3.310 \(\int \frac {1}{\sqrt {f x} (d+e x^2) (a+b x^2+c x^4)} \, dx\)

Optimal. Leaf size=866 \[ -\frac {\tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right ) e^{7/4}}{\sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}+1\right ) e^{7/4}}{\sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {\log \left (\sqrt {e} \sqrt {f} x+\sqrt {d} \sqrt {f}-\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right ) e^{7/4}}{2 \sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {\log \left (\sqrt {e} \sqrt {f} x+\sqrt {d} \sqrt {f}+\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right ) e^{7/4}}{2 \sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (\sqrt {b^2-4 a c}-b\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (\sqrt {b^2-4 a c}-b\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}} \]

[Out]

-1/2*e^(7/4)*arctan(1-e^(1/4)*2^(1/2)*(f*x)^(1/2)/d^(1/4)/f^(1/2))/d^(3/4)/(a*e^2-b*d*e+c*d^2)*2^(1/2)/f^(1/2)
+1/2*e^(7/4)*arctan(1+e^(1/4)*2^(1/2)*(f*x)^(1/2)/d^(1/4)/f^(1/2))/d^(3/4)/(a*e^2-b*d*e+c*d^2)*2^(1/2)/f^(1/2)
-1/4*e^(7/4)*ln(d^(1/2)*f^(1/2)+x*e^(1/2)*f^(1/2)-d^(1/4)*e^(1/4)*2^(1/2)*(f*x)^(1/2))/d^(3/4)/(a*e^2-b*d*e+c*
d^2)*2^(1/2)/f^(1/2)+1/4*e^(7/4)*ln(d^(1/2)*f^(1/2)+x*e^(1/2)*f^(1/2)+d^(1/4)*e^(1/4)*2^(1/2)*(f*x)^(1/2))/d^(
3/4)/(a*e^2-b*d*e+c*d^2)*2^(1/2)/f^(1/2)+1/2*c^(3/4)*arctan(2^(1/4)*c^(1/4)*(f*x)^(1/2)/(-b-(-4*a*c+b^2)^(1/2)
)^(1/4)/f^(1/2))*(2*c*d-e*(b-(-4*a*c+b^2)^(1/2)))*2^(3/4)/(a*e^2-b*d*e+c*d^2)/(-b-(-4*a*c+b^2)^(1/2))^(3/4)/(-
4*a*c+b^2)^(1/2)/f^(1/2)+1/2*c^(3/4)*arctanh(2^(1/4)*c^(1/4)*(f*x)^(1/2)/(-b-(-4*a*c+b^2)^(1/2))^(1/4)/f^(1/2)
)*(2*c*d-e*(b-(-4*a*c+b^2)^(1/2)))*2^(3/4)/(a*e^2-b*d*e+c*d^2)/(-b-(-4*a*c+b^2)^(1/2))^(3/4)/(-4*a*c+b^2)^(1/2
)/f^(1/2)-1/2*c^(3/4)*arctan(2^(1/4)*c^(1/4)*(f*x)^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(1/4)/f^(1/2))*(2*c*d-e*(b+(-
4*a*c+b^2)^(1/2)))*2^(3/4)/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(3/4)/f^(1/2)-1/2*c^
(3/4)*arctanh(2^(1/4)*c^(1/4)*(f*x)^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(1/4)/f^(1/2))*(2*c*d-e*(b+(-4*a*c+b^2)^(1/2
)))*2^(3/4)/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(3/4)/f^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 2.51, antiderivative size = 866, normalized size of antiderivative = 1.00, number of steps used = 19, number of rules used = 12, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.387, Rules used = {1269, 1424, 211, 1165, 628, 1162, 617, 204, 1422, 212, 208, 205} \[ -\frac {\tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right ) e^{7/4}}{\sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}+1\right ) e^{7/4}}{\sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {\log \left (\sqrt {e} \sqrt {f} x+\sqrt {d} \sqrt {f}-\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right ) e^{7/4}}{2 \sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {\log \left (\sqrt {e} \sqrt {f} x+\sqrt {d} \sqrt {f}+\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right ) e^{7/4}}{2 \sqrt {2} d^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (\sqrt {b^2-4 a c}-b\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (\sqrt {b^2-4 a c}-b\right )^{3/4} \left (c d^2-b e d+a e^2\right ) \sqrt {f}} \]

Antiderivative was successfully verified.

[In]

Int[1/(Sqrt[f*x]*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]

[Out]

(c^(3/4)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b - Sqrt[b^2 - 4*a*c])^(1/4
)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (c^(
3/4)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b + Sqrt[b^2 - 4*a*c])^(1/4)*Sq
rt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (e^(7/4)
*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[f*x])/(d^(1/4)*Sqrt[f])])/(Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f])
+ (e^(7/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[f*x])/(d^(1/4)*Sqrt[f])])/(Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)
*Sqrt[f]) + (c^(3/4)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b - Sqrt[b^2 -
4*a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sq
rt[f]) - (c^(3/4)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b + Sqrt[b^2 - 4*
a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[
f]) - (e^(7/4)*Log[Sqrt[d]*Sqrt[f] + Sqrt[e]*Sqrt[f]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[f*x]])/(2*Sqrt[2]*d^(3/4
)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) + (e^(7/4)*Log[Sqrt[d]*Sqrt[f] + Sqrt[e]*Sqrt[f]*x + Sqrt[2]*d^(1/4)*e^(1/4
)*Sqrt[f*x]])/(2*Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f])

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 205

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

Rule 208

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

Rule 211

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

Rule 212

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

Rule 1269

Int[((f_.)*(x_))^(m_)*((d_) + (e_.)*(x_)^2)^(q_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> With
[{k = Denominator[m]}, Dist[k/f, Subst[Int[x^(k*(m + 1) - 1)*(d + (e*x^(2*k))/f^2)^q*(a + (b*x^(2*k))/f^k + (c
*x^(4*k))/f^4)^p, x], x, (f*x)^(1/k)], x]] /; FreeQ[{a, b, c, d, e, f, p, q}, x] && NeQ[b^2 - 4*a*c, 0] && Fra
ctionQ[m] && IntegerQ[p]

Rule 1422

Int[((d_) + (e_.)*(x_)^(n_))/((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_)), x_Symbol] :> With[{q = Rt[b^2 - 4*a*
c, 2]}, Dist[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^n), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), In
t[1/(b/2 + q/2 + c*x^n), x], x]] /; FreeQ[{a, b, c, d, e, n}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && NeQ
[c*d^2 - b*d*e + a*e^2, 0] && (PosQ[b^2 - 4*a*c] ||  !IGtQ[n/2, 0])

Rule 1424

Int[((d_) + (e_.)*(x_)^(n_))^(q_)/((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_)), x_Symbol] :> Int[ExpandIntegran
d[(d + e*x^n)^q/(a + b*x^n + c*x^(2*n)), x], x] /; FreeQ[{a, b, c, d, e, n}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4
*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[q]

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {f x} \left (d+e x^2\right ) \left (a+b x^2+c x^4\right )} \, dx &=\frac {2 \operatorname {Subst}\left (\int \frac {1}{\left (d+\frac {e x^4}{f^2}\right ) \left (a+\frac {b x^4}{f^2}+\frac {c x^8}{f^4}\right )} \, dx,x,\sqrt {f x}\right )}{f}\\ &=\frac {2 \operatorname {Subst}\left (\int \left (\frac {e^2 f^2}{\left (c d^2-b d e+a e^2\right ) \left (d f^2+e x^4\right )}+\frac {c d f^4-b e f^4-c e f^2 x^4}{\left (c d^2-b d e+a e^2\right ) \left (a f^4+b f^2 x^4+c x^8\right )}\right ) \, dx,x,\sqrt {f x}\right )}{f}\\ &=\frac {2 \operatorname {Subst}\left (\int \frac {c d f^4-b e f^4-c e f^2 x^4}{a f^4+b f^2 x^4+c x^8} \, dx,x,\sqrt {f x}\right )}{\left (c d^2-b d e+a e^2\right ) f}+\frac {\left (2 e^2 f\right ) \operatorname {Subst}\left (\int \frac {1}{d f^2+e x^4} \, dx,x,\sqrt {f x}\right )}{c d^2-b d e+a e^2}\\ &=\frac {e^2 \operatorname {Subst}\left (\int \frac {\sqrt {d} f-\sqrt {e} x^2}{d f^2+e x^4} \, dx,x,\sqrt {f x}\right )}{\sqrt {d} \left (c d^2-b d e+a e^2\right )}+\frac {e^2 \operatorname {Subst}\left (\int \frac {\sqrt {d} f+\sqrt {e} x^2}{d f^2+e x^4} \, dx,x,\sqrt {f x}\right )}{\sqrt {d} \left (c d^2-b d e+a e^2\right )}-\frac {\left (c \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) f\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b f^2}{2}+\frac {1}{2} \sqrt {b^2-4 a c} f^2+c x^4} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) f\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b f^2}{2}-\frac {1}{2} \sqrt {b^2-4 a c} f^2+c x^4} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \left (c d^2-b d e+a e^2\right )}\\ &=\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {d} f}{\sqrt {e}}-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f} x}{\sqrt [4]{e}}+x^2} \, dx,x,\sqrt {f x}\right )}{2 \sqrt {d} \left (c d^2-b d e+a e^2\right )}+\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {d} f}{\sqrt {e}}+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f} x}{\sqrt [4]{e}}+x^2} \, dx,x,\sqrt {f x}\right )}{2 \sqrt {d} \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}} f-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \sqrt {-b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}+\frac {\left (c \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}} f+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \sqrt {-b-\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}-\frac {\left (c \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}} f-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \sqrt {-b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}-\frac {\left (c \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}} f+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {f x}\right )}{\sqrt {b^2-4 a c} \sqrt {-b+\sqrt {b^2-4 a c}} \left (c d^2-b d e+a e^2\right )}-\frac {e^{7/4} \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f}}{\sqrt [4]{e}}+2 x}{-\frac {\sqrt {d} f}{\sqrt {e}}-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f} x}{\sqrt [4]{e}}-x^2} \, dx,x,\sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {e^{7/4} \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f}}{\sqrt [4]{e}}-2 x}{-\frac {\sqrt {d} f}{\sqrt {e}}+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {f} x}{\sqrt [4]{e}}-x^2} \, dx,x,\sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}\\ &=\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {e^{7/4} \log \left (\sqrt {d} \sqrt {f}+\sqrt {e} \sqrt {f} x-\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {e^{7/4} \log \left (\sqrt {d} \sqrt {f}+\sqrt {e} \sqrt {f} x+\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {e^{7/4} \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right )}{\sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {e^{7/4} \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right )}{\sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}\\ &=\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {e^{7/4} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right )}{\sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {e^{7/4} \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{e} \sqrt {f x}}{\sqrt [4]{d} \sqrt {f}}\right )}{\sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {c^{3/4} \left (2 c d-\left (b-\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {c^{3/4} \left (2 c d-\left (b+\sqrt {b^2-4 a c}\right ) e\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {f x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}} \sqrt {f}}\right )}{\sqrt [4]{2} \sqrt {b^2-4 a c} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}-\frac {e^{7/4} \log \left (\sqrt {d} \sqrt {f}+\sqrt {e} \sqrt {f} x-\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}+\frac {e^{7/4} \log \left (\sqrt {d} \sqrt {f}+\sqrt {e} \sqrt {f} x+\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {f x}\right )}{2 \sqrt {2} d^{3/4} \left (c d^2-b d e+a e^2\right ) \sqrt {f}}\\ \end {align*}

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Mathematica [C]  time = 0.38, size = 267, normalized size = 0.31 \[ \frac {\sqrt {x} \left (\sqrt {2} e^{7/4} \left (-\log \left (-\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {x}+\sqrt {d}+\sqrt {e} x\right )+\log \left (\sqrt {2} \sqrt [4]{d} \sqrt [4]{e} \sqrt {x}+\sqrt {d}+\sqrt {e} x\right )-2 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{e} \sqrt {x}}{\sqrt [4]{d}}\right )+2 \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{e} \sqrt {x}}{\sqrt [4]{d}}+1\right )\right )-2 d^{3/4} \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\& ,\frac {\text {$\#$1}^4 c e \log \left (\sqrt {x}-\text {$\#$1}\right )+b e \log \left (\sqrt {x}-\text {$\#$1}\right )-c d \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\& \right ]\right )}{4 d^{3/4} \sqrt {f x} \left (e (a e-b d)+c d^2\right )} \]

Antiderivative was successfully verified.

[In]

Integrate[1/(Sqrt[f*x]*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]

[Out]

(Sqrt[x]*(Sqrt[2]*e^(7/4)*(-2*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sq
rt[x])/d^(1/4)] - Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] + Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e
^(1/4)*Sqrt[x] + Sqrt[e]*x]) - 2*d^(3/4)*RootSum[a + b*#1^4 + c*#1^8 & , (-(c*d*Log[Sqrt[x] - #1]) + b*e*Log[S
qrt[x] - #1] + c*e*Log[Sqrt[x] - #1]*#1^4)/(b*#1^3 + 2*c*#1^7) & ]))/(4*d^(3/4)*(c*d^2 + e*(-(b*d) + a*e))*Sqr
t[f*x])

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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/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x, algorithm="fricas")

[Out]

Timed out

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x, algorithm="giac")

[Out]

sage2

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maple [C]  time = 0.10, size = 336, normalized size = 0.39 \[ \frac {f \left (-\RootOf \left (c \,\textit {\_Z}^{8}+b \,f^{2} \textit {\_Z}^{4}+a \,f^{4}\right )^{4} c e -b e \,f^{2}+c d \,f^{2}\right ) \ln \left (-\RootOf \left (c \,\textit {\_Z}^{8}+b \,f^{2} \textit {\_Z}^{4}+a \,f^{4}\right )+\sqrt {f x}\right )}{2 \left (a \,e^{2}-d e b +c \,d^{2}\right ) \left (2 \RootOf \left (c \,\textit {\_Z}^{8}+b \,f^{2} \textit {\_Z}^{4}+a \,f^{4}\right )^{7} c +\RootOf \left (c \,\textit {\_Z}^{8}+b \,f^{2} \textit {\_Z}^{4}+a \,f^{4}\right )^{3} b \,f^{2}\right )}+\frac {\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}} \sqrt {2}\, e^{2} \arctan \left (\frac {\sqrt {2}\, \sqrt {f x}}{\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}}}-1\right )}{2 \left (a \,e^{2}-d e b +c \,d^{2}\right ) d f}+\frac {\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}} \sqrt {2}\, e^{2} \arctan \left (\frac {\sqrt {2}\, \sqrt {f x}}{\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}}}+1\right )}{2 \left (a \,e^{2}-d e b +c \,d^{2}\right ) d f}+\frac {\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}} \sqrt {2}\, e^{2} \ln \left (\frac {f x +\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}} \sqrt {f x}\, \sqrt {2}+\sqrt {\frac {d \,f^{2}}{e}}}{f x -\left (\frac {d \,f^{2}}{e}\right )^{\frac {1}{4}} \sqrt {f x}\, \sqrt {2}+\sqrt {\frac {d \,f^{2}}{e}}}\right )}{4 \left (a \,e^{2}-d e b +c \,d^{2}\right ) d f} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x)

[Out]

1/2*f/(a*e^2-b*d*e+c*d^2)*sum((-_R^4*c*e-b*e*f^2+c*d*f^2)/(2*_R^7*c+_R^3*b*f^2)*ln((f*x)^(1/2)-_R),_R=RootOf(_
Z^8*c+_Z^4*b*f^2+a*f^4))+1/4/f*e^2/(a*e^2-b*d*e+c*d^2)*(d*f^2/e)^(1/4)/d*2^(1/2)*ln((f*x+(d*f^2/e)^(1/4)*(f*x)
^(1/2)*2^(1/2)+(d*f^2/e)^(1/2))/(f*x-(d*f^2/e)^(1/4)*(f*x)^(1/2)*2^(1/2)+(d*f^2/e)^(1/2)))+1/2/f*e^2/(a*e^2-b*
d*e+c*d^2)*(d*f^2/e)^(1/4)/d*2^(1/2)*arctan(2^(1/2)/(d*f^2/e)^(1/4)*(f*x)^(1/2)+1)+1/2/f*e^2/(a*e^2-b*d*e+c*d^
2)*(d*f^2/e)^(1/4)/d*2^(1/2)*arctan(2^(1/2)/(d*f^2/e)^(1/4)*(f*x)^(1/2)-1)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {2 \, e^{2} \sqrt {x}}{c d^{3} \sqrt {f} - b d^{2} e \sqrt {f} + a d e^{2} \sqrt {f}} + \frac {\frac {2 \, \sqrt {2} e^{2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} d^{\frac {1}{4}} e^{\frac {1}{4}} + 2 \, \sqrt {e} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {d} \sqrt {e}}}\right )}{\sqrt {d} \sqrt {\sqrt {d} \sqrt {e}}} + \frac {2 \, \sqrt {2} e^{2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} d^{\frac {1}{4}} e^{\frac {1}{4}} - 2 \, \sqrt {e} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {d} \sqrt {e}}}\right )}{\sqrt {d} \sqrt {\sqrt {d} \sqrt {e}}} + \frac {\sqrt {2} e^{\frac {7}{4}} \log \left (\sqrt {2} d^{\frac {1}{4}} e^{\frac {1}{4}} \sqrt {x} + \sqrt {e} x + \sqrt {d}\right )}{d^{\frac {3}{4}}} - \frac {\sqrt {2} e^{\frac {7}{4}} \log \left (-\sqrt {2} d^{\frac {1}{4}} e^{\frac {1}{4}} \sqrt {x} + \sqrt {e} x + \sqrt {d}\right )}{d^{\frac {3}{4}}}}{4 \, {\left (c d^{2} \sqrt {f} - b d e \sqrt {f} + a e^{2} \sqrt {f}\right )}} + \frac {2 \, \sqrt {x}}{a d \sqrt {f}} + \int -\frac {{\left (c^{2} d - b c e\right )} x^{\frac {7}{2}} + {\left (b c d - b^{2} e + a c e\right )} x^{\frac {3}{2}}}{a^{3} e^{2} \sqrt {f} + {\left (a^{2} c e^{2} \sqrt {f} + {\left (c^{2} d^{2} \sqrt {f} - b c d e \sqrt {f}\right )} a\right )} x^{4} + {\left (c d^{2} \sqrt {f} - b d e \sqrt {f}\right )} a^{2} + {\left (a^{2} b e^{2} \sqrt {f} + {\left (b c d^{2} \sqrt {f} - b^{2} d e \sqrt {f}\right )} a\right )} x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x, algorithm="maxima")

[Out]

-2*e^2*sqrt(x)/(c*d^3*sqrt(f) - b*d^2*e*sqrt(f) + a*d*e^2*sqrt(f)) + 1/4*(2*sqrt(2)*e^2*arctan(1/2*sqrt(2)*(sq
rt(2)*d^(1/4)*e^(1/4) + 2*sqrt(e)*sqrt(x))/sqrt(sqrt(d)*sqrt(e)))/(sqrt(d)*sqrt(sqrt(d)*sqrt(e))) + 2*sqrt(2)*
e^2*arctan(-1/2*sqrt(2)*(sqrt(2)*d^(1/4)*e^(1/4) - 2*sqrt(e)*sqrt(x))/sqrt(sqrt(d)*sqrt(e)))/(sqrt(d)*sqrt(sqr
t(d)*sqrt(e))) + sqrt(2)*e^(7/4)*log(sqrt(2)*d^(1/4)*e^(1/4)*sqrt(x) + sqrt(e)*x + sqrt(d))/d^(3/4) - sqrt(2)*
e^(7/4)*log(-sqrt(2)*d^(1/4)*e^(1/4)*sqrt(x) + sqrt(e)*x + sqrt(d))/d^(3/4))/(c*d^2*sqrt(f) - b*d*e*sqrt(f) +
a*e^2*sqrt(f)) + 2*sqrt(x)/(a*d*sqrt(f)) + integrate(-((c^2*d - b*c*e)*x^(7/2) + (b*c*d - b^2*e + a*c*e)*x^(3/
2))/(a^3*e^2*sqrt(f) + (a^2*c*e^2*sqrt(f) + (c^2*d^2*sqrt(f) - b*c*d*e*sqrt(f))*a)*x^4 + (c*d^2*sqrt(f) - b*d*
e*sqrt(f))*a^2 + (a^2*b*e^2*sqrt(f) + (b*c*d^2*sqrt(f) - b^2*d*e*sqrt(f))*a)*x^2), x)

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mupad [B]  time = 6.84, size = 43112, normalized size = 49.78 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((f*x)^(1/2)*(d + e*x^2)*(a + b*x^2 + c*x^4)),x)

[Out]

symsum(log(-root(8388608*a^7*b*c^11*d^18*e*f^6*h^12 - 513802240*a^10*b^2*c^7*d^11*e^8*f^6*h^12 - 381681664*a^1
1*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^2*c^8*d^13*e^6*f^6*h^12 - 300941312*a^9*b^5*c^5*d^10*e^9*f^6*h^1
2 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 + 293601280*a^10*b^3*c^6*d^10*e^9*f^6*h^12 + 293601280*a^9*b^3*c^7
*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^8*e^11*f^6*h^12 - 168820736*a^7*b^5*c^7*d^14*e^5*f^6*h^12 + 1660
68224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 146800640*a^12*b^2*c^5*d^7*e^12*f^6*h^12 - 146800640*a^8*b^2*c^9*d^15*e^
4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f^6*h^12 + 124780544*a^8*b^4*c^7*d^13*e^6*f^6*h^12 + 119275520*a^
9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b^3*c^5*d^8*e^11*f^6*h^12 + 117440512*a^8*b^3*c^8*d^14*e^5*f^6*h^
12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 + 102760448*a^7*b^6*c^6*d^13*e^6*f^6*h^12 + 91750400*a^11*b^4*c^4
*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15*e^4*f^6*h^12 - 71065600*a^7*b^8*c^4*d^11*e^8*f^6*h^12 - 5344460
8*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 40370176*a^9*b^7*c^3*d^8*e^11*f^6*h
^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 - 36700160*a^11*b^5*c^3*d^6*e^13*f^6*h^12 - 36700160*a^6*b^5*c^8*
d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*e^9*f^6*h^12 + 34078720*a^7*b^7*c^5*d^12*e^7*f^6*h^12 + 26214400
*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 22118400*a^7*b^9*c^3*d^10*e^9*f^6*h
^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 - 20971520*a^13*b^2*c^4*d^5*e^14*f^6*h^12 - 20971520*a^7*b^2*c^10
*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6*e^13*f^6*h^12 + 18350080*a^5*b^7*c^7*d^16*e^3*f^6*h^12 - 166297
60*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^5*b^8*c^6*d^15*e^4*f^6*h^12 - 10485760*a^11*b^6*c^2*d^5*e^14*f^6
*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12 + 9175040*a^10*b^6*c^3*d^7*e^12*f^6*h^12 + 9175040*a^6*b^6*c^7*
d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e^15*f^6*h^12 + 5619712*a^7*b^10*c^2*d^9*e^10*f^6*h^12 + 5619712*
a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b^11*c^2*d^10*e^9*f^6*h^12 - 5570560*a^5*b^11*c^3*d^12*e^7*f^6*h^
12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4358144*a^5*b^9*c^5*d^14*e^5*f^6*h^12 + 4259840*a^6*b^10*c^3*d^11
*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*f^6*h^12 - 3440640*a^4*b^9*c^6*d^16*e^3*f^6*h^12 + 3145728*a^12*
b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c^4*d^14*e^5*f^6*h^12 + 1802240*a^4*b^8*c^7*d^17*e^2*f^6*h^12 + 1
556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 1048576*a^14*b^2*c^3*d^3*e^16*f^6*h^12 + 688128*a^4*b^12*c^3*d^13*e^6*
f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^12 - 286720*a^3*b^12*c^4*d^15*e^4*f^6*h^12 + 229376*a^3*b^13*c^3
*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*e^3*f^6*h^12 + 163840*a^4*b^13*c^2*d^12*e^7*f^6*h^12 - 114688*a^
3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10*c^6*d^17*e^2*f^6*h^12 + 293601280*a^11*b*c^7*d^10*e^9*f^6*h^12
+ 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176160768*a^12*b*c^6*d^8*e^11*f^6*h^12 + 176160768*a^9*b*c^9*d^14*e
^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6*h^12 + 58720256*a^8*b*c^10*d^16*e^3*f^6*h^12 + 8388608*a^14*b*c
^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^18*e*f^6*h^12 + 3899392*a^8*b^10*c*d^7*e^12*f^6*h^12 - 3440640*a
^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c^9*d^18*e*f^6*h^12 - 2523136*a^7*b^11*c*d^8*e^11*f^6*h^12 + 1802
240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*b^12*c*d^9*e^10*f^6*h^12 - 524288*a^11*b^7*c*d^4*e^15*f^6*h^12 -
524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a^5*b^13*c*d^10*e^9*f^6*h^12 - 163840*a^4*b^14*c*d^11*e^8*f^6*h^1
2 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768*a^3*b^15*c*d^12*e^7*f^6*h^12 + 32768*a^3*b^9*c^7*d^18*e*f^6*h^1
2 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 - 58720256*a^12*c^7*d^9*e^10*f^6*h^12 - 58720256*a^10*c^9*d^13*e^6*f^6
*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^12 - 29360128*a^9*c^10*d^15*e^4*f^6*h^12 - 8388608*a^14*c^5*d^5*e^14*
f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12 - 1048576*a^15*c^4*d^3*e^16*f^6*h^12 - 286720*a^7*b^12*d^7*e^12*
f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 + 229376*a^6*b^13*d^8*e^11*f^6*h^12 - 114688*a^9*b^10*d^5*e^14*f^
6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 32768*a^10*b^9*d^4*e^15*f^6*h^12 + 32768*a^4*b^15*d^10*e^9*f^6*h^
12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^3*b^16*d^11*e^8*f^6*h^12 + 1048576*a^6*b^2*c^11*d^19*f^6*h^12 -
393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^8*c^8*d^19*f^6*h^12 - 1048576
*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14*e*f^4*h^8 - 16384*a^7*b^7*c*
d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6*f^4*h^8 - 1865728*a^6*b^3*c^6*d^7
*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7*f^4*h^8 + 1584384*a^5*b^5*c^
5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^9*e^6*f^4*h^8 - 1261568*a^4*b
^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c^5*d^5*e^10*f^4*h^8 + 1106176
*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b^7*c^6*d^11*e^4*f^4*h^8 - 795
648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2*b^6*c^7*d^12*e^3*f^4*h^8 + 6
86080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*a^8*b^3*c^4*d^3*e^12*f^4*h^8
+ 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 441856*a^6*b^5*c^4*d^5*e^10*f^4*
h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 - 366592*a^6*b^6*c^3*d^4*e^11*f
^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8 - 348672*a^2*b^5*c^8*d^13*e^2
*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8 + 294912*a^8*b^4*c^3*d^2*e^13*f^4*h^8 + 210944*a^4*b^3*c^8*d^11
*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^4*h^8 - 131072*a^9*b^2*c^4*d^
2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^5*f^4*h^8 - 104448*a^2*b^10*c
^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e^12*f^4*h^8 - 74240*a^4*b^9*c
^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*e^8*f^4*h^8 + 36864*a^5*b^7*c
^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*e^12*f^4*h^8 + 909312*a^8*b*c
^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^12*f^4*h^8 - 651264*a^5*b*c^9*d^11*e^4*f^4*h^8 - 573440*a^6*b*c^8
*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f^4*h^8 + 211456*a*b^9*c^5*d^1
1*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^4*h^8 - 157696*a*b^10*c^4*d^1
0*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4*h^8 + 92160*a^2*b^4*c^9*d^14
*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4*h^8 + 23552*a^6*b^8*c*d^2*e^13*f^
4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 9472*a^5*b^9*c*d^3*e^12*f^4*h^
8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^11*c^4*d^11*e^4*f^4*h^8 + 1433
6*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9*e^6*f^4*h^8 - 7168*b^9*c^6*d
^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^8 - 262144*a^10*c^5*d^2*e^13*
f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 98304*a^5*c^10*d^12*e^3*f^4*h^8 + 65536*a^6*c^9*d^10*e^5*f^4*h^8 -
1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^3*e^12*f^4*h^8 + 768*a^3*b^12
*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*h^8 - 10240*a^2*b^3*c^10*d^15
*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*c^11*d^14*e*f^4*h^8 + 1024*a^
6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8 + 12288*a^3*b*c^11*d^15*f^4*h
^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15*f^4*h^8 - 256*b^7*c^8*d^15*f
^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^8*e^3*f^2*h^4 + 11520*a^3*b^3
*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^8*f^2*h^4 + 3200*a^2*b^4*c^5*
d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^4 - 10880*a^3*b^4*c^4*d*e^10*
f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 4672*a^2*b^6*c^3*d*e^10*f^2*h^4
+ 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*d^3*e^8*f^2*h^4 + 192*a^2*b*c
^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^4 + 64*a*b^3*c^7*d^6*e^5*f^2*
h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^8*f^2*h^4 + 64*b^3*c^8*d^8*e^
3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^7*d^3*e^8*f^2*h^4 - 96*a^2*c^
9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h^4 + 3696*a^3*b^5*c^3*e^11*f^2*h^4
- 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^2*f^2*h^4 + 1792*a^5*b*c^5*e^
11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^11*f^2*h^4 - 16*c^11*d^11*f^2
*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k)*(root(8388608*a^7*b*c^11*d^18*e*f^6*h^12 - 513802240*a^10*b^2*c^7
*d^11*e^8*f^6*h^12 - 381681664*a^11*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^2*c^8*d^13*e^6*f^6*h^12 - 3009
41312*a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 + 293601280*a^10*b^3*c^6*d^10*e^
9*f^6*h^12 + 293601280*a^9*b^3*c^7*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^8*e^11*f^6*h^12 - 168820736*a^
7*b^5*c^7*d^14*e^5*f^6*h^12 + 166068224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 146800640*a^12*b^2*c^5*d^7*e^12*f^6*h^
12 - 146800640*a^8*b^2*c^9*d^15*e^4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f^6*h^12 + 124780544*a^8*b^4*c^
7*d^13*e^6*f^6*h^12 + 119275520*a^9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b^3*c^5*d^8*e^11*f^6*h^12 + 117
440512*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 + 102760448*a^7*b^6*c^6*d^13*e^
6*f^6*h^12 + 91750400*a^11*b^4*c^4*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15*e^4*f^6*h^12 - 71065600*a^7*b
^8*c^4*d^11*e^8*f^6*h^12 - 53444608*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 4
0370176*a^9*b^7*c^3*d^8*e^11*f^6*h^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 - 36700160*a^11*b^5*c^3*d^6*e^1
3*f^6*h^12 - 36700160*a^6*b^5*c^8*d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*e^9*f^6*h^12 + 34078720*a^7*b^
7*c^5*d^12*e^7*f^6*h^12 + 26214400*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 2
2118400*a^7*b^9*c^3*d^10*e^9*f^6*h^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 - 20971520*a^13*b^2*c^4*d^5*e^1
4*f^6*h^12 - 20971520*a^7*b^2*c^10*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6*e^13*f^6*h^12 + 18350080*a^5*
b^7*c^7*d^16*e^3*f^6*h^12 - 16629760*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^5*b^8*c^6*d^15*e^4*f^6*h^12 -
10485760*a^11*b^6*c^2*d^5*e^14*f^6*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12 + 9175040*a^10*b^6*c^3*d^7*e^
12*f^6*h^12 + 9175040*a^6*b^6*c^7*d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e^15*f^6*h^12 + 5619712*a^7*b^1
0*c^2*d^9*e^10*f^6*h^12 + 5619712*a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b^11*c^2*d^10*e^9*f^6*h^12 - 55
70560*a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4358144*a^5*b^9*c^5*d^14*e^5*f^
6*h^12 + 4259840*a^6*b^10*c^3*d^11*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*f^6*h^12 - 3440640*a^4*b^9*c^6
*d^16*e^3*f^6*h^12 + 3145728*a^12*b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c^4*d^14*e^5*f^6*h^12 + 1802240
*a^4*b^8*c^7*d^17*e^2*f^6*h^12 + 1556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 1048576*a^14*b^2*c^3*d^3*e^16*f^6*h^
12 + 688128*a^4*b^12*c^3*d^13*e^6*f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^12 - 286720*a^3*b^12*c^4*d^15*
e^4*f^6*h^12 + 229376*a^3*b^13*c^3*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*e^3*f^6*h^12 + 163840*a^4*b^13
*c^2*d^12*e^7*f^6*h^12 - 114688*a^3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10*c^6*d^17*e^2*f^6*h^12 + 29360
1280*a^11*b*c^7*d^10*e^9*f^6*h^12 + 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176160768*a^12*b*c^6*d^8*e^11*f^6
*h^12 + 176160768*a^9*b*c^9*d^14*e^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6*h^12 + 58720256*a^8*b*c^10*d^
16*e^3*f^6*h^12 + 8388608*a^14*b*c^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^18*e*f^6*h^12 + 3899392*a^8*b^
10*c*d^7*e^12*f^6*h^12 - 3440640*a^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c^9*d^18*e*f^6*h^12 - 2523136*a
^7*b^11*c*d^8*e^11*f^6*h^12 + 1802240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*b^12*c*d^9*e^10*f^6*h^12 - 524
288*a^11*b^7*c*d^4*e^15*f^6*h^12 - 524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a^5*b^13*c*d^10*e^9*f^6*h^12 -
163840*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768*a^3*b^15*c*d^12*e^7*f^6*h^12
+ 32768*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 - 58720256*a^12*c^7*d^9*e^10*f^6*h^1
2 - 58720256*a^10*c^9*d^13*e^6*f^6*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^12 - 29360128*a^9*c^10*d^15*e^4*f^6
*h^12 - 8388608*a^14*c^5*d^5*e^14*f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12 - 1048576*a^15*c^4*d^3*e^16*f^
6*h^12 - 286720*a^7*b^12*d^7*e^12*f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 + 229376*a^6*b^13*d^8*e^11*f^6*
h^12 - 114688*a^9*b^10*d^5*e^14*f^6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 32768*a^10*b^9*d^4*e^15*f^6*h^1
2 + 32768*a^4*b^15*d^10*e^9*f^6*h^12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^3*b^16*d^11*e^8*f^6*h^12 + 104
8576*a^6*b^2*c^11*d^19*f^6*h^12 - 393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a
^3*b^8*c^8*d^19*f^6*h^12 - 1048576*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8
*d^14*e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6
*f^4*h^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^
8*e^7*f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e^5*f^4*h^8 - 1433600*a^5*b^3*c
^7*d^9*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d^12*e^3*f^4*h^8 - 1110016*a^7*
b^3*c^5*d^5*e^10*f^4*h^8 + 1106176*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*
a^2*b^7*c^6*d^11*e^4*f^4*h^8 - 795648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b^8*c^4*d^8*e^7*f^4*h^8 + 71475
2*a^2*b^6*c^7*d^12*e^3*f^4*h^8 + 686080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 59
5968*a^8*b^3*c^4*d^3*e^12*f^4*h^8 + 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096*a^2*b^8*c^5*d^10*e^5*f^4*h^8
+ 441856*a^6*b^5*c^4*d^5*e^10*f^4*h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376832*a^4*b^2*c^9*d^12*e^3*f^4*h
^8 - 366592*a^6*b^6*c^3*d^4*e^11*f^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4
*h^8 - 348672*a^2*b^5*c^8*d^13*e^2*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8 + 294912*a^8*b^4*c^3*d^2*e^13
*f^4*h^8 + 210944*a^4*b^3*c^8*d^11*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e
^8*f^4*h^8 - 131072*a^9*b^2*c^4*d^2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f^4*h^8 - 129024*a^3*b^6*c^6*d^
10*e^5*f^4*h^8 - 104448*a^2*b^10*c^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*
d^3*e^12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2
*d^7*e^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2
*d^3*e^12*f^4*h^8 + 909312*a^8*b*c^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^12*f^4*h^8 - 651264*a^5*b*c^9*d
^11*e^4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f^4*h^8 + 217088*a^7*b*c^7*d^7*
e^8*f^4*h^8 + 211456*a*b^9*c^5*d^11*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4*h^8 - 172032*a*b^8*c^6*d^12*e
^3*f^4*h^8 - 157696*a*b^10*c^4*d^10*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^1
4*f^4*h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4
*h^8 + 23552*a^6*b^8*c*d^2*e^13*f^4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13312*a^4*b^10*c*d^4*e^11*f^4*h^
8 - 9472*a^5*b^9*c*d^3*e^12*f^4*h^8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2*b^12*c*d^6*e^9*f^4*h^8 - 1792
0*b^11*c^4*d^11*e^4*f^4*h^8 + 14336*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^
2*d^9*e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f
^4*h^8 - 262144*a^10*c^5*d^2*e^13*f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 98304*a^5*c^10*d^12*e^3*f^4*h^8 +
65536*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^
11*d^3*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^4*h^8 - 24576*a^9*b^4*c^2*e^15
*f^4*h^8 - 10240*a^2*b^3*c^10*d^15*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*b^8*c^7*d^14*e*f^4*h^8 + 32768
*a^4*c^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4
*h^8 + 12288*a^3*b*c^11*d^15*f^4*h^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^7*e^8*f^4*h^8 - 65536*a^11*c^4
*e^15*f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c
^9*d^8*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d
^3*e^8*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f
^2*h^4 - 10880*a^3*b^4*c^4*d*e^10*f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7680*a^4*b*c^6*d^2*e^9*f^2*h^4
+ 4672*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6
*c^4*d^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f
^2*h^4 + 64*a*b^3*c^7*d^6*e^5*f^2*h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d
^3*e^8*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a
^4*c^7*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h
^4 + 3696*a^3*b^5*c^3*e^11*f^2*h^4 - 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d
^9*e^2*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9
*c*e^11*f^2*h^4 - 16*c^11*d^11*f^2*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k)*(root(8388608*a^7*b*c^11*d^18*e
*f^6*h^12 - 513802240*a^10*b^2*c^7*d^11*e^8*f^6*h^12 - 381681664*a^11*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^
9*b^2*c^8*d^13*e^6*f^6*h^12 - 300941312*a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^1
2 + 293601280*a^10*b^3*c^6*d^10*e^9*f^6*h^12 + 293601280*a^9*b^3*c^7*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^
4*d^8*e^11*f^6*h^12 - 168820736*a^7*b^5*c^7*d^14*e^5*f^6*h^12 + 166068224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 1468
00640*a^12*b^2*c^5*d^7*e^12*f^6*h^12 - 146800640*a^8*b^2*c^9*d^15*e^4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^
10*f^6*h^12 + 124780544*a^8*b^4*c^7*d^13*e^6*f^6*h^12 + 119275520*a^9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^
11*b^3*c^5*d^8*e^11*f^6*h^12 + 117440512*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^
12 + 102760448*a^7*b^6*c^6*d^13*e^6*f^6*h^12 + 91750400*a^11*b^4*c^4*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*
d^15*e^4*f^6*h^12 - 71065600*a^7*b^8*c^4*d^11*e^8*f^6*h^12 - 53444608*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608
*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 40370176*a^9*b^7*c^3*d^8*e^11*f^6*h^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^
12 - 36700160*a^11*b^5*c^3*d^6*e^13*f^6*h^12 - 36700160*a^6*b^5*c^8*d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d
^10*e^9*f^6*h^12 + 34078720*a^7*b^7*c^5*d^12*e^7*f^6*h^12 + 26214400*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400
*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 22118400*a^7*b^9*c^3*d^10*e^9*f^6*h^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^
12 - 20971520*a^13*b^2*c^4*d^5*e^14*f^6*h^12 - 20971520*a^7*b^2*c^10*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2
*d^6*e^13*f^6*h^12 + 18350080*a^5*b^7*c^7*d^16*e^3*f^6*h^12 - 16629760*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 1662976
0*a^5*b^8*c^6*d^15*e^4*f^6*h^12 - 10485760*a^11*b^6*c^2*d^5*e^14*f^6*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*
h^12 + 9175040*a^10*b^6*c^3*d^7*e^12*f^6*h^12 + 9175040*a^6*b^6*c^7*d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d
^4*e^15*f^6*h^12 + 5619712*a^7*b^10*c^2*d^9*e^10*f^6*h^12 + 5619712*a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a
^6*b^11*c^2*d^10*e^9*f^6*h^12 - 5570560*a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12
+ 4358144*a^5*b^9*c^5*d^14*e^5*f^6*h^12 + 4259840*a^6*b^10*c^3*d^11*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*
e^4*f^6*h^12 - 3440640*a^4*b^9*c^6*d^16*e^3*f^6*h^12 + 3145728*a^12*b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^
11*c^4*d^14*e^5*f^6*h^12 + 1802240*a^4*b^8*c^7*d^17*e^2*f^6*h^12 + 1556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 10
48576*a^14*b^2*c^3*d^3*e^16*f^6*h^12 + 688128*a^4*b^12*c^3*d^13*e^6*f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^
6*h^12 - 286720*a^3*b^12*c^4*d^15*e^4*f^6*h^12 + 229376*a^3*b^13*c^3*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d
^16*e^3*f^6*h^12 + 163840*a^4*b^13*c^2*d^12*e^7*f^6*h^12 - 114688*a^3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*
b^10*c^6*d^17*e^2*f^6*h^12 + 293601280*a^11*b*c^7*d^10*e^9*f^6*h^12 + 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 +
176160768*a^12*b*c^6*d^8*e^11*f^6*h^12 + 176160768*a^9*b*c^9*d^14*e^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13
*f^6*h^12 + 58720256*a^8*b*c^10*d^16*e^3*f^6*h^12 + 8388608*a^14*b*c^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^1
0*d^18*e*f^6*h^12 + 3899392*a^8*b^10*c*d^7*e^12*f^6*h^12 - 3440640*a^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b
^5*c^9*d^18*e*f^6*h^12 - 2523136*a^7*b^11*c*d^8*e^11*f^6*h^12 + 1802240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*
a^6*b^12*c*d^9*e^10*f^6*h^12 - 524288*a^11*b^7*c*d^4*e^15*f^6*h^12 - 524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 1638
40*a^5*b^13*c*d^10*e^9*f^6*h^12 - 163840*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 3
2768*a^3*b^15*c*d^12*e^7*f^6*h^12 + 32768*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 -
58720256*a^12*c^7*d^9*e^10*f^6*h^12 - 58720256*a^10*c^9*d^13*e^6*f^6*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^1
2 - 29360128*a^9*c^10*d^15*e^4*f^6*h^12 - 8388608*a^14*c^5*d^5*e^14*f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h
^12 - 1048576*a^15*c^4*d^3*e^16*f^6*h^12 - 286720*a^7*b^12*d^7*e^12*f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^
12 + 229376*a^6*b^13*d^8*e^11*f^6*h^12 - 114688*a^9*b^10*d^5*e^14*f^6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12
+ 32768*a^10*b^9*d^4*e^15*f^6*h^12 + 32768*a^4*b^15*d^10*e^9*f^6*h^12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 409
6*a^3*b^16*d^11*e^8*f^6*h^12 + 1048576*a^6*b^2*c^11*d^19*f^6*h^12 - 393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*
a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^8*c^8*d^19*f^6*h^12 - 1048576*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^
4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14*e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4
*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6*f^4*h^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^
5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7*f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^
10*e^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^9*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c
^8*d^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c^5*d^5*e^10*f^4*h^8 + 1106176*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5
*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b^7*c^6*d^11*e^4*f^4*h^8 - 795648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a
^3*b^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2*b^6*c^7*d^12*e^3*f^4*h^8 + 686080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 64102
4*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*a^8*b^3*c^4*d^3*e^12*f^4*h^8 + 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 51
6096*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 441856*a^6*b^5*c^4*d^5*e^10*f^4*h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 +
376832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 - 366592*a^6*b^6*c^3*d^4*e^11*f^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^
8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8 - 348672*a^2*b^5*c^8*d^13*e^2*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4
*h^8 + 294912*a^8*b^4*c^3*d^2*e^13*f^4*h^8 + 210944*a^4*b^3*c^8*d^11*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*
f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^4*h^8 - 131072*a^9*b^2*c^4*d^2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^
13*f^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^5*f^4*h^8 - 104448*a^2*b^10*c^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4
*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e^12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^
9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*e^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d
^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*e^12*f^4*h^8 + 909312*a^8*b*c^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3
*e^12*f^4*h^8 - 651264*a^5*b*c^9*d^11*e^4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^
14*f^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f^4*h^8 + 211456*a*b^9*c^5*d^11*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2
*f^4*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^4*h^8 - 157696*a*b^10*c^4*d^10*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e
*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4*h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*
h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4*h^8 + 23552*a^6*b^8*c*d^2*e^13*f^4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8
- 13312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 9472*a^5*b^9*c*d^3*e^12*f^4*h^8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144
*a^2*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^11*c^4*d^11*e^4*f^4*h^8 + 14336*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c
^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9*e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*
f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^8 - 262144*a^10*c^5*d^2*e^13*f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 +
98304*a^5*c^10*d^12*e^3*f^4*h^8 + 65536*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*
b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^3*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^1
5*f^4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*h^8 - 10240*a^2*b^3*c^10*d^15*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2
048*b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*c^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9
*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8 + 12288*a^3*b*c^11*d^15*f^4*h^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^1
5*d^7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15*f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*
b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^8*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^
2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^8*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*
f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^4 - 10880*a^3*b^4*c^4*d*e^10*f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4
- 7680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 4672*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3
*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*d^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4
*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^4 + 64*a*b^3*c^7*d^6*e^5*f^2*h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*
c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^8*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 1
6*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^7*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2
*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h^4 + 3696*a^3*b^5*c^3*e^11*f^2*h^4 - 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^
5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^2*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64
*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^11*f^2*h^4 - 16*c^11*d^11*f^2*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h,
k)^3*(root(8388608*a^7*b*c^11*d^18*e*f^6*h^12 - 513802240*a^10*b^2*c^7*d^11*e^8*f^6*h^12 - 381681664*a^11*b^2*
c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^2*c^8*d^13*e^6*f^6*h^12 - 300941312*a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 30
0941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 + 293601280*a^10*b^3*c^6*d^10*e^9*f^6*h^12 + 293601280*a^9*b^3*c^7*d^12*
e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^8*e^11*f^6*h^12 - 168820736*a^7*b^5*c^7*d^14*e^5*f^6*h^12 + 166068224*
a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 146800640*a^12*b^2*c^5*d^7*e^12*f^6*h^12 - 146800640*a^8*b^2*c^9*d^15*e^4*f^6*
h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f^6*h^12 + 124780544*a^8*b^4*c^7*d^13*e^6*f^6*h^12 + 119275520*a^9*b^4*
c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b^3*c^5*d^8*e^11*f^6*h^12 + 117440512*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 1
02760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 + 102760448*a^7*b^6*c^6*d^13*e^6*f^6*h^12 + 91750400*a^11*b^4*c^4*d^7*e
^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15*e^4*f^6*h^12 - 71065600*a^7*b^8*c^4*d^11*e^8*f^6*h^12 - 53444608*a^8*
b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 40370176*a^9*b^7*c^3*d^8*e^11*f^6*h^12 +
40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 - 36700160*a^11*b^5*c^3*d^6*e^13*f^6*h^12 - 36700160*a^6*b^5*c^8*d^16*e
^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*e^9*f^6*h^12 + 34078720*a^7*b^7*c^5*d^12*e^7*f^6*h^12 + 26214400*a^12*
b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 22118400*a^7*b^9*c^3*d^10*e^9*f^6*h^12 +
22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 - 20971520*a^13*b^2*c^4*d^5*e^14*f^6*h^12 - 20971520*a^7*b^2*c^10*d^17*
e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6*e^13*f^6*h^12 + 18350080*a^5*b^7*c^7*d^16*e^3*f^6*h^12 - 16629760*a^9
*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^5*b^8*c^6*d^15*e^4*f^6*h^12 - 10485760*a^11*b^6*c^2*d^5*e^14*f^6*h^12
- 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12 + 9175040*a^10*b^6*c^3*d^7*e^12*f^6*h^12 + 9175040*a^6*b^6*c^7*d^15*e
^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e^15*f^6*h^12 + 5619712*a^7*b^10*c^2*d^9*e^10*f^6*h^12 + 5619712*a^5*b^
10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b^11*c^2*d^10*e^9*f^6*h^12 - 5570560*a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4
358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4358144*a^5*b^9*c^5*d^14*e^5*f^6*h^12 + 4259840*a^6*b^10*c^3*d^11*e^8*f
^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*f^6*h^12 - 3440640*a^4*b^9*c^6*d^16*e^3*f^6*h^12 + 3145728*a^12*b^5*c^
2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c^4*d^14*e^5*f^6*h^12 + 1802240*a^4*b^8*c^7*d^17*e^2*f^6*h^12 + 1556480
*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 1048576*a^14*b^2*c^3*d^3*e^16*f^6*h^12 + 688128*a^4*b^12*c^3*d^13*e^6*f^6*h^
12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^12 - 286720*a^3*b^12*c^4*d^15*e^4*f^6*h^12 + 229376*a^3*b^13*c^3*d^14*
e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*e^3*f^6*h^12 + 163840*a^4*b^13*c^2*d^12*e^7*f^6*h^12 - 114688*a^3*b^14
*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10*c^6*d^17*e^2*f^6*h^12 + 293601280*a^11*b*c^7*d^10*e^9*f^6*h^12 + 2936
01280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176160768*a^12*b*c^6*d^8*e^11*f^6*h^12 + 176160768*a^9*b*c^9*d^14*e^5*f^6
*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6*h^12 + 58720256*a^8*b*c^10*d^16*e^3*f^6*h^12 + 8388608*a^14*b*c^4*d^4
*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^18*e*f^6*h^12 + 3899392*a^8*b^10*c*d^7*e^12*f^6*h^12 - 3440640*a^9*b^9
*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c^9*d^18*e*f^6*h^12 - 2523136*a^7*b^11*c*d^8*e^11*f^6*h^12 + 1802240*a^
10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*b^12*c*d^9*e^10*f^6*h^12 - 524288*a^11*b^7*c*d^4*e^15*f^6*h^12 - 52428
8*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a^5*b^13*c*d^10*e^9*f^6*h^12 - 163840*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65
536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768*a^3*b^15*c*d^12*e^7*f^6*h^12 + 32768*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73
400320*a^11*c^8*d^11*e^8*f^6*h^12 - 58720256*a^12*c^7*d^9*e^10*f^6*h^12 - 58720256*a^10*c^9*d^13*e^6*f^6*h^12
- 29360128*a^13*c^6*d^7*e^12*f^6*h^12 - 29360128*a^9*c^10*d^15*e^4*f^6*h^12 - 8388608*a^14*c^5*d^5*e^14*f^6*h^
12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12 - 1048576*a^15*c^4*d^3*e^16*f^6*h^12 - 286720*a^7*b^12*d^7*e^12*f^6*h^
12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 + 229376*a^6*b^13*d^8*e^11*f^6*h^12 - 114688*a^9*b^10*d^5*e^14*f^6*h^12
- 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 32768*a^10*b^9*d^4*e^15*f^6*h^12 + 32768*a^4*b^15*d^10*e^9*f^6*h^12 - 4
096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^3*b^16*d^11*e^8*f^6*h^12 + 1048576*a^6*b^2*c^11*d^19*f^6*h^12 - 393216
*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^8*c^8*d^19*f^6*h^12 - 1048576*a^7*c
^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14*e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14
*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6*f^4*h^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f
^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7*f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*
e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^9*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5
*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c^5*d^5*e^10*f^4*h^8 + 1106176*a^3*b
^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b^7*c^6*d^11*e^4*f^4*h^8 - 795648*a^
3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2*b^6*c^7*d^12*e^3*f^4*h^8 + 686080*
a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*a^8*b^3*c^4*d^3*e^12*f^4*h^8 + 5447
68*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 441856*a^6*b^5*c^4*d^5*e^10*f^4*h^8 +
393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 - 366592*a^6*b^6*c^3*d^4*e^11*f^4*h^8
+ 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8 - 348672*a^2*b^5*c^8*d^13*e^2*f^4*h
^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8 + 294912*a^8*b^4*c^3*d^2*e^13*f^4*h^8 + 210944*a^4*b^3*c^8*d^11*e^4*f
^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^4*h^8 - 131072*a^9*b^2*c^4*d^2*e^13
*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^5*f^4*h^8 - 104448*a^2*b^10*c^3*d^8
*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e^12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5
*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*e^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5
*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*e^12*f^4*h^8 + 909312*a^8*b*c^6*d^5
*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^12*f^4*h^8 - 651264*a^5*b*c^9*d^11*e^4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e
^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f^4*h^8 + 211456*a*b^9*c^5*d^11*e^4*
f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^4*h^8 - 157696*a*b^10*c^4*d^10*e^5*
f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4*h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4
*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4*h^8 + 23552*a^6*b^8*c*d^2*e^13*f^4*h^8
+ 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 9472*a^5*b^9*c*d^3*e^12*f^4*h^8 - 81
92*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^11*c^4*d^11*e^4*f^4*h^8 + 14336*b^12
*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9*e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^
2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^8 - 262144*a^10*c^5*d^2*e^13*f^4*h^
8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 98304*a^5*c^10*d^12*e^3*f^4*h^8 + 65536*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a
^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^3*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e
^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*h^8 - 10240*a^2*b^3*c^10*d^15*f^4*h
^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*c^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*
d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8 + 12288*a^3*b*c^11*d^15*f^4*h^8 + 2
816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15*f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8
- 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^8*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d
^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^8*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^
8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^4 - 10880*a^3*b^4*c^4*d*e^10*f^2*h^
4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 4672*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248
*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*d^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6
*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^4 + 64*a*b^3*c^7*d^6*e^5*f^2*h^4 -
96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^8*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*
h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^7*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*
e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h^4 + 3696*a^3*b^5*c^3*e^11*f^2*h^4 - 137
6*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^2*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2
*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^11*f^2*h^4 - 16*c^11*d^11*f^2*h^4 -
16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k)*(root(8388608*a^7*b*c^11*d^18*e*f^6*h^12 - 513802240*a^10*b^2*c^7*d^11*
e^8*f^6*h^12 - 381681664*a^11*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^2*c^8*d^13*e^6*f^6*h^12 - 300941312*
a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 + 293601280*a^10*b^3*c^6*d^10*e^9*f^6*
h^12 + 293601280*a^9*b^3*c^7*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^8*e^11*f^6*h^12 - 168820736*a^7*b^5*
c^7*d^14*e^5*f^6*h^12 + 166068224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 146800640*a^12*b^2*c^5*d^7*e^12*f^6*h^12 - 1
46800640*a^8*b^2*c^9*d^15*e^4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f^6*h^12 + 124780544*a^8*b^4*c^7*d^13
*e^6*f^6*h^12 + 119275520*a^9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b^3*c^5*d^8*e^11*f^6*h^12 + 117440512
*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 + 102760448*a^7*b^6*c^6*d^13*e^6*f^6*
h^12 + 91750400*a^11*b^4*c^4*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15*e^4*f^6*h^12 - 71065600*a^7*b^8*c^4
*d^11*e^8*f^6*h^12 - 53444608*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 4037017
6*a^9*b^7*c^3*d^8*e^11*f^6*h^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 - 36700160*a^11*b^5*c^3*d^6*e^13*f^6*
h^12 - 36700160*a^6*b^5*c^8*d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*e^9*f^6*h^12 + 34078720*a^7*b^7*c^5*
d^12*e^7*f^6*h^12 + 26214400*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 2211840
0*a^7*b^9*c^3*d^10*e^9*f^6*h^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 - 20971520*a^13*b^2*c^4*d^5*e^14*f^6*
h^12 - 20971520*a^7*b^2*c^10*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6*e^13*f^6*h^12 + 18350080*a^5*b^7*c^
7*d^16*e^3*f^6*h^12 - 16629760*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^5*b^8*c^6*d^15*e^4*f^6*h^12 - 104857
60*a^11*b^6*c^2*d^5*e^14*f^6*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12 + 9175040*a^10*b^6*c^3*d^7*e^12*f^6
*h^12 + 9175040*a^6*b^6*c^7*d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e^15*f^6*h^12 + 5619712*a^7*b^10*c^2*
d^9*e^10*f^6*h^12 + 5619712*a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b^11*c^2*d^10*e^9*f^6*h^12 - 5570560*
a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4358144*a^5*b^9*c^5*d^14*e^5*f^6*h^12
+ 4259840*a^6*b^10*c^3*d^11*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*f^6*h^12 - 3440640*a^4*b^9*c^6*d^16*
e^3*f^6*h^12 + 3145728*a^12*b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c^4*d^14*e^5*f^6*h^12 + 1802240*a^4*b
^8*c^7*d^17*e^2*f^6*h^12 + 1556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 1048576*a^14*b^2*c^3*d^3*e^16*f^6*h^12 + 6
88128*a^4*b^12*c^3*d^13*e^6*f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^12 - 286720*a^3*b^12*c^4*d^15*e^4*f^
6*h^12 + 229376*a^3*b^13*c^3*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*e^3*f^6*h^12 + 163840*a^4*b^13*c^2*d
^12*e^7*f^6*h^12 - 114688*a^3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10*c^6*d^17*e^2*f^6*h^12 + 293601280*a
^11*b*c^7*d^10*e^9*f^6*h^12 + 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176160768*a^12*b*c^6*d^8*e^11*f^6*h^12
+ 176160768*a^9*b*c^9*d^14*e^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6*h^12 + 58720256*a^8*b*c^10*d^16*e^3
*f^6*h^12 + 8388608*a^14*b*c^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^18*e*f^6*h^12 + 3899392*a^8*b^10*c*d
^7*e^12*f^6*h^12 - 3440640*a^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c^9*d^18*e*f^6*h^12 - 2523136*a^7*b^1
1*c*d^8*e^11*f^6*h^12 + 1802240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*b^12*c*d^9*e^10*f^6*h^12 - 524288*a^
11*b^7*c*d^4*e^15*f^6*h^12 - 524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a^5*b^13*c*d^10*e^9*f^6*h^12 - 163840
*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768*a^3*b^15*c*d^12*e^7*f^6*h^12 + 3276
8*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 - 58720256*a^12*c^7*d^9*e^10*f^6*h^12 - 58
720256*a^10*c^9*d^13*e^6*f^6*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^12 - 29360128*a^9*c^10*d^15*e^4*f^6*h^12
- 8388608*a^14*c^5*d^5*e^14*f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12 - 1048576*a^15*c^4*d^3*e^16*f^6*h^12
- 286720*a^7*b^12*d^7*e^12*f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 + 229376*a^6*b^13*d^8*e^11*f^6*h^12 -
114688*a^9*b^10*d^5*e^14*f^6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 32768*a^10*b^9*d^4*e^15*f^6*h^12 + 32
768*a^4*b^15*d^10*e^9*f^6*h^12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^3*b^16*d^11*e^8*f^6*h^12 + 1048576*a
^6*b^2*c^11*d^19*f^6*h^12 - 393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^8
*c^8*d^19*f^6*h^12 - 1048576*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14*
e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6*f^4*h
^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7*
f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^9
*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c^
5*d^5*e^10*f^4*h^8 + 1106176*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b^
7*c^6*d^11*e^4*f^4*h^8 - 795648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2*
b^6*c^7*d^12*e^3*f^4*h^8 + 686080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*a
^8*b^3*c^4*d^3*e^12*f^4*h^8 + 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 4418
56*a^6*b^5*c^4*d^5*e^10*f^4*h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 - 3
66592*a^6*b^6*c^3*d^4*e^11*f^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8 -
348672*a^2*b^5*c^8*d^13*e^2*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8 + 294912*a^8*b^4*c^3*d^2*e^13*f^4*h
^8 + 210944*a^4*b^3*c^8*d^11*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^4
*h^8 - 131072*a^9*b^2*c^4*d^2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^5
*f^4*h^8 - 104448*a^2*b^10*c^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e^
12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*e
^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*e
^12*f^4*h^8 + 909312*a^8*b*c^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^12*f^4*h^8 - 651264*a^5*b*c^9*d^11*e^
4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f^
4*h^8 + 211456*a*b^9*c^5*d^11*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^4
*h^8 - 157696*a*b^10*c^4*d^10*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4*
h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4*h^8 +
23552*a^6*b^8*c*d^2*e^13*f^4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 94
72*a^5*b^9*c*d^3*e^12*f^4*h^8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^11
*c^4*d^11*e^4*f^4*h^8 + 14336*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9*
e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^8
- 262144*a^10*c^5*d^2*e^13*f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 98304*a^5*c^10*d^12*e^3*f^4*h^8 + 65536
*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^3
*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*h
^8 - 10240*a^2*b^3*c^10*d^15*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*c
^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8 +
12288*a^3*b*c^11*d^15*f^4*h^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15*
f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^8
*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^8
*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^4
- 10880*a^3*b^4*c^4*d*e^10*f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 4672
*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*d
^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^4
+ 64*a*b^3*c^7*d^6*e^5*f^2*h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^8
*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^7
*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h^4 + 3
696*a^3*b^5*c^3*e^11*f^2*h^4 - 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^2
*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^1
1*f^2*h^4 - 16*c^11*d^11*f^2*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k)^3*(root(8388608*a^7*b*c^11*d^18*e*f^6
*h^12 - 513802240*a^10*b^2*c^7*d^11*e^8*f^6*h^12 - 381681664*a^11*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^
2*c^8*d^13*e^6*f^6*h^12 - 300941312*a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 +
293601280*a^10*b^3*c^6*d^10*e^9*f^6*h^12 + 293601280*a^9*b^3*c^7*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^
8*e^11*f^6*h^12 - 168820736*a^7*b^5*c^7*d^14*e^5*f^6*h^12 + 166068224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 14680064
0*a^12*b^2*c^5*d^7*e^12*f^6*h^12 - 146800640*a^8*b^2*c^9*d^15*e^4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f
^6*h^12 + 124780544*a^8*b^4*c^7*d^13*e^6*f^6*h^12 + 119275520*a^9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b
^3*c^5*d^8*e^11*f^6*h^12 + 117440512*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 +
102760448*a^7*b^6*c^6*d^13*e^6*f^6*h^12 + 91750400*a^11*b^4*c^4*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15
*e^4*f^6*h^12 - 71065600*a^7*b^8*c^4*d^11*e^8*f^6*h^12 - 53444608*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6
*b^8*c^5*d^13*e^6*f^6*h^12 + 40370176*a^9*b^7*c^3*d^8*e^11*f^6*h^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 -
36700160*a^11*b^5*c^3*d^6*e^13*f^6*h^12 - 36700160*a^6*b^5*c^8*d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*
e^9*f^6*h^12 + 34078720*a^7*b^7*c^5*d^12*e^7*f^6*h^12 + 26214400*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6
*b^4*c^9*d^17*e^2*f^6*h^12 + 22118400*a^7*b^9*c^3*d^10*e^9*f^6*h^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 -
20971520*a^13*b^2*c^4*d^5*e^14*f^6*h^12 - 20971520*a^7*b^2*c^10*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6
*e^13*f^6*h^12 + 18350080*a^5*b^7*c^7*d^16*e^3*f^6*h^12 - 16629760*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^
5*b^8*c^6*d^15*e^4*f^6*h^12 - 10485760*a^11*b^6*c^2*d^5*e^14*f^6*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12
+ 9175040*a^10*b^6*c^3*d^7*e^12*f^6*h^12 + 9175040*a^6*b^6*c^7*d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e
^15*f^6*h^12 + 5619712*a^7*b^10*c^2*d^9*e^10*f^6*h^12 + 5619712*a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b
^11*c^2*d^10*e^9*f^6*h^12 - 5570560*a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4
358144*a^5*b^9*c^5*d^14*e^5*f^6*h^12 + 4259840*a^6*b^10*c^3*d^11*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*
f^6*h^12 - 3440640*a^4*b^9*c^6*d^16*e^3*f^6*h^12 + 3145728*a^12*b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c
^4*d^14*e^5*f^6*h^12 + 1802240*a^4*b^8*c^7*d^17*e^2*f^6*h^12 + 1556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 104857
6*a^14*b^2*c^3*d^3*e^16*f^6*h^12 + 688128*a^4*b^12*c^3*d^13*e^6*f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^
12 - 286720*a^3*b^12*c^4*d^15*e^4*f^6*h^12 + 229376*a^3*b^13*c^3*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*
e^3*f^6*h^12 + 163840*a^4*b^13*c^2*d^12*e^7*f^6*h^12 - 114688*a^3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10
*c^6*d^17*e^2*f^6*h^12 + 293601280*a^11*b*c^7*d^10*e^9*f^6*h^12 + 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176
160768*a^12*b*c^6*d^8*e^11*f^6*h^12 + 176160768*a^9*b*c^9*d^14*e^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6
*h^12 + 58720256*a^8*b*c^10*d^16*e^3*f^6*h^12 + 8388608*a^14*b*c^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^
18*e*f^6*h^12 + 3899392*a^8*b^10*c*d^7*e^12*f^6*h^12 - 3440640*a^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c
^9*d^18*e*f^6*h^12 - 2523136*a^7*b^11*c*d^8*e^11*f^6*h^12 + 1802240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*
b^12*c*d^9*e^10*f^6*h^12 - 524288*a^11*b^7*c*d^4*e^15*f^6*h^12 - 524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a
^5*b^13*c*d^10*e^9*f^6*h^12 - 163840*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768
*a^3*b^15*c*d^12*e^7*f^6*h^12 + 32768*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 - 5872
0256*a^12*c^7*d^9*e^10*f^6*h^12 - 58720256*a^10*c^9*d^13*e^6*f^6*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^12 -
29360128*a^9*c^10*d^15*e^4*f^6*h^12 - 8388608*a^14*c^5*d^5*e^14*f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12
- 1048576*a^15*c^4*d^3*e^16*f^6*h^12 - 286720*a^7*b^12*d^7*e^12*f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 +
229376*a^6*b^13*d^8*e^11*f^6*h^12 - 114688*a^9*b^10*d^5*e^14*f^6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 3
2768*a^10*b^9*d^4*e^15*f^6*h^12 + 32768*a^4*b^15*d^10*e^9*f^6*h^12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^
3*b^16*d^11*e^8*f^6*h^12 + 1048576*a^6*b^2*c^11*d^19*f^6*h^12 - 393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*
b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^8*c^8*d^19*f^6*h^12 - 1048576*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*
e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14*e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8
+ 2429952*a^4*b^5*c^6*d^9*e^6*f^4*h^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^
4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7*f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e
^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^9*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d
^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c^5*d^5*e^10*f^4*h^8 + 1106176*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6
*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b^7*c^6*d^11*e^4*f^4*h^8 - 795648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b
^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2*b^6*c^7*d^12*e^3*f^4*h^8 + 686080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^
6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*a^8*b^3*c^4*d^3*e^12*f^4*h^8 + 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096
*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 441856*a^6*b^5*c^4*d^5*e^10*f^4*h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376
832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 - 366592*a^6*b^6*c^3*d^4*e^11*f^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 -
356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8 - 348672*a^2*b^5*c^8*d^13*e^2*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8
+ 294912*a^8*b^4*c^3*d^2*e^13*f^4*h^8 + 210944*a^4*b^3*c^8*d^11*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*
h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^4*h^8 - 131072*a^9*b^2*c^4*d^2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f
^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^5*f^4*h^8 - 104448*a^2*b^10*c^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^1
1*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e^12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^
6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*e^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e
^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*e^12*f^4*h^8 + 909312*a^8*b*c^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^1
2*f^4*h^8 - 651264*a^5*b*c^9*d^11*e^4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f
^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f^4*h^8 + 211456*a*b^9*c^5*d^11*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4
*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^4*h^8 - 157696*a*b^10*c^4*d^10*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4
*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4*h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8
+ 64512*a*b^11*c^3*d^9*e^6*f^4*h^8 + 23552*a^6*b^8*c*d^2*e^13*f^4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13
312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 9472*a^5*b^9*c*d^3*e^12*f^4*h^8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2
*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^11*c^4*d^11*e^4*f^4*h^8 + 14336*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d
^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9*e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*
h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^8 - 262144*a^10*c^5*d^2*e^13*f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 983
04*a^5*c^10*d^12*e^3*f^4*h^8 + 65536*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13
*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^3*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^
4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*h^8 - 10240*a^2*b^3*c^10*d^15*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*
b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*c^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4
*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8 + 12288*a^3*b*c^11*d^15*f^4*h^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^
7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15*f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*
c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^8*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^
9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^8*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*
h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^4 - 10880*a^3*b^4*c^4*d*e^10*f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7
680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 4672*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c
^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*d^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2
*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^4 + 64*a*b^3*c^7*d^6*e^5*f^2*h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*
d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^8*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^
4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^7*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4
- 4480*a^4*b^3*c^4*e^11*f^2*h^4 + 3696*a^3*b^5*c^3*e^11*f^2*h^4 - 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^
6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^2*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c
^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^11*f^2*h^4 - 16*c^11*d^11*f^2*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k)*(
4697620480*a^9*c^11*d^7*e^13*f^55 - 1879048192*a^6*c^14*d^13*e^7*f^55 - 2818572288*a^7*c^13*d^11*e^9*f^55 - 40
2653184*a^5*c^15*d^15*e^5*f^55 + 5637144576*a^10*c^10*d^5*e^15*f^55 + 2818572288*a^11*c^9*d^3*e^17*f^55 + 5368
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^14*f^52 + 1572864*a*b^2*c^12*d^7*e^8*f^52 - 524288*a*b^3*c^11*d^6*e^9*f^52 - 1441792*a*b^5*c^9*d^4*e^11*f^52
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024*a^2*b^6*c^7*d*e^14*f^52 - 6815744*a^3*b*c^11*d^4*e^11*f^52 + 89128960*a^3*b^4*c^8*d*e^14*f^52 + 62914560*a
^4*b*c^10*d^2*e^13*f^52 - 83886080*a^4*b^2*c^9*d*e^14*f^52 + 786432*a^2*b^2*c^11*d^5*e^10*f^52 + 5242880*a^2*b
^3*c^10*d^4*e^11*f^52 - 26214400*a^2*b^4*c^9*d^3*e^12*f^52 + 47972352*a^2*b^5*c^8*d^2*e^13*f^52 + 41943040*a^3
*b^2*c^10*d^3*e^12*f^52 - 94371840*a^3*b^3*c^9*d^2*e^13*f^52)) + 8192*b^3*c^9*e^12*f^51 + 8192*c^12*d^3*e^9*f^
51 - 32768*a*b*c^10*e^12*f^51 + 40960*a*c^11*d*e^11*f^51 - 8192*b*c^11*d^2*e^10*f^51 - 8192*b^2*c^10*d*e^11*f^
51) + 12288*c^11*e^11*f^50*(f*x)^(1/2)))*root(8388608*a^7*b*c^11*d^18*e*f^6*h^12 - 513802240*a^10*b^2*c^7*d^11
*e^8*f^6*h^12 - 381681664*a^11*b^2*c^6*d^9*e^10*f^6*h^12 - 381681664*a^9*b^2*c^8*d^13*e^6*f^6*h^12 - 300941312
*a^9*b^5*c^5*d^10*e^9*f^6*h^12 - 300941312*a^8*b^5*c^6*d^12*e^7*f^6*h^12 + 293601280*a^10*b^3*c^6*d^10*e^9*f^6
*h^12 + 293601280*a^9*b^3*c^7*d^12*e^7*f^6*h^12 - 168820736*a^10*b^5*c^4*d^8*e^11*f^6*h^12 - 168820736*a^7*b^5
*c^7*d^14*e^5*f^6*h^12 + 166068224*a^8*b^6*c^5*d^11*e^8*f^6*h^12 - 146800640*a^12*b^2*c^5*d^7*e^12*f^6*h^12 -
146800640*a^8*b^2*c^9*d^15*e^4*f^6*h^12 + 124780544*a^10*b^4*c^5*d^9*e^10*f^6*h^12 + 124780544*a^8*b^4*c^7*d^1
3*e^6*f^6*h^12 + 119275520*a^9*b^4*c^6*d^11*e^8*f^6*h^12 + 117440512*a^11*b^3*c^5*d^8*e^11*f^6*h^12 + 11744051
2*a^8*b^3*c^8*d^14*e^5*f^6*h^12 + 102760448*a^9*b^6*c^4*d^9*e^10*f^6*h^12 + 102760448*a^7*b^6*c^6*d^13*e^6*f^6
*h^12 + 91750400*a^11*b^4*c^4*d^7*e^12*f^6*h^12 + 91750400*a^7*b^4*c^8*d^15*e^4*f^6*h^12 - 71065600*a^7*b^8*c^
4*d^11*e^8*f^6*h^12 - 53444608*a^8*b^8*c^3*d^9*e^10*f^6*h^12 - 53444608*a^6*b^8*c^5*d^13*e^6*f^6*h^12 + 403701
76*a^9*b^7*c^3*d^8*e^11*f^6*h^12 + 40370176*a^6*b^7*c^6*d^14*e^5*f^6*h^12 - 36700160*a^11*b^5*c^3*d^6*e^13*f^6
*h^12 - 36700160*a^6*b^5*c^8*d^16*e^3*f^6*h^12 + 34078720*a^8*b^7*c^4*d^10*e^9*f^6*h^12 + 34078720*a^7*b^7*c^5
*d^12*e^7*f^6*h^12 + 26214400*a^12*b^4*c^3*d^5*e^14*f^6*h^12 + 26214400*a^6*b^4*c^9*d^17*e^2*f^6*h^12 + 221184
00*a^7*b^9*c^3*d^10*e^9*f^6*h^12 + 22118400*a^6*b^9*c^4*d^12*e^7*f^6*h^12 - 20971520*a^13*b^2*c^4*d^5*e^14*f^6
*h^12 - 20971520*a^7*b^2*c^10*d^17*e^2*f^6*h^12 + 18350080*a^10*b^7*c^2*d^6*e^13*f^6*h^12 + 18350080*a^5*b^7*c
^7*d^16*e^3*f^6*h^12 - 16629760*a^9*b^8*c^2*d^7*e^12*f^6*h^12 - 16629760*a^5*b^8*c^6*d^15*e^4*f^6*h^12 - 10485
760*a^11*b^6*c^2*d^5*e^14*f^6*h^12 - 10485760*a^5*b^6*c^8*d^17*e^2*f^6*h^12 + 9175040*a^10*b^6*c^3*d^7*e^12*f^
6*h^12 + 9175040*a^6*b^6*c^7*d^15*e^4*f^6*h^12 - 8388608*a^13*b^3*c^3*d^4*e^15*f^6*h^12 + 5619712*a^7*b^10*c^2
*d^9*e^10*f^6*h^12 + 5619712*a^5*b^10*c^4*d^13*e^6*f^6*h^12 - 5570560*a^6*b^11*c^2*d^10*e^9*f^6*h^12 - 5570560
*a^5*b^11*c^3*d^12*e^7*f^6*h^12 + 4358144*a^8*b^9*c^2*d^8*e^11*f^6*h^12 + 4358144*a^5*b^9*c^5*d^14*e^5*f^6*h^1
2 + 4259840*a^6*b^10*c^3*d^11*e^8*f^6*h^12 + 3899392*a^4*b^10*c^5*d^15*e^4*f^6*h^12 - 3440640*a^4*b^9*c^6*d^16
*e^3*f^6*h^12 + 3145728*a^12*b^5*c^2*d^4*e^15*f^6*h^12 - 2523136*a^4*b^11*c^4*d^14*e^5*f^6*h^12 + 1802240*a^4*
b^8*c^7*d^17*e^2*f^6*h^12 + 1556480*a^5*b^12*c^2*d^11*e^8*f^6*h^12 + 1048576*a^14*b^2*c^3*d^3*e^16*f^6*h^12 +
688128*a^4*b^12*c^3*d^13*e^6*f^6*h^12 - 393216*a^13*b^4*c^2*d^3*e^16*f^6*h^12 - 286720*a^3*b^12*c^4*d^15*e^4*f
^6*h^12 + 229376*a^3*b^13*c^3*d^14*e^5*f^6*h^12 + 229376*a^3*b^11*c^5*d^16*e^3*f^6*h^12 + 163840*a^4*b^13*c^2*
d^12*e^7*f^6*h^12 - 114688*a^3*b^14*c^2*d^13*e^6*f^6*h^12 - 114688*a^3*b^10*c^6*d^17*e^2*f^6*h^12 + 293601280*
a^11*b*c^7*d^10*e^9*f^6*h^12 + 293601280*a^10*b*c^8*d^12*e^7*f^6*h^12 + 176160768*a^12*b*c^6*d^8*e^11*f^6*h^12
+ 176160768*a^9*b*c^9*d^14*e^5*f^6*h^12 + 58720256*a^13*b*c^5*d^6*e^13*f^6*h^12 + 58720256*a^8*b*c^10*d^16*e^
3*f^6*h^12 + 8388608*a^14*b*c^4*d^4*e^15*f^6*h^12 - 8388608*a^6*b^3*c^10*d^18*e*f^6*h^12 + 3899392*a^8*b^10*c*
d^7*e^12*f^6*h^12 - 3440640*a^9*b^9*c*d^6*e^13*f^6*h^12 + 3145728*a^5*b^5*c^9*d^18*e*f^6*h^12 - 2523136*a^7*b^
11*c*d^8*e^11*f^6*h^12 + 1802240*a^10*b^8*c*d^5*e^14*f^6*h^12 + 688128*a^6*b^12*c*d^9*e^10*f^6*h^12 - 524288*a
^11*b^7*c*d^4*e^15*f^6*h^12 - 524288*a^4*b^7*c^8*d^18*e*f^6*h^12 + 163840*a^5*b^13*c*d^10*e^9*f^6*h^12 - 16384
0*a^4*b^14*c*d^11*e^8*f^6*h^12 + 65536*a^12*b^6*c*d^3*e^16*f^6*h^12 + 32768*a^3*b^15*c*d^12*e^7*f^6*h^12 + 327
68*a^3*b^9*c^7*d^18*e*f^6*h^12 - 73400320*a^11*c^8*d^11*e^8*f^6*h^12 - 58720256*a^12*c^7*d^9*e^10*f^6*h^12 - 5
8720256*a^10*c^9*d^13*e^6*f^6*h^12 - 29360128*a^13*c^6*d^7*e^12*f^6*h^12 - 29360128*a^9*c^10*d^15*e^4*f^6*h^12
- 8388608*a^14*c^5*d^5*e^14*f^6*h^12 - 8388608*a^8*c^11*d^17*e^2*f^6*h^12 - 1048576*a^15*c^4*d^3*e^16*f^6*h^1
2 - 286720*a^7*b^12*d^7*e^12*f^6*h^12 + 229376*a^8*b^11*d^6*e^13*f^6*h^12 + 229376*a^6*b^13*d^8*e^11*f^6*h^12
- 114688*a^9*b^10*d^5*e^14*f^6*h^12 - 114688*a^5*b^14*d^9*e^10*f^6*h^12 + 32768*a^10*b^9*d^4*e^15*f^6*h^12 + 3
2768*a^4*b^15*d^10*e^9*f^6*h^12 - 4096*a^11*b^8*d^3*e^16*f^6*h^12 - 4096*a^3*b^16*d^11*e^8*f^6*h^12 + 1048576*
a^6*b^2*c^11*d^19*f^6*h^12 - 393216*a^5*b^4*c^10*d^19*f^6*h^12 + 65536*a^4*b^6*c^9*d^19*f^6*h^12 - 4096*a^3*b^
8*c^8*d^19*f^6*h^12 - 1048576*a^7*c^12*d^19*f^6*h^12 + 262144*a^10*b*c^4*d*e^14*f^4*h^8 - 23552*a*b^6*c^8*d^14
*e*f^4*h^8 - 16384*a^7*b^7*c*d*e^14*f^4*h^8 - 3328*a*b^13*c*d^7*e^8*f^4*h^8 + 2429952*a^4*b^5*c^6*d^9*e^6*f^4*
h^8 - 1865728*a^6*b^3*c^6*d^7*e^8*f^4*h^8 - 1716224*a^4*b^4*c^7*d^10*e^5*f^4*h^8 + 1605632*a^6*b^2*c^7*d^8*e^7
*f^4*h^8 + 1584384*a^5*b^5*c^5*d^7*e^8*f^4*h^8 + 1572864*a^5*b^2*c^8*d^10*e^5*f^4*h^8 - 1433600*a^5*b^3*c^7*d^
9*e^6*f^4*h^8 - 1261568*a^4*b^6*c^5*d^8*e^7*f^4*h^8 - 1124352*a^3*b^4*c^8*d^12*e^3*f^4*h^8 - 1110016*a^7*b^3*c
^5*d^5*e^10*f^4*h^8 + 1106176*a^3*b^5*c^7*d^11*e^4*f^4*h^8 - 936960*a^5*b^6*c^4*d^6*e^9*f^4*h^8 - 838656*a^2*b
^7*c^6*d^11*e^4*f^4*h^8 - 795648*a^3*b^7*c^5*d^9*e^6*f^4*h^8 + 730880*a^3*b^8*c^4*d^8*e^7*f^4*h^8 + 714752*a^2
*b^6*c^7*d^12*e^3*f^4*h^8 + 686080*a^7*b^4*c^4*d^4*e^11*f^4*h^8 + 641024*a^6*b^4*c^5*d^6*e^9*f^4*h^8 - 595968*
a^8*b^3*c^4*d^3*e^12*f^4*h^8 + 544768*a^3*b^3*c^9*d^13*e^2*f^4*h^8 + 516096*a^2*b^8*c^5*d^10*e^5*f^4*h^8 + 441
856*a^6*b^5*c^4*d^5*e^10*f^4*h^8 + 393216*a^7*b^2*c^6*d^6*e^9*f^4*h^8 + 376832*a^4*b^2*c^9*d^12*e^3*f^4*h^8 -
366592*a^6*b^6*c^3*d^4*e^11*f^4*h^8 + 363520*a^4*b^8*c^3*d^6*e^9*f^4*h^8 - 356352*a^5*b^4*c^6*d^8*e^7*f^4*h^8
- 348672*a^2*b^5*c^8*d^13*e^2*f^4*h^8 - 344064*a^8*b^2*c^5*d^4*e^11*f^4*h^8 + 294912*a^8*b^4*c^3*d^2*e^13*f^4*
h^8 + 210944*a^4*b^3*c^8*d^11*e^4*f^4*h^8 - 198400*a^3*b^9*c^3*d^7*e^8*f^4*h^8 - 144640*a^4*b^7*c^4*d^7*e^8*f^
4*h^8 - 131072*a^9*b^2*c^4*d^2*e^13*f^4*h^8 - 131072*a^7*b^6*c^2*d^2*e^13*f^4*h^8 - 129024*a^3*b^6*c^6*d^10*e^
5*f^4*h^8 - 104448*a^2*b^10*c^3*d^8*e^7*f^4*h^8 + 96768*a^5*b^8*c^2*d^4*e^11*f^4*h^8 + 91904*a^7*b^5*c^3*d^3*e
^12*f^4*h^8 - 74240*a^4*b^9*c^2*d^5*e^10*f^4*h^8 - 71680*a^2*b^9*c^4*d^9*e^6*f^4*h^8 + 58368*a^2*b^11*c^2*d^7*
e^8*f^4*h^8 + 36864*a^5*b^7*c^3*d^5*e^10*f^4*h^8 - 35328*a^3*b^10*c^2*d^6*e^9*f^4*h^8 + 27136*a^6*b^7*c^2*d^3*
e^12*f^4*h^8 + 909312*a^8*b*c^6*d^5*e^10*f^4*h^8 + 815104*a^9*b*c^5*d^3*e^12*f^4*h^8 - 651264*a^5*b*c^9*d^11*e
^4*f^4*h^8 - 573440*a^6*b*c^8*d^9*e^6*f^4*h^8 - 262144*a^9*b^3*c^3*d*e^14*f^4*h^8 + 217088*a^7*b*c^7*d^7*e^8*f
^4*h^8 + 211456*a*b^9*c^5*d^11*e^4*f^4*h^8 - 204800*a^4*b*c^10*d^13*e^2*f^4*h^8 - 172032*a*b^8*c^6*d^12*e^3*f^
4*h^8 - 157696*a*b^10*c^4*d^10*e^5*f^4*h^8 - 131072*a^3*b^2*c^10*d^14*e*f^4*h^8 + 98304*a^8*b^5*c^2*d*e^14*f^4
*h^8 + 92160*a^2*b^4*c^9*d^14*e*f^4*h^8 + 84992*a*b^7*c^7*d^13*e^2*f^4*h^8 + 64512*a*b^11*c^3*d^9*e^6*f^4*h^8
+ 23552*a^6*b^8*c*d^2*e^13*f^4*h^8 + 18944*a^3*b^11*c*d^5*e^10*f^4*h^8 - 13312*a^4*b^10*c*d^4*e^11*f^4*h^8 - 9
472*a^5*b^9*c*d^3*e^12*f^4*h^8 - 8192*a*b^12*c^2*d^8*e^7*f^4*h^8 - 6144*a^2*b^12*c*d^6*e^9*f^4*h^8 - 17920*b^1
1*c^4*d^11*e^4*f^4*h^8 + 14336*b^12*c^3*d^10*e^5*f^4*h^8 + 14336*b^10*c^5*d^12*e^3*f^4*h^8 - 7168*b^13*c^2*d^9
*e^6*f^4*h^8 - 7168*b^9*c^6*d^13*e^2*f^4*h^8 - 425984*a^9*c^6*d^4*e^11*f^4*h^8 - 360448*a^8*c^7*d^6*e^9*f^4*h^
8 - 262144*a^10*c^5*d^2*e^13*f^4*h^8 - 131072*a^7*c^8*d^8*e^7*f^4*h^8 + 98304*a^5*c^10*d^12*e^3*f^4*h^8 + 6553
6*a^6*c^9*d^10*e^5*f^4*h^8 - 1536*a^5*b^10*d^2*e^13*f^4*h^8 - 1536*a^2*b^13*d^5*e^10*f^4*h^8 + 768*a^4*b^11*d^
3*e^12*f^4*h^8 + 768*a^3*b^12*d^4*e^11*f^4*h^8 + 65536*a^10*b^2*c^3*e^15*f^4*h^8 - 24576*a^9*b^4*c^2*e^15*f^4*
h^8 - 10240*a^2*b^3*c^10*d^15*f^4*h^8 + 2048*b^14*c*d^8*e^7*f^4*h^8 + 2048*b^8*c^7*d^14*e*f^4*h^8 + 32768*a^4*
c^11*d^14*e*f^4*h^8 + 1024*a^6*b^9*d*e^14*f^4*h^8 + 1024*a*b^14*d^6*e^9*f^4*h^8 + 4096*a^8*b^6*c*e^15*f^4*h^8
+ 12288*a^3*b*c^11*d^15*f^4*h^8 + 2816*a*b^5*c^9*d^15*f^4*h^8 - 256*b^15*d^7*e^8*f^4*h^8 - 65536*a^11*c^4*e^15
*f^4*h^8 - 256*b^7*c^8*d^15*f^4*h^8 - 256*a^7*b^8*e^15*f^4*h^8 - 896*a*b^8*c^2*d*e^10*f^2*h^4 + 192*a*b*c^9*d^
8*e^3*f^2*h^4 + 11520*a^3*b^3*c^5*d^2*e^9*f^2*h^4 - 5856*a^2*b^5*c^4*d^2*e^9*f^2*h^4 - 5120*a^3*b^2*c^6*d^3*e^
8*f^2*h^4 + 3200*a^2*b^4*c^5*d^3*e^8*f^2*h^4 - 640*a^2*b^3*c^6*d^4*e^7*f^2*h^4 - 96*a^2*b^2*c^7*d^5*e^6*f^2*h^
4 - 10880*a^3*b^4*c^4*d*e^10*f^2*h^4 + 10240*a^4*b^2*c^5*d*e^10*f^2*h^4 - 7680*a^4*b*c^6*d^2*e^9*f^2*h^4 + 467
2*a^2*b^6*c^3*d*e^10*f^2*h^4 + 1248*a*b^7*c^3*d^2*e^9*f^2*h^4 + 832*a^3*b*c^7*d^4*e^7*f^2*h^4 - 768*a*b^6*c^4*
d^3*e^8*f^2*h^4 + 192*a^2*b*c^8*d^6*e^5*f^2*h^4 - 192*a*b^2*c^8*d^7*e^4*f^2*h^4 + 176*a*b^5*c^5*d^4*e^7*f^2*h^
4 + 64*a*b^3*c^7*d^6*e^5*f^2*h^4 - 96*b^9*c^2*d^2*e^9*f^2*h^4 - 96*b^2*c^9*d^9*e^2*f^2*h^4 + 64*b^8*c^3*d^3*e^
8*f^2*h^4 + 64*b^3*c^8*d^8*e^3*f^2*h^4 - 16*b^7*c^4*d^4*e^7*f^2*h^4 - 16*b^4*c^7*d^7*e^4*f^2*h^4 + 2032*a^4*c^
7*d^3*e^8*f^2*h^4 - 96*a^2*c^9*d^7*e^4*f^2*h^4 - 64*a^3*c^8*d^5*e^6*f^2*h^4 - 4480*a^4*b^3*c^4*e^11*f^2*h^4 +
3696*a^3*b^5*c^3*e^11*f^2*h^4 - 1376*a^2*b^7*c^2*e^11*f^2*h^4 - 2048*a^5*c^6*d*e^10*f^2*h^4 - 64*a*c^10*d^9*e^
2*f^2*h^4 + 1792*a^5*b*c^5*e^11*f^2*h^4 + 64*b^10*c*d*e^10*f^2*h^4 + 64*b*c^10*d^10*e*f^2*h^4 + 240*a*b^9*c*e^
11*f^2*h^4 - 16*c^11*d^11*f^2*h^4 - 16*b^11*e^11*f^2*h^4 - c^7*e^7, h, k), k, 1, 12)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {f x} \left (d + e x^{2}\right ) \left (a + b x^{2} + c x^{4}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x**2+d)/(c*x**4+b*x**2+a)/(f*x)**(1/2),x)

[Out]

Integral(1/(sqrt(f*x)*(d + e*x**2)*(a + b*x**2 + c*x**4)), x)

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