3.494 \(\int \frac {1}{x^{5/2} (a+b x^2)^2 (c+d x^2)^2} \, dx\)

Optimal. Leaf size=676 \[ \frac {b^{11/4} (7 b c-15 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {-7 a^2 d^2+8 a b c d-7 b^2 c^2}{6 a^2 c^2 x^{3/2} (b c-a d)^2}+\frac {d^{11/4} (15 b c-7 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {b}{2 a x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right ) (b c-a d)}+\frac {d (a d+b c)}{2 a c x^{3/2} \left (c+d x^2\right ) (b c-a d)^2} \]

[Out]

1/6*(-7*a^2*d^2+8*a*b*c*d-7*b^2*c^2)/a^2/c^2/(-a*d+b*c)^2/x^(3/2)+1/2*d*(a*d+b*c)/a/c/(-a*d+b*c)^2/x^(3/2)/(d*
x^2+c)+1/2*b/a/(-a*d+b*c)/x^(3/2)/(b*x^2+a)/(d*x^2+c)+1/8*b^(11/4)*(-15*a*d+7*b*c)*arctan(1-b^(1/4)*2^(1/2)*x^
(1/2)/a^(1/4))/a^(11/4)/(-a*d+b*c)^3*2^(1/2)-1/8*b^(11/4)*(-15*a*d+7*b*c)*arctan(1+b^(1/4)*2^(1/2)*x^(1/2)/a^(
1/4))/a^(11/4)/(-a*d+b*c)^3*2^(1/2)+1/8*d^(11/4)*(-7*a*d+15*b*c)*arctan(1-d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(
11/4)/(-a*d+b*c)^3*2^(1/2)-1/8*d^(11/4)*(-7*a*d+15*b*c)*arctan(1+d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(11/4)/(-a
*d+b*c)^3*2^(1/2)+1/16*b^(11/4)*(-15*a*d+7*b*c)*ln(a^(1/2)+x*b^(1/2)-a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(11/4)
/(-a*d+b*c)^3*2^(1/2)-1/16*b^(11/4)*(-15*a*d+7*b*c)*ln(a^(1/2)+x*b^(1/2)+a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(1
1/4)/(-a*d+b*c)^3*2^(1/2)+1/16*d^(11/4)*(-7*a*d+15*b*c)*ln(c^(1/2)+x*d^(1/2)-c^(1/4)*d^(1/4)*2^(1/2)*x^(1/2))/
c^(11/4)/(-a*d+b*c)^3*2^(1/2)-1/16*d^(11/4)*(-7*a*d+15*b*c)*ln(c^(1/2)+x*d^(1/2)+c^(1/4)*d^(1/4)*2^(1/2)*x^(1/
2))/c^(11/4)/(-a*d+b*c)^3*2^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 0.97, antiderivative size = 676, normalized size of antiderivative = 1.00, number of steps used = 23, number of rules used = 11, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.458, Rules used = {466, 472, 579, 583, 522, 211, 1165, 628, 1162, 617, 204} \[ -\frac {7 a^2 d^2-8 a b c d+7 b^2 c^2}{6 a^2 c^2 x^{3/2} (b c-a d)^2}+\frac {b^{11/4} (7 b c-15 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {b}{2 a x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right ) (b c-a d)}+\frac {d (a d+b c)}{2 a c x^{3/2} \left (c+d x^2\right ) (b c-a d)^2} \]

Antiderivative was successfully verified.

[In]

Int[1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]

[Out]

-(7*b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2)/(6*a^2*c^2*(b*c - a*d)^2*x^(3/2)) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*
x^(3/2)*(c + d*x^2)) + b/(2*a*(b*c - a*d)*x^(3/2)*(a + b*x^2)*(c + d*x^2)) + (b^(11/4)*(7*b*c - 15*a*d)*ArcTan
[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) - (b^(11/4)*(7*b*c - 15*a*d)*ArcTa
n[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (d^(11/4)*(15*b*c - 7*a*d)*ArcT
an[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (d^(11/4)*(15*b*c - 7*a*d)*Arc
Tan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) + (b^(11/4)*(7*b*c - 15*a*d)*Lo
g[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) - (b^(11/4)*(7*b*
c - 15*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (
d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(b*c
- a*d)^3) - (d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]
*c^(11/4)*(b*c - a*d)^3)

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 211

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

Rule 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 522

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

Rule 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 583

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

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 {1}{x^{5/2} \left (a+b x^2\right )^2 \left (c+d x^2\right )^2} \, dx &=2 \operatorname {Subst}\left (\int \frac {1}{x^4 \left (a+b x^4\right )^2 \left (c+d x^4\right )^2} \, dx,x,\sqrt {x}\right )\\ &=\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {-7 b c+4 a d-11 b d x^4}{x^4 \left (a+b x^4\right ) \left (c+d x^4\right )^2} \, dx,x,\sqrt {x}\right )}{2 a (b c-a d)}\\ &=\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {-4 \left (7 b^2 c^2-8 a b c d+7 a^2 d^2\right )-28 b d (b c+a d) x^4}{x^4 \left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{8 a c (b c-a d)^2}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {-12 (b c+a d) \left (7 b^2 c^2-15 a b c d+7 a^2 d^2\right )-12 b d \left (7 b^2 c^2-8 a b c d+7 a^2 d^2\right ) x^4}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{24 a^2 c^2 (b c-a d)^2}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\left (b^3 (7 b c-15 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 a^2 (b c-a d)^3}-\frac {\left (d^3 (15 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{c+d x^4} \, dx,x,\sqrt {x}\right )}{2 c^2 (b c-a d)^3}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\left (b^3 (7 b c-15 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^{5/2} (b c-a d)^3}-\frac {\left (b^3 (7 b c-15 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^{5/2} (b c-a d)^3}-\frac {\left (d^3 (15 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}-\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{4 c^{5/2} (b c-a d)^3}-\frac {\left (d^3 (15 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}+\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{4 c^{5/2} (b c-a d)^3}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\left (b^{5/2} (7 b c-15 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^{5/2} (b c-a d)^3}-\frac {\left (b^{5/2} (7 b c-15 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^{5/2} (b c-a d)^3}+\frac {\left (b^{11/4} (7 b c-15 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^{11/4} (b c-a d)^3}+\frac {\left (b^{11/4} (7 b c-15 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^{11/4} (b c-a d)^3}-\frac {\left (d^{5/2} (15 b c-7 a d)\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 )}{8 c^{5/2} (b c-a d)^3}-\frac {\left (d^{5/2} (15 b c-7 a d)\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 )}{8 c^{5/2} (b c-a d)^3}+\frac {\left (d^{11/4} (15 b c-7 a d)\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 )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {\left (d^{11/4} (15 b c-7 a d)\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 )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {\left (b^{11/4} (7 b c-15 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^{11/4} (b c-a d)^3}+\frac {\left (b^{11/4} (7 b c-15 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^{11/4} (b c-a d)^3}-\frac {\left (d^{11/4} (15 b c-7 a d)\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 )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {\left (d^{11/4} (15 b c-7 a d)\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 )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}\\ &=-\frac {7 b^2 c^2-8 a b c d+7 a^2 d^2}{6 a^2 c^2 (b c-a d)^2 x^{3/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{3/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{3/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (b c-a d)^3}+\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^{11/4} (7 b c-15 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}-\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (b c-a d)^3}\\ \end {align*}

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Mathematica [A]  time = 6.16, size = 676, normalized size = 1.00 \[ -\frac {b^{11/4} (15 a d-7 b c) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {b^{11/4} (15 a d-7 b c) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {b^{11/4} (15 a d-7 b c) \tan ^{-1}\left (\frac {2 \sqrt [4]{b} \sqrt {x}-\sqrt {2} \sqrt [4]{a}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}+\frac {b^{11/4} (15 a d-7 b c) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a}+2 \sqrt [4]{b} \sqrt {x}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4} (b c-a d)^3}-\frac {b^3 \sqrt {x}}{2 a^2 \left (a+b x^2\right ) (a d-b c)^2}-\frac {2}{3 a^2 c^2 x^{3/2}}-\frac {d^{11/4} (15 b c-7 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (a d-b c)^3}+\frac {d^{11/4} (15 b c-7 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{11/4} (a d-b c)^3}+\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (\frac {2 \sqrt [4]{d} \sqrt {x}-\sqrt {2} \sqrt [4]{c}}{\sqrt {2} \sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (a d-b c)^3}+\frac {d^{11/4} (15 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c}+2 \sqrt [4]{d} \sqrt {x}}{\sqrt {2} \sqrt [4]{c}}\right )}{4 \sqrt {2} c^{11/4} (a d-b c)^3}-\frac {d^3 \sqrt {x}}{2 c^2 \left (c+d x^2\right ) (b c-a d)^2} \]

Antiderivative was successfully verified.

[In]

Integrate[1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]

[Out]

-2/(3*a^2*c^2*x^(3/2)) - (b^3*Sqrt[x])/(2*a^2*(-(b*c) + a*d)^2*(a + b*x^2)) - (d^3*Sqrt[x])/(2*c^2*(b*c - a*d)
^2*(c + d*x^2)) + (b^(11/4)*(-7*b*c + 15*a*d)*ArcTan[(-(Sqrt[2]*a^(1/4)) + 2*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4)
)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (b^(11/4)*(-7*b*c + 15*a*d)*ArcTan[(Sqrt[2]*a^(1/4) + 2*b^(1/4)*Sqrt[
x])/(Sqrt[2]*a^(1/4))])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (d^(11/4)*(15*b*c - 7*a*d)*ArcTan[(-(Sqrt[2]*c^(1
/4)) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(4*Sqrt[2]*c^(11/4)*(-(b*c) + a*d)^3) + (d^(11/4)*(15*b*c - 7*a*
d)*ArcTan[(Sqrt[2]*c^(1/4) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(4*Sqrt[2]*c^(11/4)*(-(b*c) + a*d)^3) - (b
^(11/4)*(-7*b*c + 15*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c
- a*d)^3) + (b^(11/4)*(-7*b*c + 15*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2
]*a^(11/4)*(b*c - a*d)^3) - (d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]
*x])/(8*Sqrt[2]*c^(11/4)*(-(b*c) + a*d)^3) + (d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*
Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(-(b*c) + a*d)^3)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="fricas")

[Out]

Timed out

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giac [A]  time = 2.03, size = 1012, normalized size = 1.50 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="giac")

[Out]

-1/4*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(
a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(7
*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(
1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(15*(c*d
^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(
sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/4*(15*(c*d^3)^(1/
4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2
)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/8*(7*(a*b^3)^(1/4)*b^3*
c - 15*(a*b^3)^(1/4)*a*b^2*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2
)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + 1/8*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b
^2*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqr
t(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/8*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*log(sqrt(2)*sqrt(
x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a
^3*c^3*d^3) + 1/8*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sq
rt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/2*(b^3*
c^2*d*x^(5/2) + a^2*b*d^3*x^(5/2) + b^3*c^3*sqrt(x) + a^3*d^3*sqrt(x))/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2
*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)) - 2/3/(a^2*c^2*x^(3/2))

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maple [A]  time = 0.03, size = 825, normalized size = 1.22 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)

[Out]

-1/2*b^3/a/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*d+1/2*b^4/a^2/(a*d-b*c)^3*x^(1/2)/(b*x^2+a)*c-15/8*b^3/a^2/(a*d-b*c)^
3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*d+7/8*b^4/a^3/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arct
an(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)*c-15/8*b^3/a^2/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^
(1/2)-1)*d+7/8*b^4/a^3/(a*d-b*c)^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)*c-15/16*b^3/a^2/(
a*d-b*c)^3*(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+7/16*b^4/a^3/(a*d-b*c)^3*(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-1/2*d^4/c^2/(a*d-b*c)^3*x^(1/2)/(d*x^2+c)*a+1/2*d^3/c/(a*d-b*c)^3*
x^(1/2)/(d*x^2+c)*b-7/8*d^4/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*a+15/8*d
^3/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)*b-7/16*d^4/c^3/(a*d-b*c)^3*(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+15
/16*d^3/c^2/(a*d-b*c)^3*(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-7/8*d^4/c^3/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*
a+15/8*d^3/c^2/(a*d-b*c)^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)*b-2/3/a^2/c^2/x^(3/2)

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maxima [A]  time = 2.69, size = 761, normalized size = 1.13 \[ -\frac {{\left (\frac {2 \, \sqrt {2} {\left (7 \, b c - 15 \, a d\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {2 \, \sqrt {2} {\left (7 \, b c - 15 \, a d\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {\sqrt {2} {\left (7 \, b c - 15 \, a d\right )} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}} - \frac {\sqrt {2} {\left (7 \, b c - 15 \, a d\right )} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}}\right )} b^{3}}{16 \, {\left (a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right )}} - \frac {4 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2} + {\left (7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 7 \, a^{2} b d^{3}\right )} x^{4} + {\left (7 \, b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right )} x^{2}}{6 \, {\left ({\left (a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right )} x^{\frac {11}{2}} + {\left (a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right )} x^{\frac {7}{2}} + {\left (a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right )} x^{\frac {3}{2}}\right )}} - \frac {\frac {2 \, \sqrt {2} {\left (15 \, b c d^{3} - 7 \, a d^{4}\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} + 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {c} \sqrt {\sqrt {c} \sqrt {d}}} + \frac {2 \, \sqrt {2} {\left (15 \, b c d^{3} - 7 \, a d^{4}\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} - 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {c} \sqrt {\sqrt {c} \sqrt {d}}} + \frac {\sqrt {2} {\left (15 \, b c d^{3} - 7 \, a d^{4}\right )} \log \left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {3}{4}} d^{\frac {1}{4}}} - \frac {\sqrt {2} {\left (15 \, b c d^{3} - 7 \, a d^{4}\right )} \log \left (-\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {3}{4}} d^{\frac {1}{4}}}}{16 \, {\left (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}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="maxima")

[Out]

-1/16*(2*sqrt(2)*(7*b*c - 15*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a
)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(7*b*c - 15*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*
b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(7*b*c - 15*a*d)
*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(7*b*c - 15*a*d)*log(-
sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^3/(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d +
3*a^4*b*c*d^2 - a^5*d^3) - 1/6*(4*a*b^2*c^3 - 8*a^2*b*c^2*d + 4*a^3*c*d^2 + (7*b^3*c^2*d - 8*a*b^2*c*d^2 + 7*
a^2*b*d^3)*x^4 + (7*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2 + 7*a^3*d^3)*x^2)/((a^2*b^3*c^4*d - 2*a^3*b^2*c^3*
d^2 + a^4*b*c^2*d^3)*x^(11/2) + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^(7/2) + (a^3*b^2
*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*x^(3/2)) - 1/16*(2*sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*arctan(1/2*sqrt(2)*(sqrt
(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(1
5*b*c*d^3 - 7*a*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/
(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)
*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d
)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)

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mupad [B]  time = 10.59, size = 44436, normalized size = 65.73 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)

[Out]

atan((((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^
3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*
b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^
5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^1
1))^(1/4)*(((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^
14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*
a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^
18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*
c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6
- 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 857
77845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 -
2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*
d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*
b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 4634639717105
6640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 324
03938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*
d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^1
3*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*
b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*
c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) + x
^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576
128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280
640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 13193331
41676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6
863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d
^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22
*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^
42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 686354622054
4000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 13193
33141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 +
59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 42
2576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^5
7*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 2058
0*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 9
01120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244
032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a
^22*b*c*d^11))^(3/4) + 147517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^
45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*
d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^3
9*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26
*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*
b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a
^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 2610085891072
00*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 2720732828
0576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 36846375731
2*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c
^18*d^37) + x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^
40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*
d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^3
4*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24
*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*
b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^
35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^3
8*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c
^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 6615
0*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 2703
36*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 378470
4*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^
21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*1i - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d
^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11
*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5
+ 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 +
270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^1
2*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11
*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^
7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d
^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^
37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*
d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*
d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28
*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*
a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437
078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22
- 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*
c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^
49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 3038087395409
92*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 370914046771
2*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*
c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*
d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14
570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 5
58859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^
14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*
c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^3
8*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702
080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 882855
7564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 +
2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*
d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27
*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 -
3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a
^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^1
2*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*
b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3
*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(3/4) + 147517440*a^18*b^37*c^47*d^8 - 3841073152*
a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b
^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b
^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^
28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 31711555161702
4*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 3171155516
17024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325
278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70
656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 20
27474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073
152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37) - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a
^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b
^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b
^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^
28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 25027276584140
8*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 1032515594
80832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 87519896
14592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368
*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 506
25*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a
^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^
8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*
c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*1i)/(((-(2401*b^15*
c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12
+ 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 202752
0*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*
a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(((-(2401*
b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23
*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2
027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 202
7520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(1174
40512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*
b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^3
2*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^3
4*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 1606483074613
2480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 396
85869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*
d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*
b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032
320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261
116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 199
31198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936
832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) + x^(1/2)*(102760448*a^
22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^5
4*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d
^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c
^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34
*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 89043033286246
40*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049
201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 +
9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*
d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^1
3*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*
b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*
c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-
(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(409
6*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d
^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7
+ 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(3/4)
+ 147517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 3684637573
12*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 2720732828057
6*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 26100858910
7200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 4361682
21851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115
950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 -
450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^
28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*
d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^3
4 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37) + x^(1/2)*
(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 4969409105
92*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 2469634886348
8*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 16024380191
9488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 2631883
57892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160
243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 +
24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 4
96940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200
*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 -
20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^
2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 -
3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49
152*a^22*b*c*d^11))^(1/4) + ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2
*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c
^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6
*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^1
0 - 49152*a^22*b*c*d^11))^(1/4)*(((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^1
3*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b
^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^
6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^
2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 549789368
32*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^
30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*
a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255
032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 3
2403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^4
3*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^4
4*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746
132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 228
8995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31
+ 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 -
531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a
^59*b^4*c^25*d^38) - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*
b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*
c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^3
1*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a
^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 97114060855
70560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263
049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23
- 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^
35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*
b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*
a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a
^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^2
3*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a
^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*
a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a
^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*
b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(3/4) + 147517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47
382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939
463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 1495900
69231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450
764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 +
115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^
24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^2
8*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*
c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c
^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36
+ 147517440*a^47*b^8*c^18*d^37) - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71
869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989
614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 1032515
59480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250
272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 +
213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^
27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^
30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 -
6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500
*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a
^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^1
6*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b
^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 -
94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49
152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 324403
2*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a
^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*2i + 2*atan((((-(2401*b^15*c^4 + 5062
5*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^
11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8
*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c
^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(147517440*a^18*b^37
*c^47*d^8 - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b
^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120
*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a
^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b
*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6
- 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85
777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 -
2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48
*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39
*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 463463971710
56640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32
403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37
*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^
13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53
*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7
*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i
+ x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 42
2576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 5968247
1280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319
333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15
+ 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^
43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*
b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 890430332862464
0*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 68635462
20544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1
319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^3
2 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35
- 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448
*a^57*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 -
20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2
- 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 -
3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 491
52*a^22*b*c*d^11))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a
^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^
24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200
*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 43616822185
1648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 1159506
54218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450
764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 +
149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31
- 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 +
47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37)*1i + x^(1/2)*(
276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 49694091059
2*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488
*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919
488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 26318835
7892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 1602
43801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 2
4696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 49
6940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*
a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 -
20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2
- 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 -
3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 491
52*a^22*b*c*d^11))^(1/4) - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*
d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^
10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*
d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10
- 49152*a^22*b*c*d^11))^(1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*
a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^
12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16
*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^
3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*
a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^3
4*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^3
1*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^
35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827
448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 4
4611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^4
1*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^4
6*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 500618250682
3680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808
739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 37091
40467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^
58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*
b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^5
3*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^5
0*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^
29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*
a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166
702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 627
5554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^2
5 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c
^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*
b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^5
2*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^
24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4
- 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 -
49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 324
4032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 90112
0*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9
+ 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 83
98939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 14
9590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18
- 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d
^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^
31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^1
8*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*
b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b
^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*
d^36 + 147517440*a^47*b^8*c^18*d^37)*1i - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d
^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 -
8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 +
103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^
21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^2
9*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19
*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16
*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20
*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4
- 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 -
49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 324
4032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 90112
0*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4))/(((-(2401*b^15*c^4 + 50625*a^4*b^
11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*
c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4
- 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 -
901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(147517440*a^18*b^37*c^47*d^
8 - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*
d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^
9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*
c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11)
)^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 53130
0876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 8577784532
1728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995
975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 +
16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^
45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^
42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 3240393827
1559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 -
9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*
d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^
31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^
35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i + x^(1/
2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 4225761280
00*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*
a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 131933314167
6032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 68635
46220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18
- 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^4
0*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b
^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000
*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 131933314
1676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 5968
2471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576
128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^
4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*
b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 90112
0*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*
a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*
b*c*d^11))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34
*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*
c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^
28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^3
0*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240
*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 45076465786
4704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 1495900
69231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 83989
39463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401
024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37)*1i + x^(1/2)*(27659520
0*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b
^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^
29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27
*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*
a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919
488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 246963488
63488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 4969409105
92*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^1
1*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*
b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 90112
0*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*
a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*
b*c*d^11))^(1/4)*1i + ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 -
20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^
2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 -
3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49
152*a^22*b*c*d^11))^(1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b
^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^
11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*
c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3
*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*
b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^5
5*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^5
2*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^
28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 2405444282744832
0*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 446114
37078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^2
2 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^1
7*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*
a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 30380873954
0992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467
712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^
5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*
c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8
- 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^1
1 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^
47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*
b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 627555416670208
0*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 62755541
66702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8
828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d
^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*
c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9
*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^
37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94
500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 4915
2*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*
a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^2
0*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47
382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939
463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 1495900
69231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450
764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 +
115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^
24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^2
8*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*
c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c
^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36
+ 147517440*a^47*b^8*c^18*d^37)*1i - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 +
71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751
989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 1032
51559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 -
250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^2
4 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26
*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23
*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33
- 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94
500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 4915
2*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*
a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^2
0*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*1i))*(-(2401*b^15*c^4 + 50625*a^4*b^11*
d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^1
2 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 -
3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 90
1120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4) + atan(((-(2401*a^4*d^15 + 5062
5*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^
12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c
^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^1
5*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 +
50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 409
6*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b
^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4
*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(((-(2401*a^4*d^
15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23
+ 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*
a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^
8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*
a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c
^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53
*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29
*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a
^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 396858692
62602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 +
44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c
^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^
48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694
528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 199311983
90272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^
57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) + x^(1/2)*(102760448*a^22*b^3
9*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7
+ 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 -
200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^
13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*
c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^3
7*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254
400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 971140
6085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 -
4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31
*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c
^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d
^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*
a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12
*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 20
27520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027
520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4) + 147
517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^2
1*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24
*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a
^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 4361682218516
48*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654
218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 45076
4657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 1
49590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 -
8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47
382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37) + x^(1/2)*(27659
5200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^2
1*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24
*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a
^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 2631883578920
96*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801
919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 246963
48863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 4969409
10592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*
b^11*c^18*d^35))*1i - (-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 -
20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2
- 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3
244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 491
52*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^1
3 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*
d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6
- 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 -
49152*a*b^11*c^22*d))^(1/4)*(((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^
2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*
c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^1
7*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d
^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*
a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*
b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^3
3*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032
320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 3240
3938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d
^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b
^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132
480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 228899
5975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 8
5777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531
300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59
*b^4*c^25*d^38) - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^3
7*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^5
2*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c
^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33
*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 97114060855705
60*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049
201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 -
8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*
d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^1
4*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^5
0*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53
*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d
^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*
b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2
*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b
^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*
c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4) + 147517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382
401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463
680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 1495900692
31616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764
657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 11
5950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24
+ 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d
^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^2
5*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22
*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 1
47517440*a^47*b^8*c^18*d^37) - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869
242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614
592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 1032515594
80832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272
765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 21
3523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27
- 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30
+ 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 650
1304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*1i)/((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 945
00*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152
*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^
5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b
^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 -
94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 4
9152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 324403
2*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a
^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(((-(2401*a^4*d^15 + 50625*b^4*c^4*d
^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^1
2 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3
244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901
120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 -
3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467
712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540
992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182
506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 -
24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c
^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a
^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 240544428
27448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 +
5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d
^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*
d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3
657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) + x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173
568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26
*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29
*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 265769528275763
2*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 88285575
64313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6
275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d
^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18
*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^
46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750
080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 145704248
93440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^
55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4
*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^
11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d
^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8
- 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4) + 147517440*a^18*b^37*c^4
7*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2
027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70
656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 +
377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^
20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^3
2*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19
*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*
b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*
b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*
c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37) + x^(1/2)*(276595200*a^18*b^35*c^42*
d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2
412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55
777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 +
213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^
23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^2
7*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c
^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21
*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35)) + (
-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(40
96*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d
^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7
+ 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4
)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)
/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^
20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16
*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^
(1/4)*(((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*
d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b
^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5
*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22
*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 53
1300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 8577784
5321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288
995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15
+ 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24
*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640
*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 3240393
8271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26
- 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^
34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10
*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28
*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) - x^(1/
2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 4225761280
00*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*
a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 131933314167
6032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 68635
46220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18
- 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^4
0*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b
^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000
*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 131933314
1676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 5968
2471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576
128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^
4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^
3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120
*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a
^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^1
1*c^22*d))^(3/4) + 147517440*a^18*b^37*c^47*d^8 - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d
^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13
+ 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^
16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^3
6*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23
*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*
b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a
^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576
*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^
44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*
d^37) - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d
^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16
+ 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^
19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^3
1*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21
*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b
^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^
15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*
d^34 + 276595200*a^42*b^11*c^18*d^35))))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*
a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336
*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a
^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*
b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*2i + 2*atan(((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c
^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^
12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18
*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^
9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b
^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*
b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*
c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^1
4*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*a^4*d
^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23
+ 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520
*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a
^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512
*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*
c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^5
3*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^2
9*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*
a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869
262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21
+ 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*
c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a
^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 90326111669
4528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198
390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a
^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i + x^(1/2)*(102760448*a^22
*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*
d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^1
0 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^4
8*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b
^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640
*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 226304920
1254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 97
11406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^
27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*
c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^
10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^
25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2
401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*
b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3
+ 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 +
2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4)*1
i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 20274
74309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 706565
13052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377
325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 -
317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^
23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^2
9*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16
*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13
*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20
*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37)*1i + x^(1/2)*(276595200*a^18*b^35*c^42*d
^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 24
12258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 557
77785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 +
213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^2
3 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27
*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^
24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*
d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35)) - (-
(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(409
6*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^
3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7
+ 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)
*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/
(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^2
0*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*
d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(
1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2
*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^
2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*
b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2
*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978
936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 1993119839027
2*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694
528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 955241
0255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17
+ 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22
*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240
*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 1606483
0746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 -
2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d
^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^3
4 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 1174405
12*a^59*b^4*c^25*d^38)*1i - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 4531945472
0*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^2
7*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a
^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 45993568816
33280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711
406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20
- 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^
38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*
b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 265769528275763
2*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983
052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 28346679
29600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*
b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 +
66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 +
270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 378
4704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336
*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c
^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42
*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^
39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^2
6*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32
*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*
a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107
200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 272073282
80576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 3684637573
12*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*
c^18*d^37)*1i - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^3
3*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c
^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27
*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*
b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a
^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 5577778527641
6*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048
*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^
12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35)))/((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12
+ 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11
+ 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3
784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 2703
36*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d
^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d
^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5
+ 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 +
270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*a^4*d^15 + 50
625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*
a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8
*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c
^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^
38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7
+ 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 -
303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d
^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^2
6*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 3968586926260224
0*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 446114
37078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^2
4 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15
*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^5
1*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a
^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*
c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i + x^(1/2)*(102760448*a^22*b^39*c^
57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 28
34667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 2000
27983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 +
2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45
*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^
24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*
a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085
570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 459
9356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^3
0 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*
d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36
+ 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*
d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^2
3 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 202752
0*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*
a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4)*1i - 3841
073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120
*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672
*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 37732527812
6080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 3171155
51617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317
115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 +
377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^
29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^
32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 -
3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37)*1i + x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 65
01304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434
048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276
416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 21352329
3304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 2502
72765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 +
103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29
- 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 7
1869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*1i + (-(2401
*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^1
2*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2
027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 202
7520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(
2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096
*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3
+ 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 +
2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*
(147517440*a^18*b^37*c^47*d^8 - ((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*
c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^1
0*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c
^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13
*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 5497893683
2*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^3
0*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a
^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 95524102550
32320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32
403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43
*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44
*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 160648307461
32480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288
995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 +
85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 5
31300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^
59*b^4*c^25*d^38)*1i - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^2
4*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^3
4*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b
^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280
*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 971140608
5570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 22
63049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^
23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*
c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^4
7*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 20002798305280
0*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600
*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c
^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150
*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 27033
6*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*
a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10
*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d
^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13
+ 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^
16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^3
6*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23
*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*
b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a
^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576
*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^
44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*
d^37)*1i - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^4
0*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d
^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34
*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*
c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b
^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^3
5*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38
*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^
19*d^34 + 276595200*a^42*b^11*c^18*d^35))*1i))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 +
66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 +
270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 378
4704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336
*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4) - (2/(3*a*c) + (x^2*(7*a^3*d^3 + 7*b^3*c^3 - 4*a*b^2*c^2*d -
4*a^2*b*c*d^2))/(6*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^4*(7*a^2*d^2 + 7*b^2*c^2 - 8*a*b*c*d))/(
6*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^(7/2)*(a*d + b*c) + a*c*x^(3/2) + b*d*x^(11/2))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**(5/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)

[Out]

Timed out

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