\(\int \frac {x^{3/2}}{(a+b x^2)^2 (c+d x^2)^3} \, dx\) [498]

Optimal result

Integrand size = 24, antiderivative size = 703 \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=-\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}-\frac {b^{7/4} (b c+11 a d) \arctan \left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (b c+11 a d) \arctan \left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \arctan \left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \arctan \left (1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4} \]

[Out]

-1/8*b^(7/4)*(11*a*d+b*c)*arctan(1-b^(1/4)*2^(1/2)*x^(1/2)/a^(1/4))/a^(3/4)/(-a*d+b*c)^4*2^(1/2)+1/8*b^(7/4)*(
11*a*d+b*c)*arctan(1+b^(1/4)*2^(1/2)*x^(1/2)/a^(1/4))/a^(3/4)/(-a*d+b*c)^4*2^(1/2)+1/64*d^(3/4)*(-3*a^2*d^2+22
*a*b*c*d+77*b^2*c^2)*arctan(1-d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(7/4)/(-a*d+b*c)^4*2^(1/2)-1/64*d^(3/4)*(-3*a
^2*d^2+22*a*b*c*d+77*b^2*c^2)*arctan(1+d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(7/4)/(-a*d+b*c)^4*2^(1/2)-1/16*b^(7
/4)*(11*a*d+b*c)*ln(a^(1/2)+x*b^(1/2)-a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(3/4)/(-a*d+b*c)^4*2^(1/2)+1/16*b^(7/
4)*(11*a*d+b*c)*ln(a^(1/2)+x*b^(1/2)+a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(3/4)/(-a*d+b*c)^4*2^(1/2)+1/128*d^(3/
4)*(-3*a^2*d^2+22*a*b*c*d+77*b^2*c^2)*ln(c^(1/2)+x*d^(1/2)-c^(1/4)*d^(1/4)*2^(1/2)*x^(1/2))/c^(7/4)/(-a*d+b*c)
^4*2^(1/2)-1/128*d^(3/4)*(-3*a^2*d^2+22*a*b*c*d+77*b^2*c^2)*ln(c^(1/2)+x*d^(1/2)+c^(1/4)*d^(1/4)*2^(1/2)*x^(1/
2))/c^(7/4)/(-a*d+b*c)^4*2^(1/2)-3/4*d*x^(1/2)/(-a*d+b*c)^2/(d*x^2+c)^2-1/2*x^(1/2)/(-a*d+b*c)/(b*x^2+a)/(d*x^
2+c)^2-1/16*d*(a*d+23*b*c)*x^(1/2)/c/(-a*d+b*c)^3/(d*x^2+c)

Rubi [A] (verified)

Time = 0.71 (sec) , antiderivative size = 703, normalized size of antiderivative = 1.00, number of steps used = 23, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.417, Rules used = {477, 482, 541, 536, 217, 1179, 642, 1176, 631, 210} \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=-\frac {b^{7/4} \arctan \left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right ) (11 a d+b c)}{4 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} \arctan \left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right ) (11 a d+b c)}{4 \sqrt {2} a^{3/4} (b c-a d)^4}-\frac {b^{7/4} (11 a d+b c) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (11 a d+b c) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (-3 a^2 d^2+22 a b c d+77 b^2 c^2\right ) \arctan \left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (-3 a^2 d^2+22 a b c d+77 b^2 c^2\right ) \arctan \left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}+\frac {d^{3/4} \left (-3 a^2 d^2+22 a b c d+77 b^2 c^2\right ) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (-3 a^2 d^2+22 a b c d+77 b^2 c^2\right ) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d \sqrt {x} (a d+23 b c)}{16 c \left (c+d x^2\right ) (b c-a d)^3}-\frac {3 d \sqrt {x}}{4 \left (c+d x^2\right )^2 (b c-a d)^2}-\frac {\sqrt {x}}{2 \left (a+b x^2\right ) \left (c+d x^2\right )^2 (b c-a d)} \]

[In]

Int[x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^3),x]

[Out]

(-3*d*Sqrt[x])/(4*(b*c - a*d)^2*(c + d*x^2)^2) - Sqrt[x]/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) - (d*(23*b*
c + a*d)*Sqrt[x])/(16*c*(b*c - a*d)^3*(c + d*x^2)) - (b^(7/4)*(b*c + 11*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[
x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (b^(7/4)*(b*c + 11*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])
/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt
[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*
d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (b^(7/4)*(b*c + 11*a*
d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (b^(7/4)*(b
*c + 11*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (
d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*
Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*
d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*(b*c - a*d)^4)

Rule 210

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

Rule 217

Int[((a_) + (b_.)*(x_)^4)^(-1), x_Symbol] :> With[{r = Numerator[Rt[a/b, 2]], s = Denominator[Rt[a/b, 2]]}, Di
st[1/(2*r), Int[(r - s*x^2)/(a + b*x^4), x], x] + Dist[1/(2*r), Int[(r + s*x^2)/(a + b*x^4), x], x]] /; FreeQ[
{a, b}, x] && (GtQ[a/b, 0] || (PosQ[a/b] && AtomQ[SplitProduct[SumBaseQ, a]] && AtomQ[SplitProduct[SumBaseQ, b
]]))

Rule 477

Int[((e_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> With[{k = Deno
minator[m]}, Dist[k/e, Subst[Int[x^(k*(m + 1) - 1)*(a + b*(x^(k*n)/e^n))^p*(c + d*(x^(k*n)/e^n))^q, x], x, (e*
x)^(1/k)], x]] /; FreeQ[{a, b, c, d, e, p, q}, x] && NeQ[b*c - a*d, 0] && IGtQ[n, 0] && FractionQ[m] && Intege
rQ[p]

Rule 482

Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Simp[e^(n - 1
)*(e*x)^(m - n + 1)*(a + b*x^n)^(p + 1)*((c + d*x^n)^(q + 1)/(n*(b*c - a*d)*(p + 1))), x] - Dist[e^n/(n*(b*c -
a*d)*(p + 1)), Int[(e*x)^(m - n)*(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*(m - n + 1) + d*(m + n*(p + q + 1)
+ 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e, q}, x] && NeQ[b*c - a*d, 0] && IGtQ[n, 0] && LtQ[p, -1] && GeQ[n
, m - n + 1] && GtQ[m - n + 1, 0] && IntBinomialQ[a, b, c, d, e, m, n, p, q, x]

Rule 536

Int[((e_) + (f_.)*(x_)^(n_))/(((a_) + (b_.)*(x_)^(n_))*((c_) + (d_.)*(x_)^(n_))), x_Symbol] :> Dist[(b*e - a*f
)/(b*c - a*d), Int[1/(a + b*x^n), x], x] - Dist[(d*e - c*f)/(b*c - a*d), Int[1/(c + d*x^n), x], x] /; FreeQ[{a
, b, c, d, e, f, n}, x]

Rule 541

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

Rule 631

Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> With[{q = 1 - 4*Simplify[a*(c/b^2)]}, Dist[-2/b, Sub
st[Int[1/(q - x^2), x], x, 1 + 2*c*(x/b)], x] /; RationalQ[q] && (EqQ[q^2, 1] ||  !RationalQ[b^2 - 4*a*c])] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 642

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

Rule 1176

Int[((d_) + (e_.)*(x_)^2)/((a_) + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[2*(d/e), 2]}, Dist[e/(2*c), Int[1/S
imp[d/e + q*x + x^2, x], x], x] + Dist[e/(2*c), Int[1/Simp[d/e - q*x + x^2, x], x], x]] /; FreeQ[{a, c, d, e},
x] && EqQ[c*d^2 - a*e^2, 0] && PosQ[d*e]

Rule 1179

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

Rubi steps \begin{align*} \text {integral}& = 2 \text {Subst}\left (\int \frac {x^4}{\left (a+b x^4\right )^2 \left (c+d x^4\right )^3} \, dx,x,\sqrt {x}\right ) \\ & = -\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {\text {Subst}\left (\int \frac {c-11 d x^4}{\left (a+b x^4\right ) \left (c+d x^4\right )^3} \, dx,x,\sqrt {x}\right )}{2 (b c-a d)} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {\text {Subst}\left (\int \frac {4 c (2 b c+a d)-84 b c d x^4}{\left (a+b x^4\right ) \left (c+d x^4\right )^2} \, dx,x,\sqrt {x}\right )}{16 c (b c-a d)^2} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}+\frac {\text {Subst}\left (\int \frac {4 c \left (8 b^2 c^2+19 a b c d-3 a^2 d^2\right )-12 b c d (23 b c+a d) x^4}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{64 c^2 (b c-a d)^3} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}+\frac {\left (b^2 (b c+11 a d)\right ) \text {Subst}\left (\int \frac {1}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 (b c-a d)^4}-\frac {\left (d \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{c+d x^4} \, dx,x,\sqrt {x}\right )}{16 c (b c-a d)^4} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}+\frac {\left (b^2 (b c+11 a d)\right ) \text {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 \sqrt {a} (b c-a d)^4}+\frac {\left (b^2 (b c+11 a d)\right ) \text {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 \sqrt {a} (b c-a d)^4}-\frac {\left (d \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {\sqrt {c}-\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^{3/2} (b c-a d)^4}-\frac {\left (d \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {\sqrt {c}+\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^{3/2} (b c-a d)^4} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}+\frac {\left (b^{3/2} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {a} (b c-a d)^4}+\frac {\left (b^{3/2} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {a} (b c-a d)^4}-\frac {\left (b^{7/4} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}+2 x}{-\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}-\frac {\left (b^{7/4} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}-2 x}{-\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}-\frac {\left (\sqrt {d} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{\frac {\sqrt {c}}{\sqrt {d}}-\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}+x^2} \, dx,x,\sqrt {x}\right )}{64 c^{3/2} (b c-a d)^4}-\frac {\left (\sqrt {d} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{\frac {\sqrt {c}}{\sqrt {d}}+\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}+x^2} \, dx,x,\sqrt {x}\right )}{64 c^{3/2} (b c-a d)^4}+\frac {\left (d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{c}}{\sqrt [4]{d}}+2 x}{-\frac {\sqrt {c}}{\sqrt {d}}-\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}-x^2} \, dx,x,\sqrt {x}\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}+\frac {\left (d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{c}}{\sqrt [4]{d}}-2 x}{-\frac {\sqrt {c}}{\sqrt {d}}+\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}-x^2} \, dx,x,\sqrt {x}\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}-\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}+\frac {\left (b^{7/4} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}-\frac {\left (b^{7/4} (b c+11 a d)\right ) \text {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}-\frac {\left (d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}+\frac {\left (d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4} \\ & = -\frac {3 d \sqrt {x}}{4 (b c-a d)^2 \left (c+d x^2\right )^2}-\frac {\sqrt {x}}{2 (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {d (23 b c+a d) \sqrt {x}}{16 c (b c-a d)^3 \left (c+d x^2\right )}-\frac {b^{7/4} (b c+11 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (b c+11 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {b^{7/4} (b c+11 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{3/4} (b c-a d)^4}+\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4}-\frac {d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{7/4} (b c-a d)^4} \\ \end{align*}

Mathematica [A] (verified)

Time = 2.20 (sec) , antiderivative size = 392, normalized size of antiderivative = 0.56 \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\frac {-\frac {4 (b c-a d) \sqrt {x} \left (a^2 d^2 \left (-3 c+d x^2\right )+a b d \left (19 c^2+12 c d x^2+d^2 x^4\right )+b^2 c \left (8 c^2+35 c d x^2+23 d^2 x^4\right )\right )}{c \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {8 \sqrt {2} b^{7/4} (b c+11 a d) \arctan \left (\frac {\sqrt {a}-\sqrt {b} x}{\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}\right )}{a^{3/4}}+\frac {\sqrt {2} d^{3/4} \left (77 b^2 c^2+22 a b c d-3 a^2 d^2\right ) \arctan \left (\frac {\sqrt {c}-\sqrt {d} x}{\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}}\right )}{c^{7/4}}+\frac {8 \sqrt {2} b^{7/4} (b c+11 a d) \text {arctanh}\left (\frac {\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}{\sqrt {a}+\sqrt {b} x}\right )}{a^{3/4}}+\frac {\sqrt {2} d^{3/4} \left (-77 b^2 c^2-22 a b c d+3 a^2 d^2\right ) \text {arctanh}\left (\frac {\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}}{\sqrt {c}+\sqrt {d} x}\right )}{c^{7/4}}}{64 (b c-a d)^4} \]

[In]

Integrate[x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^3),x]

[Out]

((-4*(b*c - a*d)*Sqrt[x]*(a^2*d^2*(-3*c + d*x^2) + a*b*d*(19*c^2 + 12*c*d*x^2 + d^2*x^4) + b^2*c*(8*c^2 + 35*c
*d*x^2 + 23*d^2*x^4)))/(c*(a + b*x^2)*(c + d*x^2)^2) - (8*Sqrt[2]*b^(7/4)*(b*c + 11*a*d)*ArcTan[(Sqrt[a] - Sqr
t[b]*x)/(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])])/a^(3/4) + (Sqrt[2]*d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*A
rcTan[(Sqrt[c] - Sqrt[d]*x)/(Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x])])/c^(7/4) + (8*Sqrt[2]*b^(7/4)*(b*c + 11*a*d)*Ar
cTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/a^(3/4) + (Sqrt[2]*d^(3/4)*(-77*b^2*c^2 - 22*a
*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x])/(Sqrt[c] + Sqrt[d]*x)])/c^(7/4))/(64*(b*c - a*d)
^4)

Maple [A] (verified)

Time = 2.77 (sec) , antiderivative size = 364, normalized size of antiderivative = 0.52

method	result	size
derivativedivides	\(\frac {2 d \left (\frac {\frac {d \left (a^{2} d^{2}+14 a b c d -15 b^{2} c^{2}\right ) x^{\frac {5}{2}}}{32 c}+\left (\frac {11}{16} a b c d -\frac {19}{32} b^{2} c^{2}-\frac {3}{32} a^{2} d^{2}\right ) \sqrt {x}}{\left (d \,x^{2}+c \right )^{2}}+\frac {\left (3 a^{2} d^{2}-22 a b c d -77 b^{2} c^{2}\right ) \left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {2}\, \left (\ln \left (\frac {x +\left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {c}{d}}}{x -\left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {c}{d}}}\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {c}{d}\right )^{\frac {1}{4}}}+1\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {c}{d}\right )^{\frac {1}{4}}}-1\right )\right )}{256 c^{2}}\right )}{\left (a d -b c \right )^{4}}+\frac {2 b^{2} \left (\frac {\left (\frac {a d}{4}-\frac {b c}{4}\right ) \sqrt {x}}{b \,x^{2}+a}+\frac {\left (11 a d +b c \right ) \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \left (\ln \left (\frac {x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {a}{b}}}{x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {a}{b}}}\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )\right )}{32 a}\right )}{\left (a d -b c \right )^{4}}\)	\(364\)
default	\(\frac {2 d \left (\frac {\frac {d \left (a^{2} d^{2}+14 a b c d -15 b^{2} c^{2}\right ) x^{\frac {5}{2}}}{32 c}+\left (\frac {11}{16} a b c d -\frac {19}{32} b^{2} c^{2}-\frac {3}{32} a^{2} d^{2}\right ) \sqrt {x}}{\left (d \,x^{2}+c \right )^{2}}+\frac {\left (3 a^{2} d^{2}-22 a b c d -77 b^{2} c^{2}\right ) \left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {2}\, \left (\ln \left (\frac {x +\left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {c}{d}}}{x -\left (\frac {c}{d}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {c}{d}}}\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {c}{d}\right )^{\frac {1}{4}}}+1\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {c}{d}\right )^{\frac {1}{4}}}-1\right )\right )}{256 c^{2}}\right )}{\left (a d -b c \right )^{4}}+\frac {2 b^{2} \left (\frac {\left (\frac {a d}{4}-\frac {b c}{4}\right ) \sqrt {x}}{b \,x^{2}+a}+\frac {\left (11 a d +b c \right ) \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \left (\ln \left (\frac {x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {a}{b}}}{x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {x}\, \sqrt {2}+\sqrt {\frac {a}{b}}}\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )+2 \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )\right )}{32 a}\right )}{\left (a d -b c \right )^{4}}\)	\(364\)

[In]

int(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x,method=_RETURNVERBOSE)

[Out]

2*d/(a*d-b*c)^4*((1/32*d*(a^2*d^2+14*a*b*c*d-15*b^2*c^2)/c*x^(5/2)+(11/16*a*b*c*d-19/32*b^2*c^2-3/32*a^2*d^2)*
x^(1/2))/(d*x^2+c)^2+1/256*(3*a^2*d^2-22*a*b*c*d-77*b^2*c^2)/c^2*(c/d)^(1/4)*2^(1/2)*(ln((x+(c/d)^(1/4)*x^(1/2
)*2^(1/2)+(c/d)^(1/2))/(x-(c/d)^(1/4)*x^(1/2)*2^(1/2)+(c/d)^(1/2)))+2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+2*
arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)))+2*b^2/(a*d-b*c)^4*((1/4*a*d-1/4*b*c)*x^(1/2)/(b*x^2+a)+1/32*(11*a*d+b*
c)*(a/b)^(1/4)/a*2^(1/2)*(ln((x+(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^(1/2))/(x-(a/b)^(1/4)*x^(1/2)*2^(1/2)+(a/b)^
(1/2)))+2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+2*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)))

Fricas [F(-1)]

Timed out. \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\text {Timed out} \]

[In]

integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="fricas")

[Out]

Timed out

Sympy [F(-1)]

Timed out. \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\text {Timed out} \]

[In]

integrate(x**(3/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 889, normalized size of antiderivative = 1.26 \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\frac {{\left (\frac {2 \, \sqrt {2} {\left (b c + 11 \, a d\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {2 \, \sqrt {2} {\left (b c + 11 \, a d\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {\sqrt {2} {\left (b c + 11 \, a d\right )} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}} - \frac {\sqrt {2} {\left (b c + 11 \, a d\right )} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}}\right )} b^{2}}{16 \, {\left (b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right )}} - \frac {{\left (23 \, b^{2} c d^{2} + a b d^{3}\right )} x^{\frac {9}{2}} + {\left (35 \, b^{2} c^{2} d + 12 \, a b c d^{2} + a^{2} d^{3}\right )} x^{\frac {5}{2}} + {\left (8 \, b^{2} c^{3} + 19 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right )} \sqrt {x}}{16 \, {\left (a b^{3} c^{6} - 3 \, a^{2} b^{2} c^{5} d + 3 \, a^{3} b c^{4} d^{2} - a^{4} c^{3} d^{3} + {\left (b^{4} c^{4} d^{2} - 3 \, a b^{3} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d^{4} - a^{3} b c d^{5}\right )} x^{6} + {\left (2 \, b^{4} c^{5} d - 5 \, a b^{3} c^{4} d^{2} + 3 \, a^{2} b^{2} c^{3} d^{3} + a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right )} x^{4} + {\left (b^{4} c^{6} - a b^{3} c^{5} d - 3 \, a^{2} b^{2} c^{4} d^{2} + 5 \, a^{3} b c^{3} d^{3} - 2 \, a^{4} c^{2} d^{4}\right )} x^{2}\right )}} - \frac {\frac {2 \, \sqrt {2} {\left (77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} + 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {c} \sqrt {\sqrt {c} \sqrt {d}}} + \frac {2 \, \sqrt {2} {\left (77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} - 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {c} \sqrt {\sqrt {c} \sqrt {d}}} + \frac {\sqrt {2} {\left (77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right )} \log \left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {3}{4}} d^{\frac {1}{4}}} - \frac {\sqrt {2} {\left (77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right )} \log \left (-\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {3}{4}} d^{\frac {1}{4}}}}{128 \, {\left (b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}\right )}} \]

[In]

integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="maxima")

[Out]

1/16*(2*sqrt(2)*(b*c + 11*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*s
qrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b*c + 11*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/
4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b*c + 11*a*d)*log(sq
rt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b*c + 11*a*d)*log(-sqrt(2)*a
^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^2/(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*
d^2 - 4*a^3*b*c*d^3 + a^4*d^4) - 1/16*((23*b^2*c*d^2 + a*b*d^3)*x^(9/2) + (35*b^2*c^2*d + 12*a*b*c*d^2 + a^2*d
^3)*x^(5/2) + (8*b^2*c^3 + 19*a*b*c^2*d - 3*a^2*c*d^2)*sqrt(x))/(a*b^3*c^6 - 3*a^2*b^2*c^5*d + 3*a^3*b*c^4*d^2
- a^4*c^3*d^3 + (b^4*c^4*d^2 - 3*a*b^3*c^3*d^3 + 3*a^2*b^2*c^2*d^4 - a^3*b*c*d^5)*x^6 + (2*b^4*c^5*d - 5*a*b^
3*c^4*d^2 + 3*a^2*b^2*c^3*d^3 + a^3*b*c^2*d^4 - a^4*c*d^5)*x^4 + (b^4*c^6 - a*b^3*c^5*d - 3*a^2*b^2*c^4*d^2 +
5*a^3*b*c^3*d^3 - 2*a^4*c^2*d^4)*x^2) - 1/128*(2*sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*arctan(1/2*
sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) +
2*sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*
sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2
*d^3)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(77*b^2*c^2*d + 2
2*a*b*c*d^2 - 3*a^2*d^3)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^4*c
^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1217 vs. \(2 (547) = 1094\).

Time = 0.55 (sec) , antiderivative size = 1217, normalized size of antiderivative = 1.73 \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\text {Too large to display} \]

[In]

integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="giac")

[Out]

1/4*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^
(1/4))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3 + sqrt
(2)*a^5*d^4) + 1/4*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2
*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^
4*b*c*d^3 + sqrt(2)*a^5*d^4) - 1/32*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2
*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5
*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) - 1/32*(77*(c*d^3)^(1/4)*b^2*c
^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))
/(c/d)^(1/4))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 +
sqrt(2)*a^4*c^2*d^4) + 1/8*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x
+ sqrt(a/b))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3
+ sqrt(2)*a^5*d^4) - 1/8*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x
+ sqrt(a/b))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3
+ sqrt(2)*a^5*d^4) - 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(
sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*
d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) + 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c
*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a
*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) - 1/2*b^2*sqrt(x)/((b^
3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) - 1/16*(15*b*c*d^2*x^(5/2) + a*d^3*x^(5/2) + 19*
b*c^2*d*sqrt(x) - 3*a*c*d^2*sqrt(x))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(d*x^2 + c)^2)

Mupad [B] (verification not implemented)

Time = 12.53 (sec) , antiderivative size = 50125, normalized size of antiderivative = 71.30 \[ \int \frac {x^{3/2}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx=\text {Too large to display} \]

[In]

int(x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)

[Out]

((x^(1/2)*(8*b^2*c^2 - 3*a^2*d^2 + 19*a*b*c*d))/(16*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^
(5/2)*(a^2*d^3 + 35*b^2*c^2*d + 12*a*b*c*d^2))/(16*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b
*d*x^(9/2)*(a*d^2 + 23*b*c*d))/(16*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))/(a*c^2 + x^2*(b*c^2
+ 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) + 2*atan(((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*
b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*
d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15
*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73
282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^
8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d
^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 26843545
6*a*b^15*c^22*d))^(1/4)*((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6
*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376
*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*
c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 1343
51945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*
b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^
12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*((((891*a^
9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (10777
7537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*
a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13
*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^
5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 +
286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 401
74904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*
b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435
456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*
d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 2159227
69920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^
5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 -
268435456*a*b^15*c^22*d))^(3/4)*(((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^
2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d
^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*
a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d
^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 19193135
1040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^
4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(
8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232
*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 +
212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12
*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 12
05248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*
a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14
*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8
*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/
2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^
22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3
770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280
643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 54298
06497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 6544750
01856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b
^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 235929
6*a^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*
a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11
*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*
d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 15
3*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*1i) + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454
702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 809
9206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^
3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^
20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 3
1824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a
^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*
c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))) - (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^
7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^
8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b
*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 7328
2879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*
b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^1
1 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*
a*b^15*c^22*d))^(1/4)*((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d
^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a
^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^
21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351
945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^
7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12
- 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*((((891*a^9*
b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (1077775
37*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^
5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13*c
^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*
b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 28
6*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174
904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^
3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 26843545
6*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^
4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769
920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*
c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 26
8435456*a*b^15*c^22*d))^(3/4)*(((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*
b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9
- 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^
2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5
+ 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 1919313510
40*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*
c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(81
92*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a
^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 2
12486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b
^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205
248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^
20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d
^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b
^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (x^(1/2)
*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22
*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 377
0791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 1128064
3522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806
497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001
856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8
*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*
a^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^
3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c
^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^
11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*
a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*1i) - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 83045470
2*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 80992
06482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*
d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20
*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 318
24*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^1
1*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^
7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))))/((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*
c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8
+ 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c
^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 732828
79488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^
8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11
+ 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*
b^15*c^22*d))^(1/4)*((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5
- 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7
*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21
*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 13435194
5728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*
c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 -
9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*((((891*a^9*b^
7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537
*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*
b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13*c^4
*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^
8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*
a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 4017490
4*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*
c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*
a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4
- 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 21592276992
0*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^
12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 2684
35456*a*b^15*c^22*d))^(3/4)*(((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^
6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 -
2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*
b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 +
134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040
*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^
11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(8192
*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5
*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212
486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^1
2*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 120524
8*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20
*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3
+ 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5
*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/2)*(
16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d
^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 37707
91231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 112806435
22560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 542980649
7792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 65447500185
6*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c
^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^
23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*
b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^1
5*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11
+ 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^
16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*1i)*1i + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 8304547
02*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099
206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3
*d^14 + 10537245*a^8*b^11*c^2*d^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*
c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 -
31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824
*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^
3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))) + (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*
b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*
d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15
*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73
282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^
8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d
^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 26843545
6*a*b^15*c^22*d))^(1/4)*((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6
*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376
*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*
c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 1343
51945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*
b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^
12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*((((891*a^
9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (10777
7537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*
a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13
*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^
5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 +
286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 401
74904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*
b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435
456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*
d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 2159227
69920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^
5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 -
268435456*a*b^15*c^22*d))^(3/4)*(((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^
2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d
^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*
a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d
^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 19193135
1040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^
4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(
8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232
*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 +
212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12
*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 12
05248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*
a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14
*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8
*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (x^(1/
2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^
22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3
770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280
643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 54298
06497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 6544750
01856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b
^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 235929
6*a^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*
a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11
*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*
d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 15
3*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*1i)*1i - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830
454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 +
8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12
*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b
^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d
^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 3
1824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^1
5*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 4017490
4*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*
c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*
a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4
- 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 21592276992
0*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^
12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 2684
35456*a*b^15*c^22*d))^(1/4) - atan(((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2
+ 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 -
2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^
6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*
d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^
2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^
2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d
^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^
10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6
*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b
^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^2
1*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17
*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193
363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10
*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^
6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12
+ 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*
c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^1
1*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976
*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20
*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12
- 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15
+ 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 -
1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 722678
5792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4
*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b
*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 +
18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a
^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b
^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b^7*
d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536
*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328
*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 4685
8240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 -
2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4) + ((891*a^9*b^7*d^15)/8192
+ (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b^14*c^7
*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c^4*d^11
)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b
*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716
*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10
- 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^
9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^
14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^1
0*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13
*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^
17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*1i - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830
454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 +
8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12
*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b
^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d
^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 3
1824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^1
5*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))) - (-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*
c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d +
491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5
+ 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d
^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^
3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3
*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15
*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11
*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*
c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b
^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^2
3*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c
^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^9*b^15*c^15*d^12 - 23106969
6*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^11*c^1
1*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^17*b^
7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^
4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b
^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286
*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a
*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 -
366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 707004
8845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 10296755
748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 327497338
0608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*
a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^
24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22
+ a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4
- 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620
*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13
*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(
-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 +
4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a
^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715
520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7
454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4)
+ ((891*a^9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/204
8 - (107777537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 +
(7338751*a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)/(b^13*c^17
- a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1
287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*
d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324
*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*
c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*
c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*
b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^
16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*1i + (x^(1/2)*(9801*a^10*b^9*d^17 + 3
5532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295
711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^
4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*
a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*
d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 4
3758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*
a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))))/((-(b^11*c^4 + 14641*
a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16
- 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 -
17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^
8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4
*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 1
4641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16
*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d
^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c
^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^
4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22
*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^1
9*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^
9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^
15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^
8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*
d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^
4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8
- 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/2)*(16777216*
b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 4346
4523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*
a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^1
0*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13
*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^
11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 -
4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^
2*d^27))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^
3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 4375
8*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^1
2*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d
^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^
10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^
6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 468582
40*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 178
91328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 6
5536*a^18*b*c*d^15))^(3/4) + ((891*a^9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192
- (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (3960657
7*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9
*c^2*d^13)/256)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3
+ 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5
*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4
+ 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*
b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^
12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b
^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^1
5*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4) - (x^(1/2)
*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341
*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12
- 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22
+ a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4
- 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620
*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13
*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))) +
(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16
+ 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720
*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 527
15520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 +
7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4
)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19
*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 74
54720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7
+ 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d
^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))
^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 +
9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^1
6*d^11 + 212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330
624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d
^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^2
2 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b
^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 +
1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)
+ (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3
*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*
d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13
+ 11280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16
- 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 +
654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 1170761318
4*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26
+ 2359296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 -
816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7
*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*
c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15
+ 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*
b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*
c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b
^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^
13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*
a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4) + ((891*a^9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*
a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6
*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)
/2048 + (5265*a^7*b^9*c^2*d^13)/256)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 -
286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^
10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12
*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*
a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3
+ 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*
d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c
^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^
15))^(1/4) + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^1
0*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403
540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15
))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 30
60*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*
b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*
c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 -
18*a*b^17*c^21*d)))))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c
^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^
13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a
^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 1789132
8*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536
*a^18*b*c*d^15))^(1/4)*2i + 2*atan(((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2
+ 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 -
2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^
6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*
d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^
2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^
2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d
^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^
10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6
*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b
^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^2
1*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17
*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193
363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10
*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^
6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12
+ 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*
c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^1
1*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976
*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20
*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12
- 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15
+ 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 -
1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 722678
5792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4
*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^1
7*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5
+ 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 4375
8*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^1
4*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b
^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65
536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891
328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 4
6858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12
- 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4)*1i + (((891*a^9*b^7*d^15
)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b
^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c
^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13*c^4*d^13
+ 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12
*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b
^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 +
726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*
a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800
768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32
800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13
+ 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4) + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d
^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7
*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*
a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*
a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c
^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^1
0 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 81
6*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))) - (-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3
*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15
*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11
*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*
c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b
^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 532
4*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15
*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11
*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12
*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a
^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^2
3*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b
^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^9*b^15*c^15*d^12 - 231
069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^1
1*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^
17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^
13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*
a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9
+ 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) + (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663
296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*
d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7
070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 102
96755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274
973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 16242651
9552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c
^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27)*1i)/(65536*(b^
18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c
^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8
- 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8
568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^2
1*d)))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^1
9*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7
454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7
+ 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*
d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15)
)^(3/4)*1i + (((891*a^9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8
*c*d^14)/2048 - (107777537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*
d^10)/2048 + (7338751*a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)
*1i)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*
b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 -
715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4 + 14641*a^
4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 -
65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17
891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8
- 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d
^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4) - (x^(1/2)*(9801*a^10
*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c
^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 11796710
2*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*
d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*
b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^
13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^
13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d))))/((-(b^11*c^
4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3
*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c
^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*
b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^
15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(((((-(b^
11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 409
6*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b
^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*
a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 74547
20*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*(819
2*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 - 1723648*a^4*b^20*c^20*d^7 + 9439232*a^
5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^10 - 150731776*a^8*b^16*c^16*d^11 + 21
2486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a^11*b^13*c^13*d^14 - 122330624*a^12*b^
12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^17 + 1309696*a^15*b^9*c^9*d^18 + 12052
48*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^21 - 17152*a^19*b^5*c^5*d^22 + 768*a^2
0*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^
3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^
5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d) - (x^(1/2)*
(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*
d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770
791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643
522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 54298064
97792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 6544750018
56*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*
c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a
^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3
*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^
15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^1
1 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a
^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*
d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2
- 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10
*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c
^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2
*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4)*1i + (((891*a^9*b^7*d^15)/8192 + (77*b^16*c^9*d^6)/16 - (33367697*a*b^
15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b^14*c^7*d^8)/2048 - (83346257*a^3*b^13*c^6*d^9
)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c^4*d^11)/4096 + (198309*a^6*b^10*c^3*d^12)/204
8 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 -
286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^
10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12
*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*
a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3
+ 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*
d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c
^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^
15))^(1/4)*1i + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*
b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987
403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d
^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^
3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 4375
8*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^1
2*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d
^16 - 18*a*b^17*c^21*d))) + (-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*
b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*
a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 4685
8240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 1
7891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 -
65536*a^18*b*c*d^15))^(1/4)*(((((-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 +
44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 229
3760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 -
46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^1
0 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d
^14 - 65536*a^18*b*c*d^15))^(1/4)*(8192*a^2*b^22*c^22*d^5 - 2048*a*b^23*c^23*d^4 + 142592*a^3*b^21*c^21*d^6 -
1723648*a^4*b^20*c^20*d^7 + 9439232*a^5*b^19*c^19*d^8 - 32966656*a^6*b^18*c^18*d^9 + 81665024*a^7*b^17*c^17*d^
10 - 150731776*a^8*b^16*c^16*d^11 + 212486144*a^9*b^15*c^15*d^12 - 231069696*a^10*b^14*c^14*d^13 + 193363456*a
^11*b^13*c^13*d^14 - 122330624*a^12*b^12*c^12*d^15 + 55883776*a^13*b^11*c^11*d^16 - 16185344*a^14*b^10*c^10*d^
17 + 1309696*a^15*b^9*c^9*d^18 + 1205248*a^16*b^8*c^8*d^19 - 622592*a^17*b^7*c^7*d^20 + 145408*a^18*b^6*c^6*d^
21 - 17152*a^19*b^5*c^5*d^22 + 768*a^20*b^4*c^4*d^23))/(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^
2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6
- 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^
6*d^11 - 13*a*b^12*c^16*d) + (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^2
5*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1
452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 100681
31053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 797128
5237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 16710689
09568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^1
8*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 -
72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*
d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564
*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b
^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^
8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 +
5324*a^3*b^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*
b^15*c^15*d + 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*
b^11*c^11*d^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*
a^12*b^7*c^7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 22937
60*a^16*b^3*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(3/4)*1i + (((891*a^9*b^7*d^15)/8192 +
(77*b^16*c^9*d^6)/16 - (33367697*a*b^15*c^8*d^7)/8192 - (6291*a^8*b^8*c*d^14)/2048 - (107777537*a^2*b^14*c^7*
d^8)/2048 - (83346257*a^3*b^13*c^6*d^9)/1024 - (39606577*a^4*b^12*c^5*d^10)/2048 + (7338751*a^5*b^11*c^4*d^11)
/4096 + (198309*a^6*b^10*c^3*d^12)/2048 + (5265*a^7*b^9*c^2*d^13)/256)*1i)/(b^13*c^17 - a^13*c^4*d^13 + 13*a^1
2*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1
716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d
^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b^8*c*d^3 + 726*a^2
*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d + 491520*a^5*b^14
*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d^5 + 32800768*a^9*
b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^7*d^9 + 32800768*a
^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3*c^3*d^13 + 491520
*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4)*1i - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 +
830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10
+ 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b
^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15)*1i)/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^
2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^1
6*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10
- 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*
a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))))*(-(b^11*c^4 + 14641*a^4*b^7*d^4 + 5324*a^3*b
^8*c*d^3 + 726*a^2*b^9*c^2*d^2 + 44*a*b^10*c^3*d)/(4096*a^19*d^16 + 4096*a^3*b^16*c^16 - 65536*a^4*b^15*c^15*d
+ 491520*a^5*b^14*c^14*d^2 - 2293760*a^6*b^13*c^13*d^3 + 7454720*a^7*b^12*c^12*d^4 - 17891328*a^8*b^11*c^11*d
^5 + 32800768*a^9*b^10*c^10*d^6 - 46858240*a^10*b^9*c^9*d^7 + 52715520*a^11*b^8*c^8*d^8 - 46858240*a^12*b^7*c^
7*d^9 + 32800768*a^13*b^6*c^6*d^10 - 17891328*a^14*b^5*c^5*d^11 + 7454720*a^15*b^4*c^4*d^12 - 2293760*a^16*b^3
*c^3*d^13 + 491520*a^17*b^2*c^2*d^14 - 65536*a^18*b*c*d^15))^(1/4) - atan(((((891*a^9*b^7*d^15 + 39424*b^16*c^
9*d^6 - 33367697*a*b^15*c^8*d^7 - 25164*a^8*b^8*c*d^14 - 431110148*a^2*b^14*c^7*d^8 - 666770056*a^3*b^13*c^6*d
^9 - 158426308*a^4*b^12*c^5*d^10 + 14677502*a^5*b^11*c^4*d^11 + 793236*a^6*b^10*c^3*d^12 + 168480*a^7*b^9*c^2*
d^13)/(8192*(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 7
15*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9
*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) + (((-(81*a^8*d
^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787
226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 +
16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*
d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 1919313
51040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6
*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 +
2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(67108864*a^2*b^22*c^22*d^5 - 16777216*a*b^23*
c^23*d^4 + 1168113664*a^3*b^21*c^21*d^6 - 14120124416*a^4*b^20*c^20*d^7 + 77326188544*a^5*b^19*c^19*d^8 - 2700
62845952*a^6*b^18*c^18*d^9 + 668999876608*a^7*b^17*c^17*d^10 - 1234794708992*a^8*b^16*c^16*d^11 + 174068649164
8*a^9*b^15*c^15*d^12 - 1892922949632*a^10*b^14*c^14*d^13 + 1584033431552*a^11*b^13*c^13*d^14 - 1002132471808*a
^12*b^12*c^12*d^15 + 457799892992*a^13*b^11*c^11*d^16 - 132590338048*a^14*b^10*c^10*d^17 + 10729029632*a^15*b^
9*c^9*d^18 + 9873391616*a^16*b^8*c^8*d^19 - 5100273664*a^17*b^7*c^7*d^20 + 1191182336*a^18*b^6*c^6*d^21 - 1405
09184*a^19*b^5*c^5*d^22 + 6291456*a^20*b^4*c^4*d^23))/(8192*(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 +
78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^1
1*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b
^2*c^6*d^11 - 13*a*b^12*c^16*d)) - (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a
^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d
^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 -
10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 +
7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 16
71068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 72267857
92*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d
^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c
^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18
564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^1
0*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4
*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*
c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7
+ 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*
d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a
^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*
d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 732828
79488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^
2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(3/4))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 +
11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a
^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 +
2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5
*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^
8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 3053453
3120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22
*d))^(1/4) - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^1
0*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403
540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15
))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 30
60*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*
b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*
c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 -
18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5
- 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*
b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*
d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945
728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c
^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 -
9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*1i - (((891*a^9
*b^7*d^15 + 39424*b^16*c^9*d^6 - 33367697*a*b^15*c^8*d^7 - 25164*a^8*b^8*c*d^14 - 431110148*a^2*b^14*c^7*d^8 -
666770056*a^3*b^13*c^6*d^9 - 158426308*a^4*b^12*c^5*d^10 + 14677502*a^5*b^11*c^4*d^11 + 793236*a^6*b^10*c^3*d
^12 + 168480*a^7*b^9*c^2*d^13)/(8192*(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 -
286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^
10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12
*c^16*d)) + (((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416
184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^
10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 -
9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^
6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^
9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 939524
0960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*(67108864*a^2*b^22*c^
22*d^5 - 16777216*a*b^23*c^23*d^4 + 1168113664*a^3*b^21*c^21*d^6 - 14120124416*a^4*b^20*c^20*d^7 + 77326188544
*a^5*b^19*c^19*d^8 - 270062845952*a^6*b^18*c^18*d^9 + 668999876608*a^7*b^17*c^17*d^10 - 1234794708992*a^8*b^16
*c^16*d^11 + 1740686491648*a^9*b^15*c^15*d^12 - 1892922949632*a^10*b^14*c^14*d^13 + 1584033431552*a^11*b^13*c^
13*d^14 - 1002132471808*a^12*b^12*c^12*d^15 + 457799892992*a^13*b^11*c^11*d^16 - 132590338048*a^14*b^10*c^10*d
^17 + 10729029632*a^15*b^9*c^9*d^18 + 9873391616*a^16*b^8*c^8*d^19 - 5100273664*a^17*b^7*c^7*d^20 + 1191182336
*a^18*b^6*c^6*d^21 - 140509184*a^19*b^5*c^5*d^22 + 6291456*a^20*b^4*c^4*d^23))/(8192*(b^13*c^17 - a^13*c^4*d^1
3 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^
12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10
*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) + (x^(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^2
6*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366
041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^20*c^18*d^11 + 7070048845
824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17*c^15*d^14 - 102967557488
64*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*c^12*d^17 + 3274973380608
*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9*d^20 - 162426519552*a^17
*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 +
842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22 + a^
18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 85
68*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9
*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5
*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81
*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6
- 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*
c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13
*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 1
91931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^
10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*
d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(3/4))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 +
40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*
a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 26
8435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c
^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215
922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^1
1*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^1
4 - 268435456*a*b^15*c^22*d))^(1/4) + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18
*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^
4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 1
0537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 8
16*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b
^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^
11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 +
153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 +
11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^
6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 +
2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*
b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8
- 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533
120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*
d))^(1/4)*1i)/((((891*a^9*b^7*d^15 + 39424*b^16*c^9*d^6 - 33367697*a*b^15*c^8*d^7 - 25164*a^8*b^8*c*d^14 - 431
110148*a^2*b^14*c^7*d^8 - 666770056*a^3*b^13*c^6*d^9 - 158426308*a^4*b^12*c^5*d^10 + 14677502*a^5*b^11*c^4*d^1
1 + 793236*a^6*b^10*c^3*d^12 + 168480*a^7*b^9*c^2*d^13)/(8192*(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12
+ 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c
^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11
*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) + (((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 117394
20*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*
c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 201326
5920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c
^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191
931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^
12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1
/4)*(67108864*a^2*b^22*c^22*d^5 - 16777216*a*b^23*c^23*d^4 + 1168113664*a^3*b^21*c^21*d^6 - 14120124416*a^4*b^
20*c^20*d^7 + 77326188544*a^5*b^19*c^19*d^8 - 270062845952*a^6*b^18*c^18*d^9 + 668999876608*a^7*b^17*c^17*d^10
- 1234794708992*a^8*b^16*c^16*d^11 + 1740686491648*a^9*b^15*c^15*d^12 - 1892922949632*a^10*b^14*c^14*d^13 + 1
584033431552*a^11*b^13*c^13*d^14 - 1002132471808*a^12*b^12*c^12*d^15 + 457799892992*a^13*b^11*c^11*d^16 - 1325
90338048*a^14*b^10*c^10*d^17 + 10729029632*a^15*b^9*c^9*d^18 + 9873391616*a^16*b^8*c^8*d^19 - 5100273664*a^17*
b^7*c^7*d^20 + 1191182336*a^18*b^6*c^6*d^21 - 140509184*a^19*b^5*c^5*d^22 + 6291456*a^20*b^4*c^4*d^23))/(8192*
(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c
^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a
^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) - (x^(1/2)*(16777216*b^27*c
^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24*c^22*d^7 + 4346452377
6*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10 - 3770791231488*a^7*b^
20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11280643522560*a^10*b^17
*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 5429806497792*a^13*b^14*
c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 654475001856*a^16*b^11*c^9
*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^19*b^8*c^6*d^23 - 46776
97536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 2359296*a^23*b^4*c^2*d^27
))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 30
60*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*
b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*
c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 -
18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5
- 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*
b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*
d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945
728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c
^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 -
9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(3/4))*(-(81*a^8*d^11
+ 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226
*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16
777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3
+ 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 1919313510
40*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^
13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 20
13265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4) - (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^
10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16
*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554
584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 +
153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^
12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12
*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14
- 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 +
40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a
^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268
435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^
19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 2159
22769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11
*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14
- 268435456*a*b^15*c^22*d))^(1/4) + (((891*a^9*b^7*d^15 + 39424*b^16*c^9*d^6 - 33367697*a*b^15*c^8*d^7 - 2516
4*a^8*b^8*c*d^14 - 431110148*a^2*b^14*c^7*d^8 - 666770056*a^3*b^13*c^6*d^9 - 158426308*a^4*b^12*c^5*d^10 + 146
77502*a^5*b^11*c^4*d^11 + 793236*a^6*b^10*c^3*d^12 + 168480*a^7*b^9*c^2*d^13)/(8192*(b^13*c^17 - a^13*c^4*d^13
+ 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^1
2*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*
b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) + (((-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*
a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^
3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^
15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 -
73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*
a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12
*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435
456*a*b^15*c^22*d))^(1/4)*(67108864*a^2*b^22*c^22*d^5 - 16777216*a*b^23*c^23*d^4 + 1168113664*a^3*b^21*c^21*d^
6 - 14120124416*a^4*b^20*c^20*d^7 + 77326188544*a^5*b^19*c^19*d^8 - 270062845952*a^6*b^18*c^18*d^9 + 668999876
608*a^7*b^17*c^17*d^10 - 1234794708992*a^8*b^16*c^16*d^11 + 1740686491648*a^9*b^15*c^15*d^12 - 1892922949632*a
^10*b^14*c^14*d^13 + 1584033431552*a^11*b^13*c^13*d^14 - 1002132471808*a^12*b^12*c^12*d^15 + 457799892992*a^13
*b^11*c^11*d^16 - 132590338048*a^14*b^10*c^10*d^17 + 10729029632*a^15*b^9*c^9*d^18 + 9873391616*a^16*b^8*c^8*d
^19 - 5100273664*a^17*b^7*c^7*d^20 + 1191182336*a^18*b^6*c^6*d^21 - 140509184*a^19*b^5*c^5*d^22 + 6291456*a^20
*b^4*c^4*d^23))/(8192*(b^13*c^17 - a^13*c^4*d^13 + 13*a^12*b*c^5*d^12 + 78*a^2*b^11*c^15*d^2 - 286*a^3*b^10*c^
14*d^3 + 715*a^4*b^9*c^13*d^4 - 1287*a^5*b^8*c^12*d^5 + 1716*a^6*b^7*c^11*d^6 - 1716*a^7*b^6*c^10*d^7 + 1287*a
^8*b^5*c^9*d^8 - 715*a^9*b^4*c^8*d^9 + 286*a^10*b^3*c^7*d^10 - 78*a^11*b^2*c^6*d^11 - 13*a*b^12*c^16*d)) + (x^
(1/2)*(16777216*b^27*c^25*d^4 + 100663296*a*b^26*c^24*d^5 - 1862270976*a^2*b^25*c^23*d^6 + 3970170880*a^3*b^24
*c^22*d^7 + 43464523776*a^4*b^23*c^21*d^8 - 366041628672*a^5*b^22*c^20*d^9 + 1452876496896*a^6*b^21*c^19*d^10
- 3770791231488*a^7*b^20*c^18*d^11 + 7070048845824*a^8*b^19*c^17*d^12 - 10068131053568*a^9*b^18*c^16*d^13 + 11
280643522560*a^10*b^17*c^15*d^14 - 10296755748864*a^11*b^16*c^14*d^15 + 7971285237760*a^12*b^15*c^13*d^16 - 54
29806497792*a^13*b^14*c^12*d^17 + 3274973380608*a^14*b^13*c^11*d^18 - 1671068909568*a^15*b^12*c^10*d^19 + 6544
75001856*a^16*b^11*c^9*d^20 - 162426519552*a^17*b^10*c^8*d^21 + 7226785792*a^18*b^9*c^7*d^22 + 11707613184*a^1
9*b^8*c^6*d^23 - 4677697536*a^20*b^7*c^5*d^24 + 842530816*a^21*b^6*c^4*d^25 - 72351744*a^22*b^5*c^3*d^26 + 235
9296*a^23*b^4*c^2*d^27))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*
a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11
*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*
d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 15
3*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 117
39420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b
^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 201
3265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^1
1*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 -
191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120
*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))
^(3/4))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^
3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(1
6777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 939524
0960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10
*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 13
4351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a
^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4) + (x^(1/2)*(9801*a^10*b^9*d
^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9
+ 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*
b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 -
18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c
^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9
+ 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3
060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 3
5153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4
*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 167772
16*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 3
0534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a
^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d
^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 201326
5920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*
b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*
d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15
*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73
282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^
8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d
^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 26843545
6*a*b^15*c^22*d))^(1/4)*2i