3.495 \(\int \frac {1}{x^{7/2} (a+b x^2)^2 (c+d x^2)^2} \, dx\)

Optimal. Leaf size=731 \[ \frac {b^{13/4} (9 b c-17 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {-9 a^2 d^2+8 a b c d-9 b^2 c^2}{10 a^2 c^2 x^{5/2} (b c-a d)^2}+\frac {(a d+b c) \left (9 a^2 d^2-17 a b c d+9 b^2 c^2\right )}{2 a^3 c^3 \sqrt {x} (b c-a d)^2}+\frac {d^{13/4} (17 b c-9 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {b}{2 a x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right ) (b c-a d)}+\frac {d (a d+b c)}{2 a c x^{5/2} \left (c+d x^2\right ) (b c-a d)^2} \]

[Out]

1/10*(-9*a^2*d^2+8*a*b*c*d-9*b^2*c^2)/a^2/c^2/(-a*d+b*c)^2/x^(5/2)+1/2*d*(a*d+b*c)/a/c/(-a*d+b*c)^2/x^(5/2)/(d
*x^2+c)+1/2*b/a/(-a*d+b*c)/x^(5/2)/(b*x^2+a)/(d*x^2+c)-1/8*b^(13/4)*(-17*a*d+9*b*c)*arctan(1-b^(1/4)*2^(1/2)*x
^(1/2)/a^(1/4))/a^(13/4)/(-a*d+b*c)^3*2^(1/2)+1/8*b^(13/4)*(-17*a*d+9*b*c)*arctan(1+b^(1/4)*2^(1/2)*x^(1/2)/a^
(1/4))/a^(13/4)/(-a*d+b*c)^3*2^(1/2)-1/8*d^(13/4)*(-9*a*d+17*b*c)*arctan(1-d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^
(13/4)/(-a*d+b*c)^3*2^(1/2)+1/8*d^(13/4)*(-9*a*d+17*b*c)*arctan(1+d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(13/4)/(-
a*d+b*c)^3*2^(1/2)+1/16*b^(13/4)*(-17*a*d+9*b*c)*ln(a^(1/2)+x*b^(1/2)-a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(13/4
)/(-a*d+b*c)^3*2^(1/2)-1/16*b^(13/4)*(-17*a*d+9*b*c)*ln(a^(1/2)+x*b^(1/2)+a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(
13/4)/(-a*d+b*c)^3*2^(1/2)+1/16*d^(13/4)*(-9*a*d+17*b*c)*ln(c^(1/2)+x*d^(1/2)-c^(1/4)*d^(1/4)*2^(1/2)*x^(1/2))
/c^(13/4)/(-a*d+b*c)^3*2^(1/2)-1/16*d^(13/4)*(-9*a*d+17*b*c)*ln(c^(1/2)+x*d^(1/2)+c^(1/4)*d^(1/4)*2^(1/2)*x^(1
/2))/c^(13/4)/(-a*d+b*c)^3*2^(1/2)+1/2*(a*d+b*c)*(9*a^2*d^2-17*a*b*c*d+9*b^2*c^2)/a^3/c^3/(-a*d+b*c)^2/x^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 1.28, antiderivative size = 731, normalized size of antiderivative = 1.00, number of steps used = 25, number of rules used = 11, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.458, Rules used = {466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628} \[ -\frac {9 a^2 d^2-8 a b c d+9 b^2 c^2}{10 a^2 c^2 x^{5/2} (b c-a d)^2}+\frac {(a d+b c) \left (9 a^2 d^2-17 a b c d+9 b^2 c^2\right )}{2 a^3 c^3 \sqrt {x} (b c-a d)^2}+\frac {b^{13/4} (9 b c-17 a d) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {b}{2 a x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right ) (b c-a d)}+\frac {d (a d+b c)}{2 a c x^{5/2} \left (c+d x^2\right ) (b c-a d)^2} \]

Antiderivative was successfully verified.

[In]

Int[1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]

[Out]

-(9*b^2*c^2 - 8*a*b*c*d + 9*a^2*d^2)/(10*a^2*c^2*(b*c - a*d)^2*x^(5/2)) + ((b*c + a*d)*(9*b^2*c^2 - 17*a*b*c*d
+ 9*a^2*d^2))/(2*a^3*c^3*(b*c - a*d)^2*Sqrt[x]) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*x^(5/2)*(c + d*x^2)) +
b/(2*a*(b*c - a*d)*x^(5/2)*(a + b*x^2)*(c + d*x^2)) - (b^(13/4)*(9*b*c - 17*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*
Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) + (b^(13/4)*(9*b*c - 17*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)
*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (d^(13/4)*(17*b*c - 9*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4
)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) + (d^(13/4)*(17*b*c - 9*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/
4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) + (b^(13/4)*(9*b*c - 17*a*d)*Log[Sqrt[a] - Sqrt[2]*a^
(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (b^(13/4)*(9*b*c - 17*a*d)*Log[Sqrt[a
] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) + (d^(13/4)*(17*b*c - 9*a
*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) - (d^(13/4)
*(17*b*c - 9*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(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 297

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

Rule 466

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

Rule 472

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

Rule 579

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

Rule 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 584

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

Rule 617

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

Rule 628

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

Rule 1162

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

Rule 1165

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

Rubi steps

\begin {align*} \int \frac {1}{x^{7/2} \left (a+b x^2\right )^2 \left (c+d x^2\right )^2} \, dx &=2 \operatorname {Subst}\left (\int \frac {1}{x^6 \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^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {-9 b c+4 a d-13 b d x^4}{x^6 \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^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {-4 \left (9 b^2 c^2-8 a b c d+9 a^2 d^2\right )-36 b d (b c+a d) x^4}{x^6 \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 {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {-20 (b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )-20 b d \left (9 b^2 c^2-8 a b c d+9 a^2 d^2\right ) x^4}{x^2 \left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{40 a^2 c^2 (b c-a d)^2}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-20 \left (9 b^4 c^4-8 a b^3 c^3 d-8 a^2 b^2 c^2 d^2-8 a^3 b c d^3+9 a^4 d^4\right )-20 b d (b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right ) x^4\right )}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{40 a^3 c^3 (b c-a d)^2}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \left (-\frac {20 b^4 c^3 (9 b c-17 a d) x^2}{(b c-a d) \left (a+b x^4\right )}-\frac {20 a^3 d^4 (-17 b c+9 a d) x^2}{(-b c+a d) \left (c+d x^4\right )}\right ) \, dx,x,\sqrt {x}\right )}{40 a^3 c^3 (b c-a d)^2}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {\left (b^4 (9 b c-17 a d)\right ) \operatorname {Subst}\left (\int \frac {x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 a^3 (b c-a d)^3}+\frac {\left (d^4 (17 b c-9 a d)\right ) \operatorname {Subst}\left (\int \frac {x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{2 c^3 (b c-a d)^3}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {\left (b^{7/2} (9 b c-17 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^3 (b c-a d)^3}+\frac {\left (b^{7/2} (9 b c-17 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^3 (b c-a d)^3}-\frac {\left (d^{7/2} (17 b c-9 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^3 (b c-a d)^3}+\frac {\left (d^{7/2} (17 b c-9 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^3 (b c-a d)^3}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {\left (b^3 (9 b c-17 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^3 (b c-a d)^3}+\frac {\left (b^3 (9 b c-17 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^3 (b c-a d)^3}+\frac {\left (b^{13/4} (9 b c-17 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^{13/4} (b c-a d)^3}+\frac {\left (b^{13/4} (9 b c-17 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^{13/4} (b c-a d)^3}+\frac {\left (d^3 (17 b c-9 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^3 (b c-a d)^3}+\frac {\left (d^3 (17 b c-9 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^3 (b c-a d)^3}+\frac {\left (d^{13/4} (17 b c-9 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^{13/4} (b c-a d)^3}+\frac {\left (d^{13/4} (17 b c-9 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^{13/4} (b c-a d)^3}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}+\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {\left (b^{13/4} (9 b c-17 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^{13/4} (b c-a d)^3}-\frac {\left (b^{13/4} (9 b c-17 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^{13/4} (b c-a d)^3}+\frac {\left (d^{13/4} (17 b c-9 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^{13/4} (b c-a d)^3}-\frac {\left (d^{13/4} (17 b c-9 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^{13/4} (b c-a d)^3}\\ &=-\frac {9 b^2 c^2-8 a b c d+9 a^2 d^2}{10 a^2 c^2 (b c-a d)^2 x^{5/2}}+\frac {(b c+a d) \left (9 b^2 c^2-17 a b c d+9 a^2 d^2\right )}{2 a^3 c^3 (b c-a d)^2 \sqrt {x}}+\frac {d (b c+a d)}{2 a c (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b}{2 a (b c-a d) x^{5/2} \left (a+b x^2\right ) \left (c+d x^2\right )}-\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {b^{13/4} (9 b c-17 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (b c-a d)^3}+\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (9 b c-17 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}-\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (b c-a d)^3}\\ \end {align*}

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Mathematica [A]  time = 6.18, size = 696, normalized size = 0.95 \[ -\frac {b^{13/4} (17 a d-9 b c) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {b^{13/4} (17 a d-9 b c) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (17 a d-9 b c) \tan ^{-1}\left (\frac {2 \sqrt [4]{b} \sqrt {x}-\sqrt {2} \sqrt [4]{a}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}-\frac {b^{13/4} (17 a d-9 b c) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a}+2 \sqrt [4]{b} \sqrt {x}}{\sqrt {2} \sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4} (b c-a d)^3}+\frac {b^4 x^{3/2}}{2 a^3 \left (a+b x^2\right ) (a d-b c)^2}+\frac {4 (a d+b c)}{a^3 c^3 \sqrt {x}}-\frac {2}{5 a^2 c^2 x^{5/2}}-\frac {d^{13/4} (17 b c-9 a d) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (a d-b c)^3}+\frac {d^{13/4} (17 b c-9 a d) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{8 \sqrt {2} c^{13/4} (a d-b c)^3}-\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (\frac {2 \sqrt [4]{d} \sqrt {x}-\sqrt {2} \sqrt [4]{c}}{\sqrt {2} \sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (a d-b c)^3}-\frac {d^{13/4} (17 b c-9 a d) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c}+2 \sqrt [4]{d} \sqrt {x}}{\sqrt {2} \sqrt [4]{c}}\right )}{4 \sqrt {2} c^{13/4} (a d-b c)^3}+\frac {d^4 x^{3/2}}{2 c^3 \left (c+d x^2\right ) (b c-a d)^2} \]

Antiderivative was successfully verified.

[In]

Integrate[1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]

[Out]

-2/(5*a^2*c^2*x^(5/2)) + (4*(b*c + a*d))/(a^3*c^3*Sqrt[x]) + (b^4*x^(3/2))/(2*a^3*(-(b*c) + a*d)^2*(a + b*x^2)
) + (d^4*x^(3/2))/(2*c^3*(b*c - a*d)^2*(c + d*x^2)) - (b^(13/4)*(-9*b*c + 17*a*d)*ArcTan[(-(Sqrt[2]*a^(1/4)) +
2*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (b^(13/4)*(-9*b*c + 17*a*d)*ArcTa
n[(Sqrt[2]*a^(1/4) + 2*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (d^(13/4)*(17
*b*c - 9*a*d)*ArcTan[(-(Sqrt[2]*c^(1/4)) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(4*Sqrt[2]*c^(13/4)*(-(b*c)
+ a*d)^3) - (d^(13/4)*(17*b*c - 9*a*d)*ArcTan[(Sqrt[2]*c^(1/4) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(4*Sqr
t[2]*c^(13/4)*(-(b*c) + a*d)^3) - (b^(13/4)*(-9*b*c + 17*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] +
Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) + (b^(13/4)*(-9*b*c + 17*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(
1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (d^(13/4)*(17*b*c - 9*a*d)*Log[Sqrt[c] - Sqrt[
2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(-(b*c) + a*d)^3) + (d^(13/4)*(17*b*c - 9*a*d)*Lo
g[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(-(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^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="fricas")

[Out]

Timed out

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giac [A]  time = 1.96, size = 1015, normalized size = 1.39 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="giac")

[Out]

1/4*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b
)^(1/4))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/4*(9*(a
*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))
/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/4*(17*(c*d^3)^(
3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)
*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/4*(17*(c*d^3)^(3/4)*b*c*
d - 9*(c*d^3)^(3/4)*a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7
- 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) - 1/8*(9*(a*b^3)^(3/4)*b^2*c - 17*(a
*b^3)^(3/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c
^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/8*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*log(-sq
rt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*
d^2 - sqrt(2)*a^7*d^3) - 1/8*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4)
+ x + sqrt(c/d))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1
/8*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)
*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/2*(b^4*c^3*d*x^(7/2) + a
^3*b*d^4*x^(7/2) + b^4*c^4*x^(3/2) + a^4*d^4*x^(3/2))/((a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*(b*d*x^4 +
b*c*x^2 + a*d*x^2 + a*c)) + 2/5*(10*b*c*x^2 + 10*a*d*x^2 - a*c)/(a^3*c^3*x^(5/2))

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maple [A]  time = 0.03, size = 849, normalized size = 1.16 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x)

[Out]

1/2*b^4/a^2/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*d-1/2*b^5/a^3/(a*d-b*c)^3*x^(3/2)/(b*x^2+a)*c+17/16*b^3/a^2/(a*d-b*c
)^3/(a/b)^(1/4)*2^(1/2)*d*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)))+17/8*b^3/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)+17/8*b^3/a^2/(a*d
-b*c)^3/(a/b)^(1/4)*2^(1/2)*d*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)-9/16*b^4/a^3/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/
2)*c*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)))-9/8*b^4/a^3/(
a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-9/8*b^4/a^3/(a*d-b*c)^3/(a/b)^(1/4)*2^(
1/2)*c*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+1/2*d^5/c^3/(a*d-b*c)^3*x^(3/2)/(d*x^2+c)*a-1/2*d^4/c^2/(a*d-b*c)
^3*x^(3/2)/(d*x^2+c)*b+9/16*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*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)))+9/8*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/
2)/(c/d)^(1/4)*x^(1/2)+1)+9/8*d^4/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-
17/16*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*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)))-17/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2
)+1)-17/8*d^3/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-2/5/a^2/c^2/x^(5/2)+
4/a^2/c^3/x^(1/2)*d+4/a^3/c^2/x^(1/2)*b

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maxima [A]  time = 2.75, size = 774, normalized size = 1.06 \[ \frac {{\left (9 \, b^{5} c - 17 \, a b^{4} d\right )} {\left (\frac {2 \, \sqrt {2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} + \frac {2 \, \sqrt {2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} - \frac {\sqrt {2} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}}\right )}}{16 \, {\left (a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right )}} + \frac {{\left (17 \, b c d^{4} - 9 \, a d^{5}\right )} {\left (\frac {2 \, \sqrt {2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} + 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {\sqrt {c} \sqrt {d}} \sqrt {d}} + \frac {2 \, \sqrt {2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} - 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {\sqrt {c} \sqrt {d}} \sqrt {d}} - \frac {\sqrt {2} \log \left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}}\right )}}{16 \, {\left (b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right )}} - \frac {4 \, a^{2} b^{2} c^{4} - 8 \, a^{3} b c^{3} d + 4 \, a^{4} c^{2} d^{2} - 5 \, {\left (9 \, b^{4} c^{3} d - 8 \, a b^{3} c^{2} d^{2} - 8 \, a^{2} b^{2} c d^{3} + 9 \, a^{3} b d^{4}\right )} x^{6} - {\left (45 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 72 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 45 \, a^{4} d^{4}\right )} x^{4} - 36 \, {\left (a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right )} x^{2}}{10 \, {\left ({\left (a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right )} x^{\frac {13}{2}} + {\left (a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right )} x^{\frac {9}{2}} + {\left (a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right )} x^{\frac {5}{2}}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm="maxima")

[Out]

1/16*(9*b^5*c - 17*a*b^4*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(s
qrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*
sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*
sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x +
sqrt(a))/(a^(1/4)*b^(3/4)))/(a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3) + 1/16*(17*b*c*d^4 - 9*a
*d^5)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt
(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(
sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x +
sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3
/4)))/(b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3) - 1/10*(4*a^2*b^2*c^4 - 8*a^3*b*c^3*d + 4*a^4*
c^2*d^2 - 5*(9*b^4*c^3*d - 8*a*b^3*c^2*d^2 - 8*a^2*b^2*c*d^3 + 9*a^3*b*d^4)*x^6 - (45*b^4*c^4 - 4*a*b^3*c^3*d
- 72*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 45*a^4*d^4)*x^4 - 36*(a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c
*d^3)*x^2)/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^(13/2) + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*
b*c^4*d^2 + a^6*c^3*d^3)*x^(9/2) + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^(5/2))

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mupad [B]  time = 14.27, size = 36571, normalized size = 50.03 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)

[Out]

2*atan((2654208*a^16*b^22*c^27*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*
a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336
*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*
a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23
*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 15169032*a^22*b^8*d^19*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13
*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*
c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4
- 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 -
901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) + 2654208*a^38*c^5*d^22*x^(1
/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3
*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b
^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5
*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11
))^(5/4) - 130671792*a^21*b^9*c*d^18*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 1
40454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d +
270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 37
84704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 27033
6*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 41877504*a^17*b^21*c^26*d*x^(1/2)*(-(6561*b^17*c^4 + 83521
*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a
^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^
8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*
c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 41877504*a^37*b*c
^6*d^21*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 4957
2*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 9
01120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244
032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a
^24*b*c*d^11))^(5/4) + 15169032*a^11*b^19*c^11*d^8*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*
b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*
b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^
7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c
^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 130671792*a^12*b^18*c^10*d^9*x^(1/2)*(-(6561
*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a
^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3
+ 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 +
2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) +
450333432*a^13*b^17*c^9*d^10*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^
2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a
^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^
19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b
^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 784872864*a^14*b^16*c^8*d^11*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*
b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b
^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8
*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d
^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) + 717087608*a^15*b^15*c^
7*d^12*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572
*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 90
1120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 32440
32*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^
24*b*c*d^11))^(1/4) - 264948264*a^16*b^14*c^6*d^13*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*
b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*
b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^
7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c
^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 264948264*a^17*b^13*c^5*d^14*x^(1/2)*(-(6561
*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a
^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3
+ 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 +
2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) +
717087608*a^18*b^12*c^4*d^15*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^
2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a
^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^
19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b
^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 784872864*a^19*b^11*c^3*d^16*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*
b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b
^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8
*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d
^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) + 450333432*a^20*b^10*c^
2*d^17*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572
*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 90
1120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 32440
32*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^
24*b*c*d^11))^(1/4) + 304971776*a^18*b^20*c^25*d^2*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*
b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*
b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^
7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c
^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 1359347712*a^19*b^19*c^24*d^3*x^(1/2)*(-(656
1*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*
a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3
+ 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 +
2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) +
4144791552*a^20*b^18*c^23*d^4*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*
a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336
*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*
a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23
*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 9148891136*a^21*b^17*c^22*d^5*x^(1/2)*(-(6561*b^17*c^4 + 83521*a
^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^1
3*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*
c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^
4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 15081504768*a^22*b^
16*c^21*d^6*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 -
49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2
- 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 -
3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 491
52*a^24*b*c*d^11))^(5/4) - 18867290112*a^23*b^15*c^20*d^7*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 1768
68*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 4915
2*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*
a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^2
2*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 18014928896*a^24*b^14*c^19*d^8*x^(1/2
)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d
)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9
*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c
^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))
^(5/4) - 13171163136*a^25*b^13*c^18*d^9*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3
+ 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d
+ 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 +
3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 27
0336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 7816740864*a^26*b^12*c^17*d^10*x^(1/2)*(-(6561*b^17*c^4
+ 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12
+ 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520
*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a
^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 555404492
8*a^27*b^11*c^16*d^11*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*
c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^1
0*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*
c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*
d^10 - 49152*a^24*b*c*d^11))^(5/4) + 7816740864*a^28*b^10*c^15*d^12*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*
d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c
^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4
- 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 -
901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 13171163136*a^29*b^9*c^14*d
^13*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*
b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 90112
0*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*
a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*
b*c*d^11))^(5/4) + 18014928896*a^30*b^8*c^13*d^14*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b
^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b
^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7
*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^
3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 18867290112*a^31*b^7*c^12*d^15*x^(1/2)*(-(656
1*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*
a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3
+ 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 +
2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) +
15081504768*a^32*b^6*c^11*d^16*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454
*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 27033
6*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704
*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^2
3*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 9148891136*a^33*b^5*c^10*d^17*x^(1/2)*(-(6561*b^17*c^4 + 83521*
a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^
13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8
*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c
^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 4144791552*a^34*b^
4*c^9*d^18*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 4
9572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2
- 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3
244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 4915
2*a^24*b*c*d^11))^(5/4) - 1359347712*a^35*b^3*c^8*d^19*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*
a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a
^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^1
8*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b
^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 304971776*a^36*b^2*c^7*d^20*x^(1/2)*(-(6
561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(409
6*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d
^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7
+ 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4)
)/(32234193*a^17*b^11*d^17 - 4782969*b^28*c^17 - 198040140*a^16*b^12*c*d^16 - 197341758*a^2*b^26*c^15*d^2 + 38
4710796*a^3*b^25*c^14*d^3 - 335988081*a^4*b^24*c^13*d^4 + 55738368*a^5*b^23*c^12*d^5 + 39223296*a^6*b^22*c^11*
d^6 + 24805376*a^7*b^21*c^10*d^7 + 12484608*a^8*b^20*c^9*d^8 + 2260992*a^9*b^19*c^8*d^9 - 5865472*a^10*b^18*c^
7*d^10 - 11894784*a^11*b^17*c^6*d^11 - 15826944*a^12*b^16*c^5*d^12 + 43224857*a^13*b^15*c^4*d^13 - 308701404*a
^14*b^14*c^3*d^14 + 413141310*a^15*b^13*c^2*d^15 + 48892572*a*b^27*c^16*d))*(-(6561*b^17*c^4 + 83521*a^4*b^13*
d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c
^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4
- 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 -
901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - (2/(5*a*c) - (18*x^2*(a*d +
b*c))/(5*a^2*c^2) + (x^4*(72*a^2*b^2*c^2*d^2 - 45*b^4*c^4 - 45*a^4*d^4 + 4*a*b^3*c^3*d + 4*a^3*b*c*d^3))/(10*
a^3*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (b*d*x^6*(a*d + b*c)*(9*a^2*d^2 + 9*b^2*c^2 - 17*a*b*c*d))/(2*a^3*c
^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^(9/2)*(a*d + b*c) + a*c*x^(5/2) + b*d*x^(13/2)) + atan((((-(6561*b^17*
c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^
12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027
520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 202752
0*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(3/4)*(x^(1/2)
*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)
/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*
c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^
5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^
(1/4)*(169869312*a^34*b^40*c^70*d^4 - 5058330624*a^35*b^39*c^69*d^5 + 72498544640*a^36*b^38*c^68*d^6 - 6659799
77728*a^37*b^37*c^67*d^7 + 4405015347200*a^38*b^36*c^66*d^8 - 22343644610560*a^39*b^35*c^65*d^9 + 903827632947
20*a^40*b^34*c^64*d^10 - 299352929075200*a^41*b^33*c^63*d^11 + 827049291808768*a^42*b^32*c^62*d^12 - 193201537
2861440*a^43*b^31*c^61*d^13 + 3854486254649344*a^44*b^30*c^60*d^14 - 6616635725053952*a^45*b^29*c^59*d^15 + 98
28748597657600*a^46*b^28*c^58*d^16 - 12696914776555520*a^47*b^27*c^57*d^17 + 14352507102822400*a^48*b^26*c^56*
d^18 - 14371219193200640*a^49*b^25*c^55*d^19 + 13121803937382400*a^50*b^24*c^54*d^20 - 11630118384435200*a^51*
b^23*c^53*d^21 + 10979630865448960*a^52*b^22*c^52*d^22 - 11630118384435200*a^53*b^21*c^51*d^23 + 1312180393738
2400*a^54*b^20*c^50*d^24 - 14371219193200640*a^55*b^19*c^49*d^25 + 14352507102822400*a^56*b^18*c^48*d^26 - 126
96914776555520*a^57*b^17*c^47*d^27 + 9828748597657600*a^58*b^16*c^46*d^28 - 6616635725053952*a^59*b^15*c^45*d^
29 + 3854486254649344*a^60*b^14*c^44*d^30 - 1932015372861440*a^61*b^13*c^43*d^31 + 827049291808768*a^62*b^12*c
^42*d^32 - 299352929075200*a^63*b^11*c^41*d^33 + 90382763294720*a^64*b^10*c^40*d^34 - 22343644610560*a^65*b^9*
c^39*d^35 + 4405015347200*a^66*b^8*c^38*d^36 - 665979977728*a^67*b^7*c^37*d^37 + 72498544640*a^68*b^6*c^36*d^3
8 - 5058330624*a^69*b^5*c^35*d^39 + 169869312*a^70*b^4*c^34*d^40) + 191102976*a^31*b^41*c^68*d^4 - 5478285312*
a^32*b^40*c^67*d^5 + 75301650432*a^33*b^39*c^66*d^6 - 660755972096*a^34*b^38*c^65*d^7 + 4157198565376*a^35*b^3
7*c^64*d^8 - 19968092536832*a^36*b^36*c^63*d^9 + 76124224225280*a^37*b^35*c^62*d^10 - 236401268359168*a^38*b^3
4*c^61*d^11 + 609010175442944*a^39*b^33*c^60*d^12 - 1318618746322944*a^40*b^32*c^59*d^13 + 2422266262192128*a^
41*b^31*c^58*d^14 - 3800365228883968*a^42*b^30*c^57*d^15 + 5115210562535424*a^43*b^29*c^56*d^16 - 592159509970
9440*a^44*b^28*c^55*d^17 + 5899320342609920*a^45*b^27*c^54*d^18 - 5044901346017280*a^46*b^26*c^53*d^19 + 36594
31378944000*a^47*b^25*c^52*d^20 - 2131419914567680*a^48*b^24*c^51*d^21 + 688340293386240*a^49*b^23*c^50*d^22 +
688340293386240*a^50*b^22*c^49*d^23 - 2131419914567680*a^51*b^21*c^48*d^24 + 3659431378944000*a^52*b^20*c^47*
d^25 - 5044901346017280*a^53*b^19*c^46*d^26 + 5899320342609920*a^54*b^18*c^45*d^27 - 5921595099709440*a^55*b^1
7*c^44*d^28 + 5115210562535424*a^56*b^16*c^43*d^29 - 3800365228883968*a^57*b^15*c^42*d^30 + 2422266262192128*a
^58*b^14*c^41*d^31 - 1318618746322944*a^59*b^13*c^40*d^32 + 609010175442944*a^60*b^12*c^39*d^33 - 236401268359
168*a^61*b^11*c^38*d^34 + 76124224225280*a^62*b^10*c^37*d^35 - 19968092536832*a^63*b^9*c^36*d^36 + 41571985653
76*a^64*b^8*c^35*d^37 - 660755972096*a^65*b^7*c^34*d^38 + 75301650432*a^66*b^6*c^33*d^39 - 5478285312*a^67*b^5
*c^32*d^40 + 191102976*a^68*b^4*c^31*d^41) + x^(1/2)*(970818048*a^29*b^37*c^54*d^12 - 21954447360*a^30*b^36*c^
53*d^13 + 234247707648*a^31*b^35*c^52*d^14 - 1568140904448*a^32*b^34*c^51*d^15 + 7387800533504*a^33*b^33*c^50*
d^16 - 26036469792256*a^34*b^32*c^49*d^17 + 71189396375552*a^35*b^31*c^48*d^18 - 154393382077440*a^36*b^30*c^4
7*d^19 + 268607771876352*a^37*b^29*c^46*d^20 - 374590800139776*a^38*b^28*c^45*d^21 + 409764654942208*a^39*b^27
*c^44*d^22 - 324787154001920*a^40*b^26*c^43*d^23 + 124213059109888*a^41*b^25*c^42*d^24 + 124213059109888*a^42*
b^24*c^41*d^25 - 324787154001920*a^43*b^23*c^40*d^26 + 409764654942208*a^44*b^22*c^39*d^27 - 374590800139776*a
^45*b^21*c^38*d^28 + 268607771876352*a^46*b^20*c^37*d^29 - 154393382077440*a^47*b^19*c^36*d^30 + 7118939637555
2*a^48*b^18*c^35*d^31 - 26036469792256*a^49*b^17*c^34*d^32 + 7387800533504*a^50*b^16*c^33*d^33 - 1568140904448
*a^51*b^15*c^32*d^34 + 234247707648*a^52*b^14*c^31*d^35 - 21954447360*a^53*b^13*c^30*d^36 + 970818048*a^54*b^1
2*c^29*d^37))*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*
a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901
120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 324403
2*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^2
4*b*c*d^11))^(1/4)*1i - ((-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d
^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^1
0*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d
^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10
- 49152*a^24*b*c*d^11))^(3/4)*(191102976*a^31*b^41*c^68*d^4 - x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 -
176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 -
49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244
032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120
*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4)*(169869312*a^34*b^40*c^70*d^4 - 505
8330624*a^35*b^39*c^69*d^5 + 72498544640*a^36*b^38*c^68*d^6 - 665979977728*a^37*b^37*c^67*d^7 + 4405015347200*
a^38*b^36*c^66*d^8 - 22343644610560*a^39*b^35*c^65*d^9 + 90382763294720*a^40*b^34*c^64*d^10 - 299352929075200*
a^41*b^33*c^63*d^11 + 827049291808768*a^42*b^32*c^62*d^12 - 1932015372861440*a^43*b^31*c^61*d^13 + 38544862546
49344*a^44*b^30*c^60*d^14 - 6616635725053952*a^45*b^29*c^59*d^15 + 9828748597657600*a^46*b^28*c^58*d^16 - 1269
6914776555520*a^47*b^27*c^57*d^17 + 14352507102822400*a^48*b^26*c^56*d^18 - 14371219193200640*a^49*b^25*c^55*d
^19 + 13121803937382400*a^50*b^24*c^54*d^20 - 11630118384435200*a^51*b^23*c^53*d^21 + 10979630865448960*a^52*b
^22*c^52*d^22 - 11630118384435200*a^53*b^21*c^51*d^23 + 13121803937382400*a^54*b^20*c^50*d^24 - 14371219193200
640*a^55*b^19*c^49*d^25 + 14352507102822400*a^56*b^18*c^48*d^26 - 12696914776555520*a^57*b^17*c^47*d^27 + 9828
748597657600*a^58*b^16*c^46*d^28 - 6616635725053952*a^59*b^15*c^45*d^29 + 3854486254649344*a^60*b^14*c^44*d^30
- 1932015372861440*a^61*b^13*c^43*d^31 + 827049291808768*a^62*b^12*c^42*d^32 - 299352929075200*a^63*b^11*c^41
*d^33 + 90382763294720*a^64*b^10*c^40*d^34 - 22343644610560*a^65*b^9*c^39*d^35 + 4405015347200*a^66*b^8*c^38*d
^36 - 665979977728*a^67*b^7*c^37*d^37 + 72498544640*a^68*b^6*c^36*d^38 - 5058330624*a^69*b^5*c^35*d^39 + 16986
9312*a^70*b^4*c^34*d^40) - 5478285312*a^32*b^40*c^67*d^5 + 75301650432*a^33*b^39*c^66*d^6 - 660755972096*a^34*
b^38*c^65*d^7 + 4157198565376*a^35*b^37*c^64*d^8 - 19968092536832*a^36*b^36*c^63*d^9 + 76124224225280*a^37*b^3
5*c^62*d^10 - 236401268359168*a^38*b^34*c^61*d^11 + 609010175442944*a^39*b^33*c^60*d^12 - 1318618746322944*a^4
0*b^32*c^59*d^13 + 2422266262192128*a^41*b^31*c^58*d^14 - 3800365228883968*a^42*b^30*c^57*d^15 + 5115210562535
424*a^43*b^29*c^56*d^16 - 5921595099709440*a^44*b^28*c^55*d^17 + 5899320342609920*a^45*b^27*c^54*d^18 - 504490
1346017280*a^46*b^26*c^53*d^19 + 3659431378944000*a^47*b^25*c^52*d^20 - 2131419914567680*a^48*b^24*c^51*d^21 +
688340293386240*a^49*b^23*c^50*d^22 + 688340293386240*a^50*b^22*c^49*d^23 - 2131419914567680*a^51*b^21*c^48*d
^24 + 3659431378944000*a^52*b^20*c^47*d^25 - 5044901346017280*a^53*b^19*c^46*d^26 + 5899320342609920*a^54*b^18
*c^45*d^27 - 5921595099709440*a^55*b^17*c^44*d^28 + 5115210562535424*a^56*b^16*c^43*d^29 - 3800365228883968*a^
57*b^15*c^42*d^30 + 2422266262192128*a^58*b^14*c^41*d^31 - 1318618746322944*a^59*b^13*c^40*d^32 + 609010175442
944*a^60*b^12*c^39*d^33 - 236401268359168*a^61*b^11*c^38*d^34 + 76124224225280*a^62*b^10*c^37*d^35 - 199680925
36832*a^63*b^9*c^36*d^36 + 4157198565376*a^64*b^8*c^35*d^37 - 660755972096*a^65*b^7*c^34*d^38 + 75301650432*a^
66*b^6*c^33*d^39 - 5478285312*a^67*b^5*c^32*d^40 + 191102976*a^68*b^4*c^31*d^41) - x^(1/2)*(970818048*a^29*b^3
7*c^54*d^12 - 21954447360*a^30*b^36*c^53*d^13 + 234247707648*a^31*b^35*c^52*d^14 - 1568140904448*a^32*b^34*c^5
1*d^15 + 7387800533504*a^33*b^33*c^50*d^16 - 26036469792256*a^34*b^32*c^49*d^17 + 71189396375552*a^35*b^31*c^4
8*d^18 - 154393382077440*a^36*b^30*c^47*d^19 + 268607771876352*a^37*b^29*c^46*d^20 - 374590800139776*a^38*b^28
*c^45*d^21 + 409764654942208*a^39*b^27*c^44*d^22 - 324787154001920*a^40*b^26*c^43*d^23 + 124213059109888*a^41*
b^25*c^42*d^24 + 124213059109888*a^42*b^24*c^41*d^25 - 324787154001920*a^43*b^23*c^40*d^26 + 409764654942208*a
^44*b^22*c^39*d^27 - 374590800139776*a^45*b^21*c^38*d^28 + 268607771876352*a^46*b^20*c^37*d^29 - 1543933820774
40*a^47*b^19*c^36*d^30 + 71189396375552*a^48*b^18*c^35*d^31 - 26036469792256*a^49*b^17*c^34*d^32 + 73878005335
04*a^50*b^16*c^33*d^33 - 1568140904448*a^51*b^15*c^32*d^34 + 234247707648*a^52*b^14*c^31*d^35 - 21954447360*a^
53*b^13*c^30*d^36 + 970818048*a^54*b^12*c^29*d^37))*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*
d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^
11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d
^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9
+ 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4)*1i)/(((-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*
a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a
^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^1
8*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b
^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(3/4)*(x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13
*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*
c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4
- 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 -
901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4)*(169869312*a^34*b^40*c^70*d^
4 - 5058330624*a^35*b^39*c^69*d^5 + 72498544640*a^36*b^38*c^68*d^6 - 665979977728*a^37*b^37*c^67*d^7 + 4405015
347200*a^38*b^36*c^66*d^8 - 22343644610560*a^39*b^35*c^65*d^9 + 90382763294720*a^40*b^34*c^64*d^10 - 299352929
075200*a^41*b^33*c^63*d^11 + 827049291808768*a^42*b^32*c^62*d^12 - 1932015372861440*a^43*b^31*c^61*d^13 + 3854
486254649344*a^44*b^30*c^60*d^14 - 6616635725053952*a^45*b^29*c^59*d^15 + 9828748597657600*a^46*b^28*c^58*d^16
- 12696914776555520*a^47*b^27*c^57*d^17 + 14352507102822400*a^48*b^26*c^56*d^18 - 14371219193200640*a^49*b^25
*c^55*d^19 + 13121803937382400*a^50*b^24*c^54*d^20 - 11630118384435200*a^51*b^23*c^53*d^21 + 10979630865448960
*a^52*b^22*c^52*d^22 - 11630118384435200*a^53*b^21*c^51*d^23 + 13121803937382400*a^54*b^20*c^50*d^24 - 1437121
9193200640*a^55*b^19*c^49*d^25 + 14352507102822400*a^56*b^18*c^48*d^26 - 12696914776555520*a^57*b^17*c^47*d^27
+ 9828748597657600*a^58*b^16*c^46*d^28 - 6616635725053952*a^59*b^15*c^45*d^29 + 3854486254649344*a^60*b^14*c^
44*d^30 - 1932015372861440*a^61*b^13*c^43*d^31 + 827049291808768*a^62*b^12*c^42*d^32 - 299352929075200*a^63*b^
11*c^41*d^33 + 90382763294720*a^64*b^10*c^40*d^34 - 22343644610560*a^65*b^9*c^39*d^35 + 4405015347200*a^66*b^8
*c^38*d^36 - 665979977728*a^67*b^7*c^37*d^37 + 72498544640*a^68*b^6*c^36*d^38 - 5058330624*a^69*b^5*c^35*d^39
+ 169869312*a^70*b^4*c^34*d^40) + 191102976*a^31*b^41*c^68*d^4 - 5478285312*a^32*b^40*c^67*d^5 + 75301650432*a
^33*b^39*c^66*d^6 - 660755972096*a^34*b^38*c^65*d^7 + 4157198565376*a^35*b^37*c^64*d^8 - 19968092536832*a^36*b
^36*c^63*d^9 + 76124224225280*a^37*b^35*c^62*d^10 - 236401268359168*a^38*b^34*c^61*d^11 + 609010175442944*a^39
*b^33*c^60*d^12 - 1318618746322944*a^40*b^32*c^59*d^13 + 2422266262192128*a^41*b^31*c^58*d^14 - 38003652288839
68*a^42*b^30*c^57*d^15 + 5115210562535424*a^43*b^29*c^56*d^16 - 5921595099709440*a^44*b^28*c^55*d^17 + 5899320
342609920*a^45*b^27*c^54*d^18 - 5044901346017280*a^46*b^26*c^53*d^19 + 3659431378944000*a^47*b^25*c^52*d^20 -
2131419914567680*a^48*b^24*c^51*d^21 + 688340293386240*a^49*b^23*c^50*d^22 + 688340293386240*a^50*b^22*c^49*d^
23 - 2131419914567680*a^51*b^21*c^48*d^24 + 3659431378944000*a^52*b^20*c^47*d^25 - 5044901346017280*a^53*b^19*
c^46*d^26 + 5899320342609920*a^54*b^18*c^45*d^27 - 5921595099709440*a^55*b^17*c^44*d^28 + 5115210562535424*a^5
6*b^16*c^43*d^29 - 3800365228883968*a^57*b^15*c^42*d^30 + 2422266262192128*a^58*b^14*c^41*d^31 - 1318618746322
944*a^59*b^13*c^40*d^32 + 609010175442944*a^60*b^12*c^39*d^33 - 236401268359168*a^61*b^11*c^38*d^34 + 76124224
225280*a^62*b^10*c^37*d^35 - 19968092536832*a^63*b^9*c^36*d^36 + 4157198565376*a^64*b^8*c^35*d^37 - 6607559720
96*a^65*b^7*c^34*d^38 + 75301650432*a^66*b^6*c^33*d^39 - 5478285312*a^67*b^5*c^32*d^40 + 191102976*a^68*b^4*c^
31*d^41) + x^(1/2)*(970818048*a^29*b^37*c^54*d^12 - 21954447360*a^30*b^36*c^53*d^13 + 234247707648*a^31*b^35*c
^52*d^14 - 1568140904448*a^32*b^34*c^51*d^15 + 7387800533504*a^33*b^33*c^50*d^16 - 26036469792256*a^34*b^32*c^
49*d^17 + 71189396375552*a^35*b^31*c^48*d^18 - 154393382077440*a^36*b^30*c^47*d^19 + 268607771876352*a^37*b^29
*c^46*d^20 - 374590800139776*a^38*b^28*c^45*d^21 + 409764654942208*a^39*b^27*c^44*d^22 - 324787154001920*a^40*
b^26*c^43*d^23 + 124213059109888*a^41*b^25*c^42*d^24 + 124213059109888*a^42*b^24*c^41*d^25 - 324787154001920*a
^43*b^23*c^40*d^26 + 409764654942208*a^44*b^22*c^39*d^27 - 374590800139776*a^45*b^21*c^38*d^28 + 2686077718763
52*a^46*b^20*c^37*d^29 - 154393382077440*a^47*b^19*c^36*d^30 + 71189396375552*a^48*b^18*c^35*d^31 - 2603646979
2256*a^49*b^17*c^34*d^32 + 7387800533504*a^50*b^16*c^33*d^33 - 1568140904448*a^51*b^15*c^32*d^34 + 23424770764
8*a^52*b^14*c^31*d^35 - 21954447360*a^53*b^13*c^30*d^36 + 970818048*a^54*b^12*c^29*d^37))*(-(6561*b^17*c^4 + 8
3521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 40
96*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^1
7*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*
b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) + ((-(6561*b^17
*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d
^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 202
7520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 20275
20*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(3/4)*(191102
976*a^31*b^41*c^68*d^4 - x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^
15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*
b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b
^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c
^2*d^10 - 49152*a^24*b*c*d^11))^(1/4)*(169869312*a^34*b^40*c^70*d^4 - 5058330624*a^35*b^39*c^69*d^5 + 72498544
640*a^36*b^38*c^68*d^6 - 665979977728*a^37*b^37*c^67*d^7 + 4405015347200*a^38*b^36*c^66*d^8 - 22343644610560*a
^39*b^35*c^65*d^9 + 90382763294720*a^40*b^34*c^64*d^10 - 299352929075200*a^41*b^33*c^63*d^11 + 827049291808768
*a^42*b^32*c^62*d^12 - 1932015372861440*a^43*b^31*c^61*d^13 + 3854486254649344*a^44*b^30*c^60*d^14 - 661663572
5053952*a^45*b^29*c^59*d^15 + 9828748597657600*a^46*b^28*c^58*d^16 - 12696914776555520*a^47*b^27*c^57*d^17 + 1
4352507102822400*a^48*b^26*c^56*d^18 - 14371219193200640*a^49*b^25*c^55*d^19 + 13121803937382400*a^50*b^24*c^5
4*d^20 - 11630118384435200*a^51*b^23*c^53*d^21 + 10979630865448960*a^52*b^22*c^52*d^22 - 11630118384435200*a^5
3*b^21*c^51*d^23 + 13121803937382400*a^54*b^20*c^50*d^24 - 14371219193200640*a^55*b^19*c^49*d^25 + 14352507102
822400*a^56*b^18*c^48*d^26 - 12696914776555520*a^57*b^17*c^47*d^27 + 9828748597657600*a^58*b^16*c^46*d^28 - 66
16635725053952*a^59*b^15*c^45*d^29 + 3854486254649344*a^60*b^14*c^44*d^30 - 1932015372861440*a^61*b^13*c^43*d^
31 + 827049291808768*a^62*b^12*c^42*d^32 - 299352929075200*a^63*b^11*c^41*d^33 + 90382763294720*a^64*b^10*c^40
*d^34 - 22343644610560*a^65*b^9*c^39*d^35 + 4405015347200*a^66*b^8*c^38*d^36 - 665979977728*a^67*b^7*c^37*d^37
+ 72498544640*a^68*b^6*c^36*d^38 - 5058330624*a^69*b^5*c^35*d^39 + 169869312*a^70*b^4*c^34*d^40) - 5478285312
*a^32*b^40*c^67*d^5 + 75301650432*a^33*b^39*c^66*d^6 - 660755972096*a^34*b^38*c^65*d^7 + 4157198565376*a^35*b^
37*c^64*d^8 - 19968092536832*a^36*b^36*c^63*d^9 + 76124224225280*a^37*b^35*c^62*d^10 - 236401268359168*a^38*b^
34*c^61*d^11 + 609010175442944*a^39*b^33*c^60*d^12 - 1318618746322944*a^40*b^32*c^59*d^13 + 2422266262192128*a
^41*b^31*c^58*d^14 - 3800365228883968*a^42*b^30*c^57*d^15 + 5115210562535424*a^43*b^29*c^56*d^16 - 59215950997
09440*a^44*b^28*c^55*d^17 + 5899320342609920*a^45*b^27*c^54*d^18 - 5044901346017280*a^46*b^26*c^53*d^19 + 3659
431378944000*a^47*b^25*c^52*d^20 - 2131419914567680*a^48*b^24*c^51*d^21 + 688340293386240*a^49*b^23*c^50*d^22
+ 688340293386240*a^50*b^22*c^49*d^23 - 2131419914567680*a^51*b^21*c^48*d^24 + 3659431378944000*a^52*b^20*c^47
*d^25 - 5044901346017280*a^53*b^19*c^46*d^26 + 5899320342609920*a^54*b^18*c^45*d^27 - 5921595099709440*a^55*b^
17*c^44*d^28 + 5115210562535424*a^56*b^16*c^43*d^29 - 3800365228883968*a^57*b^15*c^42*d^30 + 2422266262192128*
a^58*b^14*c^41*d^31 - 1318618746322944*a^59*b^13*c^40*d^32 + 609010175442944*a^60*b^12*c^39*d^33 - 23640126835
9168*a^61*b^11*c^38*d^34 + 76124224225280*a^62*b^10*c^37*d^35 - 19968092536832*a^63*b^9*c^36*d^36 + 4157198565
376*a^64*b^8*c^35*d^37 - 660755972096*a^65*b^7*c^34*d^38 + 75301650432*a^66*b^6*c^33*d^39 - 5478285312*a^67*b^
5*c^32*d^40 + 191102976*a^68*b^4*c^31*d^41) - x^(1/2)*(970818048*a^29*b^37*c^54*d^12 - 21954447360*a^30*b^36*c
^53*d^13 + 234247707648*a^31*b^35*c^52*d^14 - 1568140904448*a^32*b^34*c^51*d^15 + 7387800533504*a^33*b^33*c^50
*d^16 - 26036469792256*a^34*b^32*c^49*d^17 + 71189396375552*a^35*b^31*c^48*d^18 - 154393382077440*a^36*b^30*c^
47*d^19 + 268607771876352*a^37*b^29*c^46*d^20 - 374590800139776*a^38*b^28*c^45*d^21 + 409764654942208*a^39*b^2
7*c^44*d^22 - 324787154001920*a^40*b^26*c^43*d^23 + 124213059109888*a^41*b^25*c^42*d^24 + 124213059109888*a^42
*b^24*c^41*d^25 - 324787154001920*a^43*b^23*c^40*d^26 + 409764654942208*a^44*b^22*c^39*d^27 - 374590800139776*
a^45*b^21*c^38*d^28 + 268607771876352*a^46*b^20*c^37*d^29 - 154393382077440*a^47*b^19*c^36*d^30 + 711893963755
52*a^48*b^18*c^35*d^31 - 26036469792256*a^49*b^17*c^34*d^32 + 7387800533504*a^50*b^16*c^33*d^33 - 156814090444
8*a^51*b^15*c^32*d^34 + 234247707648*a^52*b^14*c^31*d^35 - 21954447360*a^53*b^13*c^30*d^36 + 970818048*a^54*b^
12*c^29*d^37))*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572
*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 90
1120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 32440
32*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^
24*b*c*d^11))^(1/4) + 4125976704*a^29*b^35*c^49*d^15 - 83112811776*a^30*b^34*c^48*d^16 + 791027410176*a^31*b^3
3*c^47*d^17 - 4734885844224*a^32*b^32*c^46*d^18 + 20014213844608*a^33*b^31*c^45*d^19 - 63580226479104*a^34*b^3
0*c^44*d^20 + 157689244277760*a^35*b^29*c^43*d^21 - 313010180862976*a^36*b^28*c^42*d^22 + 505524473121024*a^37
*b^27*c^41*d^23 - 671337017390592*a^38*b^26*c^40*d^24 + 737444677516800*a^39*b^25*c^39*d^25 - 671337017390592*
a^40*b^24*c^38*d^26 + 505524473121024*a^41*b^23*c^37*d^27 - 313010180862976*a^42*b^22*c^36*d^28 + 157689244277
760*a^43*b^21*c^35*d^29 - 63580226479104*a^44*b^20*c^34*d^30 + 20014213844608*a^45*b^19*c^33*d^31 - 4734885844
224*a^46*b^18*c^32*d^32 + 791027410176*a^47*b^17*c^31*d^33 - 83112811776*a^48*b^16*c^30*d^34 + 4125976704*a^49
*b^15*c^29*d^35))*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49
572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 -
901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 32
44032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152
*a^24*b*c*d^11))^(1/4)*2i + 2*atan((2654208*a^5*b^22*c^38*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 1768
68*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 4915
2*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a
^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*
b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 2654208*a^27*c^16*d^22*x^(1/2)*(-(656
1*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*
b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3
+ 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 +
2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) +
15169032*b^19*c^22*d^8*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2
*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^
10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*
c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^1
5*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 130671792*a*b^18*c^21*d^9*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13
- 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12
- 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 32
44032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 9011
20*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 41877504*a^6*b^21*c^37*d*x^(1/
2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^1
6)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*
c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^
18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d)
)^(5/4) - 41877504*a^26*b*c^17*d^21*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 14
0454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 2
70336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784
704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*
a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 450333432*a^2*b^17*c^20*d^10*x^(1/2)*(-(6561*a^4*d^17 + 835
21*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096
*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^
8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*
c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 784872864*a^3*b
^16*c^19*d^11*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15
- 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^
2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 -
3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 4
9152*a*b^11*c^24*d))^(1/4) + 717087608*a^4*b^15*c^18*d^12*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 1768
68*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 4915
2*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a
^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*
b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 264948264*a^5*b^14*c^17*d^13*x^(1/2)*
(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/
(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^2
2*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*
d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(
1/4) - 264948264*a^6*b^13*c^16*d^14*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 14
0454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 2
70336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784
704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*
a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) + 717087608*a^7*b^12*c^15*d^15*x^(1/2)*(-(6561*a^4*d^17 + 835
21*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096
*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^
8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*
c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 784872864*a^8*b
^11*c^14*d^16*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15
- 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^
2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 -
3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 4
9152*a*b^11*c^24*d))^(1/4) + 450333432*a^9*b^10*c^13*d^17*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 1768
68*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 4915
2*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a
^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*
b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) - 130671792*a^10*b^9*c^12*d^18*x^(1/2)*
(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/
(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^2
2*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*
d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(
1/4) + 15169032*a^11*b^8*c^11*d^19*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140
454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 27
0336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 37847
04*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a
^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) + 304971776*a^7*b^20*c^36*d^2*x^(1/2)*(-(6561*a^4*d^17 + 83521
*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a
^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*
c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^
17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 1359347712*a^8*b^
19*c^35*d^3*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 -
49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2
- 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3
244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 491
52*a*b^11*c^24*d))^(5/4) + 4144791552*a^9*b^18*c^34*d^4*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868
*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*
a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5
*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^
3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 9148891136*a^10*b^17*c^33*d^5*x^(1/2)*(
-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(
4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22
*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d
^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5
/4) + 15081504768*a^11*b^16*c^32*d^6*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 1
40454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 +
270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 378
4704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336
*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 18867290112*a^12*b^15*c^31*d^7*x^(1/2)*(-(6561*a^4*d^17 +
83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4
096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4
*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b
^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 18014928896*
a^13*b^14*c^30*d^8*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*
d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^
23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*
d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^1
0 - 49152*a*b^11*c^24*d))^(5/4) - 13171163136*a^14*b^13*c^29*d^9*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13
- 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12
- 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 32
44032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 9011
20*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 7816740864*a^15*b^12*c^28*d^10
*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b
*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^
3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*
b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c
^24*d))^(5/4) - 5554044928*a^16*b^11*c^27*d^11*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^
3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^
14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20
*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^
9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 7816740864*a^17*b^10*c^26*d^12*x^(1/2)*(-(6561*a
^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^1
2*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2
027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 202
7520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 13
171163136*a^18*b^9*c^25*d^13*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^
2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a
^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6
*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^
2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 18014928896*a^19*b^8*c^24*d^14*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^
4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12
*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^2
1*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*
d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 18867290112*a^20*b^7
*c^23*d^15*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 4
9572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 -
901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 32
44032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 4915
2*a*b^11*c^24*d))^(5/4) + 15081504768*a^21*b^6*c^22*d^16*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 17686
8*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152
*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^
5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b
^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 9148891136*a^22*b^5*c^21*d^17*x^(1/2)*
(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/
(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^2
2*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*
d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(
5/4) + 4144791552*a^23*b^4*c^20*d^18*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 1
40454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 +
270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 378
4704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336
*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) - 1359347712*a^24*b^3*c^19*d^19*x^(1/2)*(-(6561*a^4*d^17 + 8
3521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 40
96*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*
b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^
4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4) + 304971776*a^2
5*b^2*c^18*d^20*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^1
5 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*
d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6
- 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 -
49152*a*b^11*c^24*d))^(5/4))/(32234193*b^17*c^17*d^11 - 4782969*a^17*d^28 - 198040140*a*b^16*c^16*d^12 + 4131
41310*a^2*b^15*c^15*d^13 - 308701404*a^3*b^14*c^14*d^14 + 43224857*a^4*b^13*c^13*d^15 - 15826944*a^5*b^12*c^12
*d^16 - 11894784*a^6*b^11*c^11*d^17 - 5865472*a^7*b^10*c^10*d^18 + 2260992*a^8*b^9*c^9*d^19 + 12484608*a^9*b^8
*c^8*d^20 + 24805376*a^10*b^7*c^7*d^21 + 39223296*a^11*b^6*c^6*d^22 + 55738368*a^12*b^5*c^5*d^23 - 335988081*a
^13*b^4*c^4*d^24 + 384710796*a^14*b^3*c^3*d^25 - 197341758*a^15*b^2*c^2*d^26 + 48892572*a^16*b*c*d^27))*(-(656
1*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*
b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3
+ 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 +
2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4) +
atan((a^5*b^22*c^38*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^
2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*
c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^1
9*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d
^10 - 49152*a*b^11*c^24*d))^(5/4)*2654208i + a^27*c^16*d^22*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 17
6868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49
152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032
*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^
9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*2654208i + b^19*c^22*d^8*x^(1/2)*(-(6
561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(409
6*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^
3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7
+ 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)
*15169032i - a*b^18*c^21*d^9*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^
2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a
^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6
*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^
2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*130671792i - a^6*b^21*c^37*d*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^
4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^1
3*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^
4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8
- 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*41877504i - a^26*b*c^17*d^
21*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3
*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*
a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^
7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11
*c^24*d))^(5/4)*41877504i + a^2*b^17*c^20*d^10*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^
3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^
14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20
*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^
9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*450333432i - a^3*b^16*c^19*d^11*x^(1/2)*(-(6561*a^
4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12
*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 20
27520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027
520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*78487
2864i + a^4*b^15*c^18*d^12*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*
b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2
*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b
^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*
c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*717087608i - a^5*b^14*c^17*d^13*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c
^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^
13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d
^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8
- 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*264948264i - a^6*b^13*c^1
6*d^14*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572
*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901
120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 324403
2*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*
b^11*c^24*d))^(1/4)*264948264i + a^7*b^12*c^15*d^15*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b
^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11
*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7
*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^
16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*717087608i - a^8*b^11*c^14*d^16*x^(1/2)*(-(65
61*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096
*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3
+ 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 +
2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*
784872864i + a^9*b^10*c^13*d^17*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454
*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 27033
6*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*
a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10
*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*450333432i - a^10*b^9*c^12*d^18*x^(1/2)*(-(6561*a^4*d^17 + 83521*
b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^
12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c
^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^1
7*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*130671792i + a^11*b^
8*c^11*d^19*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 -
49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2
- 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3
244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 491
52*a*b^11*c^24*d))^(1/4)*15169032i + a^7*b^20*c^36*d^2*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*
a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a
^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*
b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3
*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*304971776i - a^8*b^19*c^35*d^3*x^(1/2)*(-(
6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(40
96*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d
^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7
+ 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4
)*1359347712i + a^9*b^18*c^34*d^4*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 1404
54*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270
336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 378470
4*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^
10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*4144791552i - a^10*b^17*c^33*d^5*x^(1/2)*(-(6561*a^4*d^17 + 835
21*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096
*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^
8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*
c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*9148891136i + a^1
1*b^16*c^32*d^6*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^1
5 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*
d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6
- 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 -
49152*a*b^11*c^24*d))^(5/4)*15081504768i - a^12*b^15*c^31*d^7*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 -
176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 -
49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244
032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120
*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18867290112i + a^13*b^14*c^30*d^8*
x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*
c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3
*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b
^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^
24*d))^(5/4)*18014928896i - a^14*b^13*c^29*d^9*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^
3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^
14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20
*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^
9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*13171163136i + a^15*b^12*c^28*d^10*x^(1/2)*(-(6561
*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b
^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 +
2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2
027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*78
16740864i - a^16*b^11*c^27*d^11*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454
*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 27033
6*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*
a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10
*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*5554044928i + a^17*b^10*c^26*d^12*x^(1/2)*(-(6561*a^4*d^17 + 8352
1*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*
a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8
*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c
^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*7816740864i - a^18
*b^9*c^25*d^13*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15
- 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d
^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6
- 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 -
49152*a*b^11*c^24*d))^(5/4)*13171163136i + a^19*b^8*c^24*d^14*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 -
176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 -
49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 32440
32*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*
a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18014928896i - a^20*b^7*c^23*d^15*x
^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c
*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*
b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^
5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^2
4*d))^(5/4)*18867290112i + a^21*b^6*c^22*d^16*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3
*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^1
4*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*
d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9
+ 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*15081504768i - a^22*b^5*c^21*d^17*x^(1/2)*(-(6561*a
^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^1
2*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2
027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 202
7520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*9148
891136i + a^23*b^4*c^20*d^18*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^
2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a
^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6
*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^
2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*4144791552i - a^24*b^3*c^19*d^19*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^
4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12
*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^2
1*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*
d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*1359347712i + a^25*b^2
*c^18*d^20*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 4
9572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 -
901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 32
44032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 4915
2*a*b^11*c^24*d))^(5/4)*304971776i)/(32234193*b^17*c^17*d^11 - 4782969*a^17*d^28 - 198040140*a*b^16*c^16*d^12
+ 413141310*a^2*b^15*c^15*d^13 - 308701404*a^3*b^14*c^14*d^14 + 43224857*a^4*b^13*c^13*d^15 - 15826944*a^5*b^1
2*c^12*d^16 - 11894784*a^6*b^11*c^11*d^17 - 5865472*a^7*b^10*c^10*d^18 + 2260992*a^8*b^9*c^9*d^19 + 12484608*a
^9*b^8*c^8*d^20 + 24805376*a^10*b^7*c^7*d^21 + 39223296*a^11*b^6*c^6*d^22 + 55738368*a^12*b^5*c^5*d^23 - 33598
8081*a^13*b^4*c^4*d^24 + 384710796*a^14*b^3*c^3*d^25 - 197341758*a^15*b^2*c^2*d^26 + 48892572*a^16*b*c*d^27))*
(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/
(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^2
2*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*
d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(
1/4)*2i

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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**(7/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)

[Out]

Timed out

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