3.5.81 \(\int \frac {\sqrt {x}}{(a+b x^2)^2 (c+d x^2)^3} \, dx\)

Optimal. Leaf size=739 \[ \frac {b^{9/4} (b c-13 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {d x^{3/2} \left (-5 a^2 d^2+21 a b c d+8 b^2 c^2\right )}{16 a c^2 \left (c+d x^2\right ) (b c-a d)^3}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}+\frac {b x^{3/2}}{2 a \left (a+b x^2\right ) \left (c+d x^2\right )^2 (b c-a d)}+\frac {d x^{3/2} (a d+2 b c)}{4 a c \left (c+d x^2\right )^2 (b c-a d)^2} \]

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Rubi [A]  time = 1.16, antiderivative size = 739, normalized size of antiderivative = 1.00, number of steps used = 24, number of rules used = 10, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.417, Rules used = {466, 472, 579, 584, 297, 1162, 617, 204, 1165, 628} \begin {gather*} \frac {d x^{3/2} \left (-5 a^2 d^2+21 a b c d+8 b^2 c^2\right )}{16 a c^2 \left (c+d x^2\right ) (b c-a d)^3}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 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^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 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^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}+\frac {b^{9/4} (b c-13 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {b x^{3/2}}{2 a \left (a+b x^2\right ) \left (c+d x^2\right )^2 (b c-a d)}+\frac {d x^{3/2} (a d+2 b c)}{4 a c \left (c+d x^2\right )^2 (b c-a d)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(d*(2*b*c + a*d)*x^(3/2))/(4*a*c*(b*c - a*d)^2*(c + d*x^2)^2) + (b*x^(3/2))/(2*a*(b*c - a*d)*(a + b*x^2)*(c +
d*x^2)^2) + (d*(8*b^2*c^2 + 21*a*b*c*d - 5*a^2*d^2)*x^(3/2))/(16*a*c^2*(b*c - a*d)^3*(c + d*x^2)) - (b^(9/4)*(
b*c - 13*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (b^(9/4)*(b*c
- 13*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) - (d^(5/4)*(117*b^
2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)
^4) + (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[
2]*c^(9/4)*(b*c - a*d)^4) + (b^(9/4)*(b*c - 13*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]
)/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) - (b^(9/4)*(b*c - 13*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] +
Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] -
Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*d)^4) - (d^(5/4)*(117*b^2*c^2 - 26*
a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*
d)^4)

Rule 204

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

Rule 297

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

Rule 466

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 472

Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> -Simp[(b*(e*x
)^(m + 1)*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*e*n*(b*c - a*d)*(p + 1)), x] + Dist[1/(a*n*(b*c - a*d)*(
p + 1)), Int[(e*x)^m*(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*b*(m + 1) + n*(b*c - a*d)*(p + 1) + d*b*(m + n*(
p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e, m, q}, x] && NeQ[b*c - a*d, 0] && IGtQ[n, 0] && LtQ[p
, -1] && IntBinomialQ[a, b, c, d, e, m, n, p, q, x]

Rule 579

Int[((g_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_)*((e_) + (f_.)*(x_)^(n_)), x
_Symbol] :> -Simp[((b*e - a*f)*(g*x)^(m + 1)*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*g*n*(b*c - a*d)*(p +
1)), x] + Dist[1/(a*n*(b*c - a*d)*(p + 1)), Int[(g*x)^m*(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*(b*e - a*f)*(
m + 1) + e*n*(b*c - a*d)*(p + 1) + d*(b*e - a*f)*(m + n*(p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d,
e, f, g, m, q}, x] && IGtQ[n, 0] && LtQ[p, -1]

Rule 584

Int[(((g_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((e_) + (f_.)*(x_)^(n_)))/((c_) + (d_.)*(x_)^(n_)), x_Sy
mbol] :> Int[ExpandIntegrand[((g*x)^m*(a + b*x^n)^p*(e + f*x^n))/(c + d*x^n), x], x] /; FreeQ[{a, b, c, d, e,
f, g, m, p}, x] && IGtQ[n, 0]

Rule 617

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 628

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 1162

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 1165

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*} \int \frac {\sqrt {x}}{\left (a+b x^2\right )^2 \left (c+d x^2\right )^3} \, dx &=2 \operatorname {Subst}\left (\int \frac {x^2}{\left (a+b x^4\right )^2 \left (c+d x^4\right )^3} \, dx,x,\sqrt {x}\right )\\ &=\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-b c+4 a d-9 b d x^4\right )}{\left (a+b x^4\right ) \left (c+d x^4\right )^3} \, dx,x,\sqrt {x}\right )}{2 a (b c-a d)}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}-\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-4 \left (2 b^2 c^2-16 a b c d+5 a^2 d^2\right )-20 b d (2 b c+a d) x^4\right )}{\left (a+b x^4\right ) \left (c+d x^4\right )^2} \, dx,x,\sqrt {x}\right )}{16 a c (b c-a d)^2}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-4 \left (8 b^3 c^3-96 a b^2 c^2 d+21 a^2 b c d^2-5 a^3 d^3\right )-4 b d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^4\right )}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{64 a c^2 (b c-a d)^3}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \left (-\frac {32 b^3 c^2 (b c-13 a d) x^2}{(b c-a d) \left (a+b x^4\right )}+\frac {4 a d^2 \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right ) x^2}{(-b c+a d) \left (c+d x^4\right )}\right ) \, dx,x,\sqrt {x}\right )}{64 a c^2 (b c-a d)^3}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}+\frac {\left (b^3 (b c-13 a d)\right ) \operatorname {Subst}\left (\int \frac {x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 a (b c-a d)^4}+\frac {\left (d^2 \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{16 c^2 (b c-a d)^4}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}-\frac {\left (b^{5/2} (b c-13 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a (b c-a d)^4}+\frac {\left (b^{5/2} (b c-13 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a (b c-a d)^4}-\frac {\left (d^{3/2} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}-\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^2 (b c-a d)^4}+\frac {\left (d^{3/2} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}+\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^2 (b c-a d)^4}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}+\frac {\left (b^2 (b c-13 a d)\right ) \operatorname {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 a (b c-a d)^4}+\frac {\left (b^2 (b c-13 a d)\right ) \operatorname {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 a (b c-a d)^4}+\frac {\left (b^{9/4} (b c-13 a d)\right ) \operatorname {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^{5/4} (b c-a d)^4}+\frac {\left (b^{9/4} (b c-13 a d)\right ) \operatorname {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^{5/4} (b c-a d)^4}+\frac {\left (d \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^2 (b c-a d)^4}+\frac {\left (d \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^2 (b c-a d)^4}+\frac {\left (d^{5/4} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^{9/4} (b c-a d)^4}+\frac {\left (d^{5/4} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^{9/4} (b c-a d)^4}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}+\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}+\frac {\left (b^{9/4} (b c-13 a d)\right ) \operatorname {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^{5/4} (b c-a d)^4}-\frac {\left (b^{9/4} (b c-13 a d)\right ) \operatorname {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^{5/4} (b c-a d)^4}+\frac {\left (d^{5/4} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^{9/4} (b c-a d)^4}-\frac {\left (d^{5/4} \left (117 b^2 c^2-26 a b c d+5 a^2 d^2\right )\right ) \operatorname {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^{9/4} (b c-a d)^4}\\ &=\frac {d (2 b c+a d) x^{3/2}}{4 a c (b c-a d)^2 \left (c+d x^2\right )^2}+\frac {b x^{3/2}}{2 a (b c-a d) \left (a+b x^2\right ) \left (c+d x^2\right )^2}+\frac {d \left (8 b^2 c^2+21 a b c d-5 a^2 d^2\right ) x^{3/2}}{16 a c^2 (b c-a d)^3 \left (c+d x^2\right )}-\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {b^{9/4} (b c-13 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}+\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}+\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (b c-13 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}-\frac {d^{5/4} \left (117 b^2 c^2-26 a b c d+5 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^{9/4} (b c-a d)^4}\\ \end {align*}

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Mathematica [A]  time = 6.28, size = 760, normalized size = 1.03 \begin {gather*} -\frac {b^{9/4} (13 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^{5/4} (b c-a d)^4}+\frac {b^{9/4} (13 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^{5/4} (b c-a d)^4}-\frac {b^{9/4} (13 a d-b c) \tan ^{-1}\left (\frac {2 \sqrt [4]{b} \sqrt {x}-\sqrt {2} \sqrt [4]{a}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}-\frac {b^{9/4} (13 a d-b c) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a}+2 \sqrt [4]{b} \sqrt {x}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{5/4} (b c-a d)^4}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 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^{9/4} (a d-b c)^4}-\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 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^{9/4} (a d-b c)^4}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (\frac {2 \sqrt [4]{d} \sqrt {x}-\sqrt {2} \sqrt [4]{c}}{\sqrt {2} \sqrt [4]{c}}\right )}{32 \sqrt {2} c^{9/4} (a d-b c)^4}+\frac {d^{5/4} \left (5 a^2 d^2-26 a b c d+117 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c}+2 \sqrt [4]{d} \sqrt {x}}{\sqrt {2} \sqrt [4]{c}}\right )}{32 \sqrt {2} c^{9/4} (a d-b c)^4}-\frac {b^3 x^{3/2}}{2 a \left (a+b x^2\right ) (a d-b c)^3}+\frac {d^2 x^{3/2} (21 b c-5 a d)}{16 c^2 \left (c+d x^2\right ) (b c-a d)^3}+\frac {d^2 x^{3/2}}{4 c \left (c+d x^2\right )^2 (b c-a d)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/2*(b^3*x^(3/2))/(a*(-(b*c) + a*d)^3*(a + b*x^2)) + (d^2*x^(3/2))/(4*c*(b*c - a*d)^2*(c + d*x^2)^2) + (d^2*(
21*b*c - 5*a*d)*x^(3/2))/(16*c^2*(b*c - a*d)^3*(c + d*x^2)) - (b^(9/4)*(-(b*c) + 13*a*d)*ArcTan[(-(Sqrt[2]*a^(
1/4)) + 2*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) - (b^(9/4)*(-(b*c) + 13*a*d)*
ArcTan[(Sqrt[2]*a^(1/4) + 2*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (d^(5/4)*
(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[(-(Sqrt[2]*c^(1/4)) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(32
*Sqrt[2]*c^(9/4)*(-(b*c) + a*d)^4) + (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[(Sqrt[2]*c^(1/4) +
2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(32*Sqrt[2]*c^(9/4)*(-(b*c) + a*d)^4) - (b^(9/4)*(-(b*c) + 13*a*d)*Log
[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (b^(9/4)*(-(b*c)
+ 13*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (d^(
5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sq
rt[2]*c^(9/4)*(-(b*c) + a*d)^4) - (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4
)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(-(b*c) + a*d)^4)

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IntegrateAlgebraic [A]  time = 2.59, size = 510, normalized size = 0.69 \begin {gather*} \frac {\left (13 a b^{9/4} d-b^{13/4} c\right ) \tan ^{-1}\left (\frac {\sqrt {a}-\sqrt {b} x}{\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}\right )}{4 \sqrt {2} a^{5/4} (a d-b c)^4}+\frac {\left (13 a b^{9/4} d-b^{13/4} c\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}{\sqrt {a}+\sqrt {b} x}\right )}{4 \sqrt {2} a^{5/4} (a d-b c)^4}-\frac {\left (5 a^2 d^{13/4}-26 a b c d^{9/4}+117 b^2 c^2 d^{5/4}\right ) \tan ^{-1}\left (\frac {\sqrt {c}-\sqrt {d} x}{\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}}\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}-\frac {\left (5 a^2 d^{13/4}-26 a b c d^{9/4}+117 b^2 c^2 d^{5/4}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}}{\sqrt {c}+\sqrt {d} x}\right )}{32 \sqrt {2} c^{9/4} (b c-a d)^4}+\frac {x^{3/2} \left (9 a^3 c d^3+5 a^3 d^4 x^2-25 a^2 b c^2 d^2-12 a^2 b c d^3 x^2+5 a^2 b d^4 x^4-25 a b^2 c^2 d^2 x^2-21 a b^2 c d^3 x^4-8 b^3 c^4-16 b^3 c^3 d x^2-8 b^3 c^2 d^2 x^4\right )}{16 a c^2 \left (a+b x^2\right ) \left (c+d x^2\right )^2 (a d-b c)^3} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(x^(3/2)*(-8*b^3*c^4 - 25*a^2*b*c^2*d^2 + 9*a^3*c*d^3 - 16*b^3*c^3*d*x^2 - 25*a*b^2*c^2*d^2*x^2 - 12*a^2*b*c*d
^3*x^2 + 5*a^3*d^4*x^2 - 8*b^3*c^2*d^2*x^4 - 21*a*b^2*c*d^3*x^4 + 5*a^2*b*d^4*x^4))/(16*a*c^2*(-(b*c) + a*d)^3
*(a + b*x^2)*(c + d*x^2)^2) + ((-(b^(13/4)*c) + 13*a*b^(9/4)*d)*ArcTan[(Sqrt[a] - Sqrt[b]*x)/(Sqrt[2]*a^(1/4)*
b^(1/4)*Sqrt[x])])/(4*Sqrt[2]*a^(5/4)*(-(b*c) + a*d)^4) - ((117*b^2*c^2*d^(5/4) - 26*a*b*c*d^(9/4) + 5*a^2*d^(
13/4))*ArcTan[(Sqrt[c] - Sqrt[d]*x)/(Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x])])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^4) + (
(-(b^(13/4)*c) + 13*a*b^(9/4)*d)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*
a^(5/4)*(-(b*c) + a*d)^4) - ((117*b^2*c^2*d^(5/4) - 26*a*b*c*d^(9/4) + 5*a^2*d^(13/4))*ArcTanh[(Sqrt[2]*c^(1/4
)*d^(1/4)*Sqrt[x])/(Sqrt[c] + Sqrt[d]*x)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^4)

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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 2.59, size = 1233, normalized size = 1.67

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="giac")

[Out]

1/2*b^3*x^(3/2)/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(b*x^2 + a)) + 1/4*((a*b^3)^(3/4)*b*c
- 13*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^
4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 1/4*((a*b
^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt
(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^
4) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*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^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^
2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4
)*a*b*c*d + 5*(c*d^3)^(3/4)*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^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3
*d^5) - 1/8*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(
2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4
) + 1/8*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*
a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) -
1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/
d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)
*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)
^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2
+ 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/16*(21*b*c*d^3*x^(7/2) - 5*a
*d^4*x^(7/2) + 25*b*c^2*d^2*x^(3/2) - 9*a*c*d^3*x^(3/2))/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2
*d^3)*(d*x^2 + c)^2)

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maple [A]  time = 0.03, size = 1100, normalized size = 1.49

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x)

[Out]

-1/2*b^3/(a*d-b*c)^4*x^(3/2)/(b*x^2+a)*d+1/2*b^4/(a*d-b*c)^4/a*x^(3/2)/(b*x^2+a)*c-13/8*b^2/(a*d-b*c)^4/(a/b)^
(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*d+1/8*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)
/(a/b)^(1/4)*x^(1/2)-1)*c-13/16*b^2/(a*d-b*c)^4/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1
/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*d+1/16*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/
4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2)))*c-13/8*b^2/(a*d-b*c)^4/(a/b)^(1/4
)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+1/8*b^3/(a*d-b*c)^4/a/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/
b)^(1/4)*x^(1/2)+1)*c+5/16*d^5/(a*d-b*c)^4/(d*x^2+c)^2/c^2*x^(7/2)*a^2-13/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(7
/2)*a*b+21/16*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^(7/2)*b^2+9/16*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^(3/2)*a^2-17/8*d^3/
(a*d-b*c)^4/(d*x^2+c)^2*x^(3/2)*a*b+25/16*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x^(3/2)*b^2+5/64*d^3/(a*d-b*c)^4/c^2/(
c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a^2-13/32*d^2/(a*d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arcta
n(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*a*b+117/64*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/
2)+1)*b^2+5/64*d^3/(a*d-b*c)^4/c^2/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a^2-13/32*d^2/(a*
d-b*c)^4/c/(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a*b+117/64*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1
/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b^2+5/128*d^3/(a*d-b*c)^4/c^2/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*
2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a^2-13/64*d^2/(a*d-b*c)^4/c/(c/d)^(1
/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))*a*b+11
7/128*d/(a*d-b*c)^4/(c/d)^(1/4)*2^(1/2)*ln((x-(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*
x^(1/2)+(c/d)^(1/2)))*b^2

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maxima [A]  time = 2.88, size = 845, normalized size = 1.14 \begin {gather*} \frac {{\left (b^{4} c - 13 \, a b^{3} d\right )} {\left (\frac {2 \, \sqrt {2} \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 {\sqrt {a} \sqrt {b}} \sqrt {b}} + \frac {2 \, \sqrt {2} \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 {\sqrt {a} \sqrt {b}} \sqrt {b}} - \frac {\sqrt {2} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}}\right )}}{16 \, {\left (a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}\right )}} + \frac {{\left (117 \, b^{2} c^{2} d^{2} - 26 \, a b c d^{3} + 5 \, a^{2} d^{4}\right )} {\left (\frac {2 \, \sqrt {2} \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 {\sqrt {c} \sqrt {d}} \sqrt {d}} + \frac {2 \, \sqrt {2} \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 {\sqrt {c} \sqrt {d}} \sqrt {d}} - \frac {\sqrt {2} \log \left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}}\right )}}{128 \, {\left (b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right )}} + \frac {{\left (8 \, b^{3} c^{2} d^{2} + 21 \, a b^{2} c d^{3} - 5 \, a^{2} b d^{4}\right )} x^{\frac {11}{2}} + {\left (16 \, b^{3} c^{3} d + 25 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right )} x^{\frac {7}{2}} + {\left (8 \, b^{3} c^{4} + 25 \, a^{2} b c^{2} d^{2} - 9 \, a^{3} c d^{3}\right )} x^{\frac {3}{2}}}{16 \, {\left (a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left (a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right )} x^{6} + {\left (2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right )} x^{4} + {\left (a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right )} x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm="maxima")

[Out]

1/16*(b^4*c - 13*a*b^3*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqr
t(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sq
rt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sq
rt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sq
rt(a))/(a^(1/4)*b^(3/4)))/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4) + 1/128*
(117*b^2*c^2*d^2 - 26*a*b*c*d^3 + 5*a^2*d^4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d
)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(
1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)
*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(
x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 +
a^4*c^2*d^4) + 1/16*((8*b^3*c^2*d^2 + 21*a*b^2*c*d^3 - 5*a^2*b*d^4)*x^(11/2) + (16*b^3*c^3*d + 25*a*b^2*c^2*d^
2 + 12*a^2*b*c*d^3 - 5*a^3*d^4)*x^(7/2) + (8*b^3*c^4 + 25*a^2*b*c^2*d^2 - 9*a^3*c*d^3)*x^(3/2))/(a^2*b^3*c^7 -
3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^
4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 +
(a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2)

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mupad [B]  time = 9.58, size = 45858, normalized size = 62.05

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(1/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)

[Out]

((x^(7/2)*(16*b^3*c^3*d - 5*a^3*d^4 + 25*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3))/(16*a*c*(b^3*c^4 - a^3*c*d^3 + 3*a^2
*b*c^2*d^2 - 3*a*b^2*c^3*d)) - (x^(3/2)*(8*b^3*c^3 - 9*a^3*d^3 + 25*a^2*b*c*d^2))/(16*a*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^2*x^(11/2)*(8*b^2*c^2 - 5*a^2*d^2 + 21*a*b*c*d))/(16*a*c*(b^3*c^4 - a^
3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/(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) - atan(((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 2958
0408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^
7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^
23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351
945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^
7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12
- 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8
*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8
+ 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216
*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a
^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*
d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 13435194
5728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^
3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*((32*b^30*c^27*d^4 - 1728*a*b^29
*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c
^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^1
1)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^1
4)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^
17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d
^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)
/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327
093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)/(a^2*b^21*c^27 - a^23*c^
6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b
^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13
*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*
b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*
b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) - (x^(1/2)*(-(625*a^
8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8
+ 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(1677721
6*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*
a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19
*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 1343519
45728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b
^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704
643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b
^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^
20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^
17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c
^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*
c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d
^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 17301504
0*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d -
18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c
^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d
^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13
+ 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*1i - (x^(1/2)*(105625*a^11*b^10*d
^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^
10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*
a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i
)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 81
6*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^
11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c
^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^1
5 + 153*a^18*b^2*c^8*d^16))) - (-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^
2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2
*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 20
13265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^
11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 -
191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 3053453312
0*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d
))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580
408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7
*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^2
3*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 1343519
45728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7
*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12
- 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*((32*b^30*c^
27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7
+ 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (11167882
83*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (253018712
7*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (80023416
93*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521
847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515
*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8
*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)/(a^2
*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c
^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^
7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16
*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^1
2*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19)
+ (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 2958
0408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^
7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^
23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351
945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^
7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12
- 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a
*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7
+ 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 182786
39468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 7823827
5600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 808770
25492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584
022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 6724685
66016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6
*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 -
18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d
^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 4
8620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568
*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*1i + (x^(1/2)
*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 412994
7458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^
6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a
^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^
4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^1
8*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^1
0 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 -
816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))))/(((1373125*a^10*b^12*d^19)/262144 + (200201625*b^22*c^10*d^9
)/262144 - (3974669595*a*b^21*c^9*d^10)/131072 - (28032875*a^9*b^13*c*d^18)/131072 + (107080445745*a^2*b^20*c^
8*d^11)/262144 - (64244120525*a^3*b^19*c^7*d^12)/32768 + (171099678425*a^4*b^18*c^6*d^13)/131072 - (3535361602
5*a^5*b^17*c^5*d^14)/65536 + (18119512885*a^6*b^16*c^4*d^15)/131072 - (820327045*a^7*b^15*c^3*d^16)/32768 + (7
56189525*a^8*b^14*c^2*d^17)/262144)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 +
210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8
*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^1
2*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280
*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^2
0*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 +
87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159
900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^1
0*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 7328287
9488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8
*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 +
30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*
b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*
d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11
- 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a
^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^
5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351
040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4
*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*(
(32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^2
7*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16
- (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 +
(2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2
+ (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4
- (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8
+ (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (51191
01*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^2
9)/16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330
*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b
^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^1
3*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a
^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2
*c^8*d^19) - (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6
*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11
- 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*
a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d
^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 19193135
1040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^
4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*
(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^2
5*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^
10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^1
3 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^
16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d
^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^2
2 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 23608688
64*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*
c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*
b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c
^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*
d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))) -
(x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18
- 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5
*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27
361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 1
53*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^1
2*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^1
4*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^
14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))) + (-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*
b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*
c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435
456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21
*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922
769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b
^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14
- 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 8755484
4*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6
*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15
+ 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^
5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d
^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 305345
33120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^
24*d))^(3/4)*((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 -
459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*
c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c
^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18
*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^1
5*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^1
2*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^2
5)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^
25*b^5*c^2*d^29)/16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c
^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6
- 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^1
0 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*
d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18
- 210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 875548
44*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^
6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15
+ 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a
^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*
d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534
533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c
^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105
746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^
7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10
*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^1
3*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^
16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^1
9*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d
^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^1
8*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d
^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 437
58*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*
a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*
c^8*d^16))) + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^1
0*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 +
3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13
*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*
b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 +
18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 4375
8*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^
16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))))*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5
- 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 12
64120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9
*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120
*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^1
8*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 7328
2879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*
b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*2i + 2*atan(((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 1665677
52*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5
*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 2
68435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12
*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 2
15922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a
^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*
d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87
554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 15990
0*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*
d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 732828794
88*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c
^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 3
0534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^
15*c^24*d))^(3/4)*(((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*
d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6
*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*
b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^1
2*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^
15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^
18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c
^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3
825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*
a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15
*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^1
1*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16
*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3
*c^9*d^18 - 210*a^21*b^2*c^8*d^19) - (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^
6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 +
159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b
*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 732
82879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8
*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^
11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 26843545
6*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^
6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 765666
3678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 570988093
76768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551
680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 3657494
1151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512
515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22
*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(6553
6*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b
^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17
*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^1
1 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153
*a^18*b^2*c^8*d^16))) - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2
213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c
^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 17210908
0*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d
- 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*
c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*
d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13
+ 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))) - (-(625*a^8*d^13 + 187388721*b^
8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^
4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 1677721
6*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 3
0534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a
^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d
^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 201326
5920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752
*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b
^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268
435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c
^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215
922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^1
1*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^
14 - 268435456*a*b^15*c^24*d))^(3/4)*(((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 3
8304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/
16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8
- (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/
2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)
/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21
)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (
30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b
^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^2
2*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d
^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^
9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14
*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d
^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166
567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120
*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16
- 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*
b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7
+ 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 732828794
88*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c
^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 118279372
80*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^2
3*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^
19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c
^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*
c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*
c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24
- 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b
^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c
^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 -
31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 3182
4*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17
*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))) + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*
a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 18
91277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*
c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 -
18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d
^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 4
8620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568
*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))))/((-(625*a^8*
d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 +
7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*
b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^
3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d
^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945
728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3
*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*
c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*
d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*
a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 305
34533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7
*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^1
0 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 20132659
20*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*(((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26
*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*
a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^
8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^
11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a
^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*
a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b
^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27
)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b
^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20
349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 29393
0*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 2
03490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5
985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) - (x^(1/2)*(-(625*a^8*d^13 + 18738872
1*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^
4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 167
77216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3
+ 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 1919313510
40*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^
15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 20
13265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c
^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 25
13987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 3539496
9403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 9206844
9878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 594489
46065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 76925
75834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 13727249203
2*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^
27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^
17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a
^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b
^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c
^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*1i - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21
*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*
a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14
+ 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^1
8*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d
^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 437
58*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*
a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*
c^8*d^16))) - ((1373125*a^10*b^12*d^19)/262144 + (200201625*b^22*c^10*d^9)/262144 - (3974669595*a*b^21*c^9*d^1
0)/131072 - (28032875*a^9*b^13*c*d^18)/131072 + (107080445745*a^2*b^20*c^8*d^11)/262144 - (64244120525*a^3*b^1
9*c^7*d^12)/32768 + (171099678425*a^4*b^18*c^6*d^13)/131072 - (35353616025*a^5*b^17*c^5*d^14)/65536 + (1811951
2885*a^6*b^16*c^4*d^15)/131072 - (820327045*a^7*b^15*c^3*d^16)/32768 + (756189525*a^8*b^14*c^2*d^17)/262144)/(
a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^1
8*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20
*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c
^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*
c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^1
9) + (-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a
^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*
d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2
- 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728
*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16
*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 939
5240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13
+ 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255
846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*
c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^1
3*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 -
191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a
^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12
*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*(((32*b^30*c^27*d^4 - 1728*a*b^29*c^26
*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d
^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8
+ (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16
+ (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8
- (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/
4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 -
(18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a
^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^23*c^6
*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^
17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*
c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b
^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b
^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(625*a^8
*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8
+ 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216
*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a
^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*
d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 13435194
5728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^
3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 7046
43072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^
24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^2
0*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^1
7*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^
14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c
^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^
23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040
*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d -
18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^
19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^
9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 +
3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*1i + (x^(1/2)*(105625*a^11*b^10*d^
19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^1
0 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a
^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)
/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816
*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^1
1*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^
13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15
+ 153*a^18*b^2*c^8*d^16)))))*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2
*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*
c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 201
3265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^1
1*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 -
191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120
*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d)
)^(1/4) - atan(((((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^
6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b
^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^
21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*
b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15
*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18
*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6
*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (382
5*a^25*b^5*c^2*d^29)/16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^
19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*
d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17
*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c
^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d
^18 - 210*a^21*b^2*c^8*d^19) - (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*
c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14
*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^1
0*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15
*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^
19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 118279
37280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*
b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20
*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^1
7*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^
14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^
11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d
^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^2
5*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^1
6*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6
- 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 3
1824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a
^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b
^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*
c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11
*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*
a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 49152
0*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(3/4)*1i - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8
+ 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c
^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 7699491
54*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a
^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*
a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^
10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c
^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))
)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*
d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 745
4720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7
+ 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*
d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15)
)^(1/4) - (((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 45
9264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^
21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^1
8*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c
^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*
c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*
c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)
/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25
*b^5*c^2*d^29)/16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^2
5*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 -
116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10
- 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^
14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 -
210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^
2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 -
2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10
*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c
^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2
*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*
a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c
^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*
d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16
*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^1
3*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^1
0*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 -
21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*
c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22
*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 318
24*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a
^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^
3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^
2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d
^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*
c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b
^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19
*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(3/4)*1i + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 1414
42353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^1
1 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7
*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^
6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^
14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^1
6*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^
12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b
^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 +
4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a
^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 527
15520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 +
7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4
))/(((1373125*a^10*b^12*d^19)/262144 + (200201625*b^22*c^10*d^9)/262144 - (3974669595*a*b^21*c^9*d^10)/131072
- (28032875*a^9*b^13*c*d^18)/131072 + (107080445745*a^2*b^20*c^8*d^11)/262144 - (64244120525*a^3*b^19*c^7*d^12
)/32768 + (171099678425*a^4*b^18*c^6*d^13)/131072 - (35353616025*a^5*b^17*c^5*d^14)/65536 + (18119512885*a^6*b
^16*c^4*d^15)/131072 - (820327045*a^7*b^15*c^3*d^16)/32768 + (756189525*a^8*b^14*c^2*d^17)/262144)/(a^2*b^21*c
^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3
+ 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203
490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 +
293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15
+ 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (((32
*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c
^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (
1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2
530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (
8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 -
(2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (
69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*
a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/
16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^
5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14
*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b
^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17
*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^
8*d^19) - (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c
^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^
13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240
*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891
328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 655
36*a^20*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d
^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 76566
63678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809
376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 9325555
1680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 365749
41151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 255751
2515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^2
2*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(655
36*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*
b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^1
7*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^
11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 15
3*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^
12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^
8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 4685
8240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 1
7891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 -
65536*a^20*b*c*d^15))^(3/4) - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*
d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4
*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 1
72109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*
c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^
7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^
9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^
11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b
^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 -
65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17
891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^
8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4
*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4) + (((32*b^30*c^27*d
^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 33
69600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a
^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^
10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a
^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*
a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^1
9*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5
*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)/(a^2*b^2
1*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*
d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 +
203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^1
1 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^
15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (x
^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*
a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3
+ 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^
9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5
*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*
d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 1071057
46944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7
*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*
b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13
*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^1
6*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19
*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^
25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18
*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^
3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 4375
8*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a
^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c
^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4
096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*
d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^
9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16
*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*
b*c*d^15))^(3/4) + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 221325
0*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^
12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8
*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*
a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*
d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 +
43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 30
60*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 878
8*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b
^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*
b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240
*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293
760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)))*(-(b^13*c^4 + 28561*a^4*b^9*d
^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 655
36*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 178913
28*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 -
46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^1
2 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)*2i + 2*atan((((((32*b^3
0*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*
d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116
788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (25301
87127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002
341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (207
9521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (6918
1515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22
*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*
1i)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^
5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14
*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b
^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17
*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^
8*d^19) - (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c
^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^
13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240
*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891
328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 655
36*a^20*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d
^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 76566
63678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809
376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 9325555
1680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 365749
41151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 255751
2515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^2
2*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(655
36*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*
b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^1
7*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^
11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 15
3*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^
12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^
8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 4685
8240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 1
7891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 -
65536*a^20*b*c*d^15))^(3/4) - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*
d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4
*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 1
72109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*
c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^
7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^
9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^
11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b
^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 -
65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17
891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^
8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4
*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4) - ((((32*b^30*c^27*
d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3
369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*
a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a
^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*
a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847
*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^
19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^
5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^
2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*
c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d
^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^1
6*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^
12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19)
+ (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(
4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13
*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b
^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^1
6*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20
*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 10
7105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 765666367897
6*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*
a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512
*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 3657494115123
2*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584
*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c
^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2
*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^
21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 +
43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18
564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*
b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*
d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*
c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^
12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328
*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*
a^20*b*c*d^15))^(3/4) + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2
213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c
^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 17210908
0*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d
- 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*
c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*
d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13
+ 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4
- 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*
a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*
a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 468
58240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 -
2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4))/(((((32*b^30*c^27*d^4 - 1
728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*
a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^2
3*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^2
0*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^
17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b
^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11
*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)
/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*
c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^
3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 20
3490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11
+ 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15
+ 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) - (x^(
1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^
21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 +
7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*
d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c
^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^
15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746
944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b
^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^
19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b
^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*
b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b
^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25
+ 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c
^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3
+ 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*
a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^1
4*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8
*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(409
6*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^
3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*
c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b
^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*
c*d^15))^(3/4)*1i - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 22132
50*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d
^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^
8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d -
18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c
^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d
^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13
+ 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 -
8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a
^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a
^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 4685
8240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 -
2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4) - ((1373125*a^10*b^12*d^19)
/262144 + (200201625*b^22*c^10*d^9)/262144 - (3974669595*a*b^21*c^9*d^10)/131072 - (28032875*a^9*b^13*c*d^18)/
131072 + (107080445745*a^2*b^20*c^8*d^11)/262144 - (64244120525*a^3*b^19*c^7*d^12)/32768 + (171099678425*a^4*b
^18*c^6*d^13)/131072 - (35353616025*a^5*b^17*c^5*d^14)/65536 + (18119512885*a^6*b^16*c^4*d^15)/131072 - (82032
7045*a^7*b^15*c^3*d^16)/32768 + (756189525*a^8*b^14*c^2*d^17)/262144)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*
b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 2
0349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 2939
30*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 -
203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 -
5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + ((((32*b^30*c^27*d^4 - 1728*a*b^29
*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c
^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^1
1)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^1
4)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^
17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d
^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)
/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327
093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^2
3*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a
^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*
b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a
^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a
^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(b^
13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 +
4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^
9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 5271
5520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 +
7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)
*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^
25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d
^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^
13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d
^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*
d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^
22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868
864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20
*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6
*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*
c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12
*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(
-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^1
6 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 745472
0*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 +
52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^1
1 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(
3/4)*1i + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^
11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396
941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3
*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b
*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 +
18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758
*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^1
6*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*
b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^
15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c
^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*
b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^
18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8
788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6
*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^1
0*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 468582
40*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 22
93760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**(1/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)

[Out]

Timed out

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