Integrand size = 34, antiderivative size = 375 \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=-\frac {9 \sqrt {1-6 b} \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right ) \left (-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3\right )^{3/2}}{10 \sqrt {2} \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right )^3}+\frac {9 \sqrt {1-6 b} \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )^2 \left (-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3\right )^{3/2}}{14 \sqrt {2} \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right )^3}-\frac {\sqrt {1-6 b} \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )^3 \left (-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3\right )^{3/2}}{6 \sqrt {2} \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right )^3}+\frac {\sqrt {1-6 b} \left (2+\frac {1-6 x}{\sqrt {1-6 b}}\right )^4 \left (-2 (1-6 b)^{3/2}+3 (1-6 b) (1-6 x)-(1-6 x)^3\right )^{3/2}}{66 \sqrt {2} \left (1-\frac {1-6 x}{\sqrt {1-6 b}}\right )^3} \] Output:
-9/20*(1-6*b)^(1/2)*(2+(1-6*x)/(1-6*b)^(1/2))*(-2*(1-6*b)^(3/2)+3*(1-6*b)* (1-6*x)-(1-6*x)^3)^(3/2)*2^(1/2)/(1-(1-6*x)/(1-6*b)^(1/2))^3+9/28*(1-6*b)^ (1/2)*(2+(1-6*x)/(1-6*b)^(1/2))^2*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6 *x)^3)^(3/2)*2^(1/2)/(1-(1-6*x)/(1-6*b)^(1/2))^3-1/12*(1-6*b)^(1/2)*(2+(1- 6*x)/(1-6*b)^(1/2))^3*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2) *2^(1/2)/(1-(1-6*x)/(1-6*b)^(1/2))^3+1/132*(1-6*b)^(1/2)*(2+(1-6*x)/(1-6*b )^(1/2))^4*(-2*(1-6*b)^(3/2)+3*(1-6*b)*(1-6*x)-(1-6*x)^3)^(3/2)*2^(1/2)/(1 -(1-6*x)/(1-6*b)^(1/2))^3
Result contains higher order function than in optimal. Order 9 vs. order 2 in optimal.
Time = 14.51 (sec) , antiderivative size = 1620, normalized size of antiderivative = 4.32 \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx =\text {Too large to display} \] Input:
Integrate[(1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108*x^3)^(3/2),x]
Output:
(77*(1 - 6*b)^(3/2)*(1 - 6*x)*(1 - Sqrt[1 - 6*b] - 54*x^2 + 108*x^3 + b*(- 9 + 6*Sqrt[1 - 6*b] + 54*x)) + (1 - Sqrt[1 - 6*b] - 54*x^2 + 108*x^3 + b*( -9 + 6*Sqrt[1 - 6*b] + 54*x))*(10 + 21*Sqrt[1 - 6*b] + 3240*b^2 + (750 - 1 26*Sqrt[1 - 6*b])*x + 270*x^2 - 15120*x^3 + 22680*x^4 + 9*b*(-55 - 14*Sqrt [1 - 6*b] + 12*(-65 + 7*Sqrt[1 - 6*b])*x + 2340*x^2)) - 1944*(1 - 6*b)^2*S qrt[(-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*S qrt[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 & , 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]))/(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])^2)]*(-Root[1 - S qrt[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])*(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 - S qrt[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...
Time = 0.47 (sec) , antiderivative size = 279, normalized size of antiderivative = 0.74, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2480, 27, 53, 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.
| \(\displaystyle \int \left (54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1\right )^{3/2} \, dx\) |
| \(\Big \downarrow \) 2480 |
| \(\displaystyle -\frac {\left (54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1\right )^{3/2} \int -7808611824626688 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}dx}{7808611824626688 \sqrt {2} \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\left (54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1\right )^{3/2} \int \left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}dx}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}}\) |
| \(\Big \downarrow \) 53 |
| \(\displaystyle \frac {\left (54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1\right )^{3/2} \int \left (-27 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2} (1-6 b)^{9/2}-9 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{7/2} (1-6 b)^{3/2}-\left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{9/2}+27 (6 b-1)^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{5/2}\right )dx}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\left (54 b x-(1-6 b)^{3/2}-9 b+108 x^3-54 x^2+1\right )^{3/2} \left (-\frac {\left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{11/2}}{33 (1-6 b)}-\frac {1}{3} \sqrt {1-6 b} \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{9/2}-\frac {9}{7} (1-6 b)^2 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{7/2}-\frac {9}{5} (1-6 b)^{7/2} \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{5/2}\right )}{\left (\left (1-\sqrt {1-6 b}\right ) (1-6 b)-6 (1-6 b) x\right )^3 \left (6 (1-6 b) x-\left (2 \sqrt {1-6 b}+1\right ) (1-6 b)\right )^{3/2}}\) |
Input:
Int[(1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108*x^3)^(3/2),x]
Output:
((1 - (1 - 6*b)^(3/2) - 9*b + 54*b*x - 54*x^2 + 108*x^3)^(3/2)*((-9*(1 - 6 *b)^(7/2)*(-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^(5/2))/5 - (9*(1 - 6*b)^2*(-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^(7/2)) /7 - (Sqrt[1 - 6*b]*(-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^( 9/2))/3 - (-((1 + 2*Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^(11/2)/(33* (1 - 6*b))))/(((1 - Sqrt[1 - 6*b])*(1 - 6*b) - 6*(1 - 6*b)*x)^3*(-((1 + 2* Sqrt[1 - 6*b])*(1 - 6*b)) + 6*(1 - 6*b)*x)^(3/2))
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_.), x_Symbol] :> Int [ExpandIntegrand[(a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0] && LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Int[(Px_)^(p_), x_Symbol] :> With[{a = Coeff[Px, x, 0], b = Coeff[Px, x, 1] , c = Coeff[Px, x, 2], d = Coeff[Px, x, 3]}, Simp[Px^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 [(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] /; EqQ[b^2*c^2 - 4*a*c^3 - 4*b^3*d + 18*a*b*c*d - 27* a^2*d^2, 0] && NeQ[c^2 - 3*b*d, 0]] /; FreeQ[p, x] && PolyQ[Px, x, 3] && ! IntegerQ[p]
Time = 0.43 (sec) , antiderivative size = 124, normalized size of antiderivative = 0.33
| method | result | size |
| gosper | \(\frac {2 \left (1+2 \sqrt {1-6 b}-6 x \right ) \left (-3150 x^{2} \sqrt {1-6 b}-3780 x^{3}+1107 \sqrt {1-6 b}\, b +1050 x \sqrt {1-6 b}+6570 b x +1890 x^{2}-272 \sqrt {1-6 b}-1095 b -1410 x +200\right ) \left (1-\left (1-6 b \right )^{\frac {3}{2}}-9 b +54 b x -54 x^{2}+108 x^{3}\right )^{\frac {3}{2}}}{1155 \left (-1+6 x +\sqrt {1-6 b}\right )^{3}}\) | \(124\) |
| risch | \(\frac {\left (22680 \sqrt {1-6 b}\, x^{4}+136080 x^{5}+42228 x^{2} \sqrt {1-6 b}\, b -15120 x^{3} \sqrt {1-6 b}+126360 b \,x^{3}-113400 x^{4}+26568 \sqrt {1-6 b}\, b^{2}-14076 \sqrt {1-6 b}\, b x -3258 x^{2} \sqrt {1-6 b}-1728 b^{2} x -63180 b \,x^{2}+16740 x^{3}-7683 \sqrt {1-6 b}\, b +1926 x \sqrt {1-6 b}+288 b^{2}+11106 b x +4230 x^{2}+560 \sqrt {1-6 b}-681 b -1278 x +88\right ) \left (-1-2 \sqrt {1-6 b}+6 x \right ) \left (-1+6 x +\sqrt {1-6 b}\right )}{2310 \sqrt {108 x^{3}+54 b x +6 \sqrt {1-6 b}\, b -54 x^{2}-9 b -\sqrt {1-6 b}+1}}\) | \(225\) |
Input:
int((1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x,method=_RETURNVERB OSE)
Output:
2/1155*(1+2*(1-6*b)^(1/2)-6*x)*(-3150*x^2*(1-6*b)^(1/2)-3780*x^3+1107*(1-6 *b)^(1/2)*b+1050*x*(1-6*b)^(1/2)+6570*b*x+1890*x^2-272*(1-6*b)^(1/2)-1095* b-1410*x+200)*(1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2)/(-1+6*x+(1 -6*b)^(1/2))^3
Time = 0.09 (sec) , antiderivative size = 173, normalized size of antiderivative = 0.46 \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\frac {{\left (136080 \, x^{6} + 540 \, {\left (276 \, b + 59\right )} x^{4} - 136080 \, x^{5} - 360 \, {\left (276 \, b - 11\right )} x^{3} + 26568 \, b^{3} + 180 \, {\left (225 \, b^{2} + 63 \, b - 8\right )} x^{2} - 12159 \, b^{2} - 20 \, {\left (675 \, b^{2} - 87 \, b + 1\right )} x + 2 \, {\left (1764 \, {\left (6 \, b - 1\right )} x^{3} - 882 \, {\left (6 \, b - 1\right )} x^{2} - 2238 \, b^{2} + 2 \, {\left (6714 \, b^{2} - 1797 \, b + 113\right )} x + 697 \, b - 54\right )} \sqrt {-6 \, b + 1} + 1954 \, b - 108\right )} \sqrt {108 \, x^{3} + 54 \, b x - 54 \, x^{2} + {\left (6 \, b - 1\right )} \sqrt {-6 \, b + 1} - 9 \, b + 1}}{1155 \, {\left (6 \, x^{2} + b - 2 \, x\right )}} \] Input:
integrate((1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x, algorithm=" fricas")
Output:
1/1155*(136080*x^6 + 540*(276*b + 59)*x^4 - 136080*x^5 - 360*(276*b - 11)* x^3 + 26568*b^3 + 180*(225*b^2 + 63*b - 8)*x^2 - 12159*b^2 - 20*(675*b^2 - 87*b + 1)*x + 2*(1764*(6*b - 1)*x^3 - 882*(6*b - 1)*x^2 - 2238*b^2 + 2*(6 714*b^2 - 1797*b + 113)*x + 697*b - 54)*sqrt(-6*b + 1) + 1954*b - 108)*sqr t(108*x^3 + 54*b*x - 54*x^2 + (6*b - 1)*sqrt(-6*b + 1) - 9*b + 1)/(6*x^2 + b - 2*x)
\[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\int \left (54 b x - 9 b + 108 x^{3} - 54 x^{2} - \left (1 - 6 b\right )^{\frac {3}{2}} + 1\right )^{\frac {3}{2}}\, dx \] Input:
integrate((1-(1-6*b)**(3/2)-9*b+54*b*x-54*x**2+108*x**3)**(3/2),x)
Output:
Integral((54*b*x - 9*b + 108*x**3 - 54*x**2 - (1 - 6*b)**(3/2) + 1)**(3/2) , x)
\[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\int { {\left (108 \, x^{3} + 54 \, b x - 54 \, x^{2} - {\left (-6 \, b + 1\right )}^{\frac {3}{2}} - 9 \, b + 1\right )}^{\frac {3}{2}} \,d x } \] Input:
integrate((1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x, algorithm=" maxima")
Output:
integrate((108*x^3 + 54*b*x - 54*x^2 - (-6*b + 1)^(3/2) - 9*b + 1)^(3/2), x)
Leaf count of result is larger than twice the leaf count of optimal. 2006 vs. \(2 (307) = 614\).
Time = 0.15 (sec) , antiderivative size = 2006, normalized size of antiderivative = 5.35 \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\text {Too large to display} \] Input:
integrate((1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x, algorithm=" giac")
Output:
1/20790*sqrt(1/2)*(332640*((6*x - 2*sqrt(-6*b + 1) - 1)^(3/2) + 6*sqrt(-6* b + 1)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1) + 3*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b^2*sgn(6*x + sqrt(-6*b + 1) - 1) + 498960*b^2*sqrt(-6*b + 1)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1)*sgn(6*x + sqrt(-6*b + 1) - 1) - 1386*(3*(6*x - 2* sqrt(-6*b + 1) - 1)^(5/2) + 10*(6*x - 2*sqrt(-6*b + 1) - 1)^(3/2)*(2*sqrt( -6*b + 1) + 1) - 15*(24*b - 4*sqrt(-6*b + 1) - 5)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b*sqrt(-6*b + 1)*sgn(6*x + sqrt(-6*b + 1) - 1) + 13860*((6*x - 2 *sqrt(-6*b + 1) - 1)^(3/2) + 6*sqrt(-6*b + 1)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1) + 3*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b*sqrt(-6*b + 1)*sgn(6*x + sqrt (-6*b + 1) - 1) - 997920*b^2*sqrt(6*x - 2*sqrt(-6*b + 1) - 1)*sgn(6*x + sq rt(-6*b + 1) - 1) + 2970*(5*(6*x - 2*sqrt(-6*b + 1) - 1)^(7/2) + 21*(6*x - 2*sqrt(-6*b + 1) - 1)^(5/2)*(2*sqrt(-6*b + 1) + 1) - 35*(24*b - 4*sqrt(-6 *b + 1) - 5)*(6*x - 2*sqrt(-6*b + 1) - 1)^(3/2) - 35*(2*(24*b - 7)*sqrt(-6 *b + 1) + 72*b - 13)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b*sgn(6*x + sqrt(-6 *b + 1) - 1) - 20790*(3*(6*x - 2*sqrt(-6*b + 1) - 1)^(5/2) + 10*(6*x - 2*s qrt(-6*b + 1) - 1)^(3/2)*(2*sqrt(-6*b + 1) + 1) - 15*(24*b - 4*sqrt(-6*b + 1) - 5)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b*sgn(6*x + sqrt(-6*b + 1) - 1) - 6930*((6*x - 2*sqrt(-6*b + 1) - 1)^(3/2) + 6*sqrt(-6*b + 1)*sqrt(6*x - 2*sqrt(-6*b + 1) - 1) + 3*sqrt(6*x - 2*sqrt(-6*b + 1) - 1))*b*sgn(6*x + sq rt(-6*b + 1) - 1) - 187110*b*sqrt(-6*b + 1)*sqrt(6*x - 2*sqrt(-6*b + 1)...
Timed out. \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\int {\left (54\,b\,x-9\,b-{\left (1-6\,b\right )}^{3/2}-54\,x^2+108\,x^3+1\right )}^{3/2} \,d x \] Input:
int((54*b*x - 9*b - (1 - 6*b)^(3/2) - 54*x^2 + 108*x^3 + 1)^(3/2),x)
Output:
int((54*b*x - 9*b - (1 - 6*b)^(3/2) - 54*x^2 + 108*x^3 + 1)^(3/2), x)
\[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^{3/2} \, dx=\text {too large to display} \] Input:
int((1-(1-6*b)^(3/2)-9*b+54*b*x-54*x^2+108*x^3)^(3/2),x)
Output:
( - 2592*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**2 + 3528*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*x + 276*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 - 588*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)*x + 26*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) + 23328*sqrt( - 6*b + 1)*int(sq rt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 108*x**3 - 54* x**2 + 1)/(8*b**2 + 60*b*x**2 - 20*b*x - b + 72*x**4 - 48*x**3 + 2*x**2 + 2*x),x)*b**3 - 9072*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)/(8*b**2 + 60*b*x**2 - 20*b*x - b + 72*x**4 - 48*x**3 + 2*x**2 + 2*x),x)*b**2 + 1080*sqrt( - 6*b + 1)*int(sqrt(6*sqrt( - 6*b + 1)*b - sqrt( - 6*b + 1) + 54*b*x - 9*b + 10 8*x**3 - 54*x**2 + 1)/(8*b**2 + 60*b*x**2 - 20*b*x - b + 72*x**4 - 48*x**3 + 2*x**2 + 2*x),x)*b - 36*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)/(8*b**2 + 60*b *x**2 - 20*b*x - b + 72*x**4 - 48*x**3 + 2*x**2 + 2*x),x) + 279936*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)*x**3)/(8*b**2 + 60*b*x**2 - 20*b*x - b + 72*...