - Sqrt[1 - 6*b] - 9*b + 6*Sqrt[1 - 6*b]*b + 54* 
b*#1 - 54*#1^2 + 108*#1^3 & , 1]) + f*EllipticE[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...
 

Rubi [A] (verified)

Time = 0.69 (sec) , antiderivative size = 226, normalized size of antiderivative = 1.01, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2489, 27, 90, 73, 217}

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.

\(\displaystyle \int \frac {e+f x}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}} \, dx\)

\(\Big \downarrow \) 2489

\(\displaystyle -\frac {157464 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \int -\frac {e+f x}{157464 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}dx}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \int \frac {e+f x}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}dx}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\)

\(\Big \downarrow \) 90

\(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \left (\frac {1}{6} \left (-\sqrt {1-6 b} f+6 e+f\right ) \int \frac {1}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}dx-\frac {f \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{18 (1-6 b)^2}\right )}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\)

\(\Big \downarrow \) 73

\(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \left (\frac {\left (-\sqrt {1-6 b} f+6 e+f\right ) \int \frac {1}{-3 (1-6 b)^{3/2}+\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)-6 x (1-6 b)}d\sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{18 (1-6 b)}-\frac {f \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{18 (1-6 b)^2}\right )}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\)

\(\Big \downarrow \) 217

\(\displaystyle \frac {\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right ) \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)} \left (-\frac {\arctan \left (\frac {\sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{\sqrt {3} (1-6 b)^{3/4}}\right ) \left (-\sqrt {1-6 b} f+6 e+f\right )}{18 \sqrt {3} (1-6 b)^{7/4}}-\frac {f \sqrt {6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)}}{18 (1-6 b)^2}\right )}{\sqrt {54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1}}\)

Input:

Int[(e + f*x)/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]*(-1/18*(f*Sqrt[-((1 + 2*Sqrt[1 - 6*b])*(1 
- 6*b)) + 6*(1 - 6*b)*x])/(1 - 6*b)^2 - ((6*e + f - Sqrt[1 - 6*b]*f)*ArcTa 
n[Sqrt[-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x]/(Sqrt[3]*(1 - 6 
*b)^(3/4))])/(18*Sqrt[3]*(1 - 6*b)^(7/4))))/Sqrt[1 - (1 - 6*b)^(3/2) - 9*b 
 + 54*b*x - 54*x^2 + 108*x^3]
 

Defintions of rubi rules used

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 73

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[ 
{p = Denominator[m]}, Simp[p/b   Subst[Int[x^(p*(m + 1) - 1)*(c - a*(d/b) + 
 d*(x^p/b))^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] && Lt 
Q[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntL 
inearQ[a, b, c, d, m, n, x]
 

rule 90

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p 
_.), x_] :> Simp[b*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(d*f*(n + p + 2))), 
 x] + Simp[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)))/(d*f*(n + p 
+ 2))   Int[(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n, 
p}, x] && NeQ[n + p + 2, 0]
 

rule 217

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 2489

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]
 

Maple [F]

\[\int \frac {f x +e}{\sqrt {1-\left (1-6 b \right )^{\frac {3}{2}}-9 b +54 b x -54 x^{2}+108 x^{3}}}d x\]

Input:

int((f*x+e)/(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)/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 498 vs. \(2 (187) = 374\).

Time = 0.16 (sec) , antiderivative size = 1130, normalized size of antiderivative = 5.04 \[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {Too large to display} \] Input:

integrate((f*x+e)/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, alg 
orithm="fricas")
 

Output:

[1/54*(3*sqrt(1/3)*(6*x^2 + b - 2*x)*sqrt((6*(6*b - 1)*e*f + (6*b - 1)*f^2 
 - ((3*b - 1)*f^2 - 18*e^2 - 6*e*f)*sqrt(-6*b + 1))/(6*b - 1))*log(-(324*( 
b*f^2 + 6*e^2 + 2*e*f)*x^4 - 216*(b*f^2 + 6*e^2 + 2*e*f)*x^3 - 54*(5*b^2 - 
 b)*e^2 - 18*(5*b^2 - b)*e*f - 9*(5*b^3 - b^2)*f^2 - 18*(6*(12*b - 5)*e^2 
+ 2*(12*b - 5)*e*f + (12*b^2 - 5*b)*f^2)*x^2 - sqrt(1/3)*(18*(6*b - 1)*f*x 
^2 + 6*(6*b - 1)*e - (18*b^2 - 15*b + 2)*f - 12*(3*(6*b - 1)*e + (6*b - 1) 
*f)*x - (18*(6*e + f)*x^2 - 6*(3*b - 1)*e - (9*b - 2)*f + 12*((3*b - 1)*f 
- 3*e)*x)*sqrt(-6*b + 1))*sqrt(108*x^3 + 54*b*x - 54*x^2 + (6*b - 1)*sqrt( 
-6*b + 1) - 9*b + 1)*sqrt((6*(6*b - 1)*e*f + (6*b - 1)*f^2 - ((3*b - 1)*f^ 
2 - 18*e^2 - 6*e*f)*sqrt(-6*b + 1))/(6*b - 1)) + 18*(6*(4*b - 1)*e^2 + 2*( 
4*b - 1)*e*f + (4*b^2 - b)*f^2)*x + 9*(b^2*f^2 - 36*(b*f^2 + 6*e^2 + 2*e*f 
)*x^3 + 6*b*e^2 + 2*b*e*f + 18*(b*f^2 + 6*e^2 + 2*e*f)*x^2 - 2*(6*(3*b + 1 
)*e^2 + 2*(3*b + 1)*e*f + (3*b^2 + b)*f^2)*x)*sqrt(-6*b + 1))/(36*x^4 + 4* 
(3*b + 1)*x^2 - 24*x^3 + b^2 - 4*b*x)) + sqrt(108*x^3 + 54*b*x - 54*x^2 + 
(6*b - 1)*sqrt(-6*b + 1) - 9*b + 1)*(6*f*x - sqrt(-6*b + 1)*f - f))/(6*x^2 
 + b - 2*x), -1/54*(6*sqrt(1/3)*(6*x^2 + b - 2*x)*sqrt(-(6*(6*b - 1)*e*f + 
 (6*b - 1)*f^2 - ((3*b - 1)*f^2 - 18*e^2 - 6*e*f)*sqrt(-6*b + 1))/(6*b - 1 
))*arctan(-1/9*sqrt(1/3)*(18*(6*b - 1)*f*x^2 - 3*(6*b - 1)*e + (36*b^2 - 1 
2*b + 1)*f + 3*(6*(6*b - 1)*e - (6*b - 1)*f)*x - (18*(6*e + f)*x^2 + 3*(12 
*b - 1)*e + (9*b - 1)*f - 3*((6*b + 1)*f + 12*e)*x)*sqrt(-6*b + 1))*sqr...
 

Sympy [F]

\[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int \frac {e + f x}{\sqrt {54 b x + 6 b \sqrt {1 - 6 b} - 9 b + 108 x^{3} - 54 x^{2} - \sqrt {1 - 6 b} + 1}}\, dx \] Input:

integrate((f*x+e)/(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)/sqrt(54*b*x + 6*b*sqrt(1 - 6*b) - 9*b + 108*x**3 - 54*x 
**2 - sqrt(1 - 6*b) + 1), x)
 

Maxima [F]

\[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int { \frac {f x + e}{\sqrt {108 \, x^{3} + 54 \, b x - 54 \, x^{2} - {\left (-6 \, b + 1\right )}^{\frac {3}{2}} - 9 \, b + 1}} \,d x } \] Input:

integrate((f*x+e)/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, alg 
orithm="maxima")
 

Output:

integrate((f*x + e)/sqrt(108*x^3 + 54*b*x - 54*x^2 - (-6*b + 1)^(3/2) - 9* 
b + 1), x)
 

Giac [F(-2)]

Exception generated. \[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x+e)/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x, alg 
orithm="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
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\int \frac {e+f\,x}{\sqrt {54\,b\,x-9\,b-{\left (1-6\,b\right )}^{3/2}-54\,x^2+108\,x^3+1}} \,d x \] Input:

int((e + f*x)/(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)/(54*b*x - 9*b - (1 - 6*b)^(3/2) - 54*x^2 + 108*x^3 + 1)^(1/2 
), x)
 

Reduce [F]

\[ \int \frac {e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx=\text {too large to display} \] Input:

int((f*x+e)/(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(1/2),x)
 

Output:

( - 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 + 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 + 
282175488*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 + 12 
46275072*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 - 12096 
6048*sqrt( - 6*b + 1)*b**3*x**6 + 120966048*sqrt( - 6*b + 1)*b**3*x**5 - 1 
381320*sqrt( - 6*b + 1)*b**3*x**4 - 21480240*sqrt( - 6*b + 1)*b**3*x**3 + 
2925024*sqrt( - 6*b + 1)*b**3*x**2 + 467240*sqrt( - 6*b + 1)*b**3*x + 6836 
*sqrt( - 6*b + 1)*b**3 + 28860192*sqrt( - 6*b + 1)*b**2*x**6 - 28860192...