\(\int \frac {1}{(d f+e f x)^3 (a+b (d+e x)^2+c (d+e x)^4)^3} \, dx\) [660]

Optimal result

Integrand size = 33, antiderivative size = 343 \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=-\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \left (b^6-10 a b^4 c+30 a^2 b^2 c^2-20 a^3 c^3\right ) \text {arctanh}\left (\frac {b+2 c (d+e x)^2}{\sqrt {b^2-4 a c}}\right )}{2 a^4 \left (b^2-4 a c\right )^{5/2} e f^3}-\frac {3 b \log (d+e x)}{a^4 e f^3}+\frac {3 b \log \left (a+b (d+e x)^2+c (d+e x)^4\right )}{4 a^4 e f^3} \]

[Out]

-3/2*(-5*a*c+b^2)*(-2*a*c+b^2)/a^3/(-4*a*c+b^2)^2/e/f^3/(e*x+d)^2+1/4*(b^2-2*a*c+b*c*(e*x+d)^2)/a/(-4*a*c+b^2)
/e/f^3/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2+1/4*(3*b^4-20*a*b^2*c+20*a^2*c^2+3*b*c*(-6*a*c+b^2)*(e*x+d)^2)/
a^2/(-4*a*c+b^2)^2/e/f^3/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)-3/2*(-20*a^3*c^3+30*a^2*b^2*c^2-10*a*b^4*c+b^6)
*arctanh((b+2*c*(e*x+d)^2)/(-4*a*c+b^2)^(1/2))/a^4/(-4*a*c+b^2)^(5/2)/e/f^3-3*b*ln(e*x+d)/a^4/e/f^3+3/4*b*ln(a
+b*(e*x+d)^2+c*(e*x+d)^4)/a^4/e/f^3

Rubi [A] (verified)

Time = 0.38 (sec) , antiderivative size = 343, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {1156, 1128, 754, 836, 814, 648, 632, 212, 642} \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\frac {3 b \log \left (a+b (d+e x)^2+c (d+e x)^4\right )}{4 a^4 e f^3}-\frac {3 b \log (d+e x)}{a^4 e f^3}-\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 e f^3 \left (b^2-4 a c\right )^2 (d+e x)^2}+\frac {20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2-20 a b^2 c+3 b^4}{4 a^2 e f^3 \left (b^2-4 a c\right )^2 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \left (-20 a^3 c^3+30 a^2 b^2 c^2-10 a b^4 c+b^6\right ) \text {arctanh}\left (\frac {b+2 c (d+e x)^2}{\sqrt {b^2-4 a c}}\right )}{2 a^4 e f^3 \left (b^2-4 a c\right )^{5/2}}+\frac {-2 a c+b^2+b c (d+e x)^2}{4 a e f^3 \left (b^2-4 a c\right ) (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2} \]

[In]

Int[1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]

[Out]

(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(2*a^3*(b^2 - 4*a*c)^2*e*f^3*(d + e*x)^2) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(
4*a*(b^2 - 4*a*c)*e*f^3*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2
+ 3*b*c*(b^2 - 6*a*c)*(d + e*x)^2)/(4*a^2*(b^2 - 4*a*c)^2*e*f^3*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4
)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*
a^4*(b^2 - 4*a*c)^(5/2)*e*f^3) - (3*b*Log[d + e*x])/(a^4*e*f^3) + (3*b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])
/(4*a^4*e*f^3)

Rule 212

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

Rule 632

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 642

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

Rule 648

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 754

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[(d + e*x)^(m + 1)*(b
*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)*((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e +
a*e^2))), x] + Dist[1/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*Simp[b*c*d*e*(2*p - m
+ 2) + b^2*e^2*(m + p + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3) - c*e*(2*c*d - b*e)*(m + 2*p + 4)*x
, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b
*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && LtQ[p, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]

Rule 814

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[Exp
andIntegrand[(d + e*x)^m*((f + g*x)/(a + b*x + c*x^2)), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 -
4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[m]

Rule 836

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[(d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x)
*((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))), x] + Dist[1/((p + 1)*(b^2 - 4*a*
c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2
*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -
b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b,
c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] ||
IntegerQ[p] || IntegersQ[2*m, 2*p])

Rule 1128

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_.), x_Symbol] :> Dist[1/2, Subst[Int[x^((m - 1)/2)*(a +
b*x + c*x^2)^p, x], x, x^2], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[(m - 1)/2]

Rule 1156

Int[(u_)^(m_.)*((a_.) + (b_.)*(v_)^2 + (c_.)*(v_)^4)^(p_.), x_Symbol] :> Dist[u^m/(Coefficient[v, x, 1]*v^m),
Subst[Int[x^m*(a + b*x^2 + c*x^(2*2))^p, x], x, v], x] /; FreeQ[{a, b, c, m, p}, x] && LinearPairQ[u, v, x]

Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {1}{x^3 \left (a+b x^2+c x^4\right )^3} \, dx,x,d+e x\right )}{e f^3} \\ & = \frac {\text {Subst}\left (\int \frac {1}{x^2 \left (a+b x+c x^2\right )^3} \, dx,x,(d+e x)^2\right )}{2 e f^3} \\ & = \frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}-\frac {\text {Subst}\left (\int \frac {-3 b^2+10 a c-4 b c x}{x^2 \left (a+b x+c x^2\right )^2} \, dx,x,(d+e x)^2\right )}{4 a \left (b^2-4 a c\right ) e f^3} \\ & = \frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}+\frac {\text {Subst}\left (\int \frac {6 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )+6 b c \left (b^2-6 a c\right ) x}{x^2 \left (a+b x+c x^2\right )} \, dx,x,(d+e x)^2\right )}{4 a^2 \left (b^2-4 a c\right )^2 e f^3} \\ & = \frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}+\frac {\text {Subst}\left (\int \left (\frac {6 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{a x^2}-\frac {6 b \left (-b^2+4 a c\right )^2}{a^2 x}+\frac {6 \left (b^6-9 a b^4 c+23 a^2 b^2 c^2-10 a^3 c^3+b c \left (b^2-4 a c\right )^2 x\right )}{a^2 \left (a+b x+c x^2\right )}\right ) \, dx,x,(d+e x)^2\right )}{4 a^2 \left (b^2-4 a c\right )^2 e f^3} \\ & = -\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 b \log (d+e x)}{a^4 e f^3}+\frac {3 \text {Subst}\left (\int \frac {b^6-9 a b^4 c+23 a^2 b^2 c^2-10 a^3 c^3+b c \left (b^2-4 a c\right )^2 x}{a+b x+c x^2} \, dx,x,(d+e x)^2\right )}{2 a^4 \left (b^2-4 a c\right )^2 e f^3} \\ & = -\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 b \log (d+e x)}{a^4 e f^3}+\frac {(3 b) \text {Subst}\left (\int \frac {b+2 c x}{a+b x+c x^2} \, dx,x,(d+e x)^2\right )}{4 a^4 e f^3}+\frac {\left (3 \left (b^6-10 a b^4 c+30 a^2 b^2 c^2-20 a^3 c^3\right )\right ) \text {Subst}\left (\int \frac {1}{a+b x+c x^2} \, dx,x,(d+e x)^2\right )}{4 a^4 \left (b^2-4 a c\right )^2 e f^3} \\ & = -\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 b \log (d+e x)}{a^4 e f^3}+\frac {3 b \log \left (a+b (d+e x)^2+c (d+e x)^4\right )}{4 a^4 e f^3}-\frac {\left (3 \left (b^6-10 a b^4 c+30 a^2 b^2 c^2-20 a^3 c^3\right )\right ) \text {Subst}\left (\int \frac {1}{b^2-4 a c-x^2} \, dx,x,b+2 c (d+e x)^2\right )}{2 a^4 \left (b^2-4 a c\right )^2 e f^3} \\ & = -\frac {3 \left (b^2-5 a c\right ) \left (b^2-2 a c\right )}{2 a^3 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {3 b^4-20 a b^2 c+20 a^2 c^2+3 b c \left (b^2-6 a c\right ) (d+e x)^2}{4 a^2 \left (b^2-4 a c\right )^2 e f^3 (d+e x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \left (b^6-10 a b^4 c+30 a^2 b^2 c^2-20 a^3 c^3\right ) \tanh ^{-1}\left (\frac {b+2 c (d+e x)^2}{\sqrt {b^2-4 a c}}\right )}{2 a^4 \left (b^2-4 a c\right )^{5/2} e f^3}-\frac {3 b \log (d+e x)}{a^4 e f^3}+\frac {3 b \log \left (a+b (d+e x)^2+c (d+e x)^4\right )}{4 a^4 e f^3} \\ \end{align*}

Mathematica [A] (verified)

Time = 6.06 (sec) , antiderivative size = 461, normalized size of antiderivative = 1.34 \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\frac {-\frac {2 a}{(d+e x)^2}+\frac {a^2 \left (b^3-3 a b c+b^2 c (d+e x)^2-2 a c^2 (d+e x)^2\right )}{\left (-b^2+4 a c\right ) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}-\frac {a \left (4 b^5-29 a b^3 c+46 a^2 b c^2+4 b^4 c (d+e x)^2-26 a b^2 c^2 (d+e x)^2+28 a^2 c^3 (d+e x)^2\right )}{\left (b^2-4 a c\right )^2 \left (a+(d+e x)^2 \left (b+c (d+e x)^2\right )\right )}-12 b \log (d+e x)+\frac {3 \left (b^6-10 a b^4 c+30 a^2 b^2 c^2-20 a^3 c^3+b^5 \sqrt {b^2-4 a c}-8 a b^3 c \sqrt {b^2-4 a c}+16 a^2 b c^2 \sqrt {b^2-4 a c}\right ) \log \left (b-\sqrt {b^2-4 a c}+2 c (d+e x)^2\right )}{\left (b^2-4 a c\right )^{5/2}}+\frac {3 \left (-b^6+10 a b^4 c-30 a^2 b^2 c^2+20 a^3 c^3+b^5 \sqrt {b^2-4 a c}-8 a b^3 c \sqrt {b^2-4 a c}+16 a^2 b c^2 \sqrt {b^2-4 a c}\right ) \log \left (b+\sqrt {b^2-4 a c}+2 c (d+e x)^2\right )}{\left (b^2-4 a c\right )^{5/2}}}{4 a^4 e f^3} \]

[In]

Integrate[1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]

[Out]

((-2*a)/(d + e*x)^2 + (a^2*(b^3 - 3*a*b*c + b^2*c*(d + e*x)^2 - 2*a*c^2*(d + e*x)^2))/((-b^2 + 4*a*c)*(a + b*(
d + e*x)^2 + c*(d + e*x)^4)^2) - (a*(4*b^5 - 29*a*b^3*c + 46*a^2*b*c^2 + 4*b^4*c*(d + e*x)^2 - 26*a*b^2*c^2*(d
+ e*x)^2 + 28*a^2*c^3*(d + e*x)^2))/((b^2 - 4*a*c)^2*(a + (d + e*x)^2*(b + c*(d + e*x)^2))) - 12*b*Log[d + e*
x] + (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3 + b^5*Sqrt[b^2 - 4*a*c] - 8*a*b^3*c*Sqrt[b^2 - 4*a*c]
+ 16*a^2*b*c^2*Sqrt[b^2 - 4*a*c])*Log[b - Sqrt[b^2 - 4*a*c] + 2*c*(d + e*x)^2])/(b^2 - 4*a*c)^(5/2) + (3*(-b^6
+ 10*a*b^4*c - 30*a^2*b^2*c^2 + 20*a^3*c^3 + b^5*Sqrt[b^2 - 4*a*c] - 8*a*b^3*c*Sqrt[b^2 - 4*a*c] + 16*a^2*b*c
^2*Sqrt[b^2 - 4*a*c])*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*(d + e*x)^2])/(b^2 - 4*a*c)^(5/2))/(4*a^4*e*f^3)

Maple [C] (verified)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 1.00 (sec) , antiderivative size = 1145, normalized size of antiderivative = 3.34

method	result	size
default	\(\text {Expression too large to display}\)	\(1145\)
risch	\(\text {Expression too large to display}\)	\(2364\)

[In]

int(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x,method=_RETURNVERBOSE)

[Out]

1/f^3*(-1/a^4*((1/2*c^2*e^5*(14*a^2*c^2-13*a*b^2*c+2*b^4)*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+3*(14*a^2*c^2-13*a*
b^2*c+2*b^4)*a*c^2*d*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+1/4*e^3*a*c*(420*a^2*c^3*d^2-390*a*b^2*c^2*d^2+60*b^4*
c*d^2+74*a^2*b*c^2-55*a*b^3*c+8*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+c*d*e^2*a*(140*a^2*c^3*d^2-130*a*b^2*c^2*d
^2+20*b^4*c*d^2+74*a^2*b*c^2-55*a*b^3*c+8*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/2*e*a*(210*a^2*c^4*d^4-195*a*b
^2*c^3*d^4+30*b^4*c^2*d^4+222*a^2*b*c^3*d^2-165*a*b^3*c^2*d^2+24*b^5*c*d^2+18*a^3*c^3+7*a^2*b^2*c^2-12*a*b^4*c
+2*b^6)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+d*a*(42*a^2*c^4*d^4-39*a*b^2*c^3*d^4+6*b^4*c^2*d^4+74*a^2*b*c^3*d^2-55*
a*b^3*c^2*d^2+8*b^5*c*d^2+18*a^3*c^3+7*a^2*b^2*c^2-12*a*b^4*c+2*b^6)/(16*a^2*c^2-8*a*b^2*c+b^4)*x+1/4/e*a*(28*
a^2*c^4*d^6-26*a*b^2*c^3*d^6+4*b^4*c^2*d^6+74*a^2*b*c^3*d^4-55*a*b^3*c^2*d^4+8*b^5*c*d^4+36*a^3*c^3*d^2+14*a^2
*b^2*c^2*d^2-24*a*b^4*c*d^2+4*b^6*d^2+58*a^3*b*c^2-36*a^2*b^3*c+5*a*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*e^4*x^
4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+3/2/(16*a^2*c^2-8*a*b^2*c+b^4
)/e*sum((e^3*b*c*(-16*a^2*c^2+8*a*b^2*c-b^4)*_R^3+3*d*e^2*b*c*(-16*a^2*c^2+8*a*b^2*c-b^4)*_R^2+e*(-48*a^2*b*c^
3*d^2+24*a*b^3*c^2*d^2-3*b^5*c*d^2+10*a^3*c^3-23*a^2*b^2*c^2+9*a*b^4*c-b^6)*_R-16*a^2*b*c^3*d^3+8*a*b^3*c^2*d^
3-b^5*c*d^3+10*a^3*c^3*d-23*a^2*b^2*c^2*d+9*a*b^4*c*d-b^6*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3
+_R*b*e+b*d)*ln(x-_R),_R=RootOf(c*e^4*_Z^4+4*c*d*e^3*_Z^3+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+d^4*
c+b*d^2+a)))-1/2/a^3/e/(e*x+d)^2-3*b*ln(e*x+d)/a^4/e)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 7550 vs. \(2 (329) = 658\).

Time = 4.42 (sec) , antiderivative size = 15231, normalized size of antiderivative = 44.41 \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\text {Too large to display} \]

[In]

integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="fricas")

[Out]

Too large to include

Sympy [F(-1)]

Timed out. \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\text {Timed out} \]

[In]

integrate(1/(e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)

[Out]

Timed out

Maxima [F]

\[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\int { \frac {1}{{\left ({\left (e x + d\right )}^{4} c + {\left (e x + d\right )}^{2} b + a\right )}^{3} {\left (e f x + d f\right )}^{3}} \,d x } \]

[In]

integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="maxima")

[Out]

-1/4*(6*(b^4*c^2 - 7*a*b^2*c^3 + 10*a^2*c^4)*e^8*x^8 + 48*(b^4*c^2 - 7*a*b^2*c^3 + 10*a^2*c^4)*d*e^7*x^7 + 3*(
4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3 + 56*(b^4*c^2 - 7*a*b^2*c^3 + 10*a^2*c^4)*d^2)*e^6*x^6 + 6*(56*(b^4*c^2
- 7*a*b^2*c^3 + 10*a^2*c^4)*d^3 + 3*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3)*d)*e^5*x^5 + 6*(b^4*c^2 - 7*a*b^2*
c^3 + 10*a^2*c^4)*d^8 + (6*b^6 - 36*a*b^4*c + 14*a^2*b^2*c^2 + 100*a^3*c^3 + 420*(b^4*c^2 - 7*a*b^2*c^3 + 10*a
^2*c^4)*d^4 + 45*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3)*d^2)*e^4*x^4 + 3*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c
^3)*d^6 + 4*(84*(b^4*c^2 - 7*a*b^2*c^3 + 10*a^2*c^4)*d^5 + 15*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3)*d^3 + 2*
(3*b^6 - 18*a*b^4*c + 7*a^2*b^2*c^2 + 50*a^3*c^3)*d)*e^3*x^3 + 2*a^2*b^4 - 16*a^3*b^2*c + 32*a^4*c^2 + 2*(3*b^
6 - 18*a*b^4*c + 7*a^2*b^2*c^2 + 50*a^3*c^3)*d^4 + (168*(b^4*c^2 - 7*a*b^2*c^3 + 10*a^2*c^4)*d^6 + 9*a*b^5 - 6
8*a^2*b^3*c + 122*a^3*b*c^2 + 45*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3)*d^4 + 12*(3*b^6 - 18*a*b^4*c + 7*a^2*
b^2*c^2 + 50*a^3*c^3)*d^2)*e^2*x^2 + (9*a*b^5 - 68*a^2*b^3*c + 122*a^3*b*c^2)*d^2 + 2*(24*(b^4*c^2 - 7*a*b^2*c
^3 + 10*a^2*c^4)*d^7 + 9*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3)*d^5 + 4*(3*b^6 - 18*a*b^4*c + 7*a^2*b^2*c^2 +
50*a^3*c^3)*d^3 + (9*a*b^5 - 68*a^2*b^3*c + 122*a^3*b*c^2)*d)*e*x)/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4
)*e^11*f^3*x^10 + 10*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^10*f^3*x^9 + (2*a^3*b^5*c - 16*a^4*b^3*c^2
+ 32*a^5*b*c^3 + 45*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^9*f^3*x^8 + 8*(15*(a^3*b^4*c^2 - 8*a^4*
b^2*c^3 + 16*a^5*c^4)*d^3 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^8*f^3*x^7 + (a^3*b^6 - 6*a^4*b^4
*c + 32*a^6*c^3 + 210*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 56*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*
b*c^3)*d^2)*e^7*f^3*x^6 + 2*(126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 56*(a^3*b^5*c - 8*a^4*b^3*c^
2 + 16*a^5*b*c^3)*d^3 + 3*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^6*f^3*x^5 + (2*a^4*b^5 - 16*a^5*b^3*c + 32
*a^6*b*c^2 + 210*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 140*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^
3)*d^4 + 15*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^5*f^3*x^4 + 4*(30*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^
5*c^4)*d^7 + 28*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 +
2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^4*f^3*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 45*(a^3*b^4*c^
2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 56*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 15*(a^3*b^6 - 6*a^4*
b^4*c + 32*a^6*c^3)*d^4 + 12*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^3*f^3*x^2 + 2*(5*(a^3*b^4*c^2 - 8*a
^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 8*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + 3*(a^3*b^6 - 6*a^4*b^4*c + 3
2*a^6*c^3)*d^5 + 4*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e^2*f^
3*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^10 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^8 + (a
^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^6 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^4 + (a^5*b^4 - 8*a^6*b^2*c
+ 16*a^7*c^2)*d^2)*e*f^3) + 3*integrate(((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^3*x^3 + 3*(b^5*c - 8*a*b^3*c^
2 + 16*a^2*b*c^3)*d*e^2*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 9*a*b^4*c + 23*a^2*b^2*c^2 - 1
0*a^3*c^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e*x + (b^6 - 9*a*b^4*c + 23*a^2*b^2*c^2 - 10*a^3*c^3)*
d)/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a), x)/((a^4*b
^4 - 8*a^5*b^2*c + 16*a^6*c^2)*f^3) - 3*b*log(e*x + d)/(a^4*e*f^3)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1791 vs. \(2 (329) = 658\).

Time = 0.43 (sec) , antiderivative size = 1791, normalized size of antiderivative = 5.22 \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\text {Too large to display} \]

[In]

integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="giac")

[Out]

3/4*((a^4*b^8*c*e^3*f^3 - 14*a^5*b^6*c^2*e^3*f^3 + 70*a^6*b^4*c^3*e^3*f^3 - 140*a^7*b^2*c^4*e^3*f^3 + 80*a^8*c
^5*e^3*f^3)*sqrt(b^2 - 4*a*c)*log(abs(b*e^2*x^2 + sqrt(b^2 - 4*a*c)*e^2*x^2 + 2*b*d*e*x + 2*sqrt(b^2 - 4*a*c)*
d*e*x + b*d^2 + sqrt(b^2 - 4*a*c)*d^2 + 2*a)) - (a^4*b^8*c*e^3*f^3 - 14*a^5*b^6*c^2*e^3*f^3 + 70*a^6*b^4*c^3*e
^3*f^3 - 140*a^7*b^2*c^4*e^3*f^3 + 80*a^8*c^5*e^3*f^3)*sqrt(b^2 - 4*a*c)*log(abs(-b*e^2*x^2 + sqrt(b^2 - 4*a*c
)*e^2*x^2 - 2*b*d*e*x + 2*sqrt(b^2 - 4*a*c)*d*e*x - b*d^2 + sqrt(b^2 - 4*a*c)*d^2 - 2*a)))/(a^8*b^8*c*e^4*f^6
- 16*a^9*b^6*c^2*e^4*f^6 + 96*a^10*b^4*c^3*e^4*f^6 - 256*a^11*b^2*c^4*e^4*f^6 + 256*a^12*c^5*e^4*f^6) - 1/4*(6
*b^4*c^2*e^8*x^8 - 42*a*b^2*c^3*e^8*x^8 + 60*a^2*c^4*e^8*x^8 + 48*b^4*c^2*d*e^7*x^7 - 336*a*b^2*c^3*d*e^7*x^7
+ 480*a^2*c^4*d*e^7*x^7 + 168*b^4*c^2*d^2*e^6*x^6 - 1176*a*b^2*c^3*d^2*e^6*x^6 + 1680*a^2*c^4*d^2*e^6*x^6 + 33
6*b^4*c^2*d^3*e^5*x^5 - 2352*a*b^2*c^3*d^3*e^5*x^5 + 3360*a^2*c^4*d^3*e^5*x^5 + 420*b^4*c^2*d^4*e^4*x^4 - 2940
*a*b^2*c^3*d^4*e^4*x^4 + 4200*a^2*c^4*d^4*e^4*x^4 + 12*b^5*c*e^6*x^6 - 87*a*b^3*c^2*e^6*x^6 + 138*a^2*b*c^3*e^
6*x^6 + 336*b^4*c^2*d^5*e^3*x^3 - 2352*a*b^2*c^3*d^5*e^3*x^3 + 3360*a^2*c^4*d^5*e^3*x^3 + 72*b^5*c*d*e^5*x^5 -
522*a*b^3*c^2*d*e^5*x^5 + 828*a^2*b*c^3*d*e^5*x^5 + 168*b^4*c^2*d^6*e^2*x^2 - 1176*a*b^2*c^3*d^6*e^2*x^2 + 16
80*a^2*c^4*d^6*e^2*x^2 + 180*b^5*c*d^2*e^4*x^4 - 1305*a*b^3*c^2*d^2*e^4*x^4 + 2070*a^2*b*c^3*d^2*e^4*x^4 + 48*
b^4*c^2*d^7*e*x - 336*a*b^2*c^3*d^7*e*x + 480*a^2*c^4*d^7*e*x + 240*b^5*c*d^3*e^3*x^3 - 1740*a*b^3*c^2*d^3*e^3
*x^3 + 2760*a^2*b*c^3*d^3*e^3*x^3 + 6*b^4*c^2*d^8 - 42*a*b^2*c^3*d^8 + 60*a^2*c^4*d^8 + 180*b^5*c*d^4*e^2*x^2
- 1305*a*b^3*c^2*d^4*e^2*x^2 + 2070*a^2*b*c^3*d^4*e^2*x^2 + 6*b^6*e^4*x^4 - 36*a*b^4*c*e^4*x^4 + 14*a^2*b^2*c^
2*e^4*x^4 + 100*a^3*c^3*e^4*x^4 + 72*b^5*c*d^5*e*x - 522*a*b^3*c^2*d^5*e*x + 828*a^2*b*c^3*d^5*e*x + 24*b^6*d*
e^3*x^3 - 144*a*b^4*c*d*e^3*x^3 + 56*a^2*b^2*c^2*d*e^3*x^3 + 400*a^3*c^3*d*e^3*x^3 + 12*b^5*c*d^6 - 87*a*b^3*c
^2*d^6 + 138*a^2*b*c^3*d^6 + 36*b^6*d^2*e^2*x^2 - 216*a*b^4*c*d^2*e^2*x^2 + 84*a^2*b^2*c^2*d^2*e^2*x^2 + 600*a
^3*c^3*d^2*e^2*x^2 + 24*b^6*d^3*e*x - 144*a*b^4*c*d^3*e*x + 56*a^2*b^2*c^2*d^3*e*x + 400*a^3*c^3*d^3*e*x + 6*b
^6*d^4 - 36*a*b^4*c*d^4 + 14*a^2*b^2*c^2*d^4 + 100*a^3*c^3*d^4 + 9*a*b^5*e^2*x^2 - 68*a^2*b^3*c*e^2*x^2 + 122*
a^3*b*c^2*e^2*x^2 + 18*a*b^5*d*e*x - 136*a^2*b^3*c*d*e*x + 244*a^3*b*c^2*d*e*x + 9*a*b^5*d^2 - 68*a^2*b^3*c*d^
2 + 122*a^3*b*c^2*d^2 + 2*a^2*b^4 - 16*a^3*b^2*c + 32*a^4*c^2)/((a^3*b^4*e*f^3 - 8*a^4*b^2*c*e*f^3 + 16*a^5*c^
2*e*f^3)*(c*e^5*x^5 + 5*c*d*e^4*x^4 + 10*c*d^2*e^3*x^3 + 10*c*d^3*e^2*x^2 + 5*c*d^4*e*x + b*e^3*x^3 + c*d^5 +
3*b*d*e^2*x^2 + 3*b*d^2*e*x + b*d^3 + a*e*x + a*d)^2) + 3/4*b*log(abs(c*e^4*x^4 + 4*c*d*e^3*x^3 + 6*c*d^2*e^2*
x^2 + 4*c*d^3*e*x + c*d^4 + b*e^2*x^2 + 2*b*d*e*x + b*d^2 + a))/(a^4*e*f^3) - 3*b*log(abs(e*x + d))/(a^4*e*f^3
)

Mupad [B] (verification not implemented)

Time = 24.18 (sec) , antiderivative size = 25334, normalized size of antiderivative = 73.86 \[ \int \frac {1}{(d f+e f x)^3 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx=\text {Too large to display} \]

[In]

int(1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x)

[Out]

(log(((27*c^5*e^16*x^2*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)^3)/(a^9*f^9*(4*a*c - b^2)^6) - ((3*b - 3*a^4*e*f^3*(-(b^
6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2/(a^8*e^2*f^6*(4*a*c - b^2)^5))^(1/2))*((9*c^3*e^15*(b^4 + 10*a
^2*c^2 - 7*a*b^2*c)*(4*b^6 - 10*a^3*c^3 + 6*b^5*c*d^2 + 71*a^2*b^2*c^2 - 33*a*b^4*c - 47*a*b^3*c^2*d^2 + 90*a^
2*b*c^3*d^2))/(a^6*f^6*(4*a*c - b^2)^4) - ((3*b - 3*a^4*e*f^3*(-(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*
c)^2/(a^8*e^2*f^6*(4*a*c - b^2)^5))^(1/2))*((6*c^2*e^16*(2*b^7 - 20*a^3*b*c^3 + b^6*c*d^2 + 46*a^2*b^3*c^2 + 1
00*a^3*c^4*d^2 - 18*a*b^5*c - 2*a*b^4*c^2*d^2 - 30*a^2*b^2*c^3*d^2))/(a^3*f^3*(4*a*c - b^2)^2) + (b*c^2*e^16*(
3*b - 3*a^4*e*f^3*(-(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2/(a^8*e^2*f^6*(4*a*c - b^2)^5))^(1/2))*(
a*b + 3*b^2*d^2 + 3*b^2*e^2*x^2 - 10*a*c*d^2 + 6*b^2*d*e*x - 10*a*c*e^2*x^2 - 20*a*c*d*e*x))/(a^4*f^3) + (6*c^
3*e^18*x^2*(b^6 + 100*a^3*c^3 - 30*a^2*b^2*c^2 - 2*a*b^4*c))/(a^3*f^3*(4*a*c - b^2)^2) + (12*c^3*d*e^17*x*(b^6
+ 100*a^3*c^3 - 30*a^2*b^2*c^2 - 2*a*b^4*c))/(a^3*f^3*(4*a*c - b^2)^2)))/(4*a^4*e*f^3) + (9*b*c^4*e^17*x^2*(6
*b^8 + 900*a^4*c^4 + 479*a^2*b^4*c^2 - 1100*a^3*b^2*c^3 - 89*a*b^6*c))/(a^6*f^6*(4*a*c - b^2)^4) + (18*b*c^4*d
*e^16*x*(6*b^8 + 900*a^4*c^4 + 479*a^2*b^4*c^2 - 1100*a^3*b^2*c^3 - 89*a*b^6*c))/(a^6*f^6*(4*a*c - b^2)^4)))/(
4*a^4*e*f^3) + (27*c^4*e^14*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)^2*(b^5 + 16*a^2*b*c^2 + b^4*c*d^2 + 10*a^2*c^3*d^2
- 8*a*b^3*c - 7*a*b^2*c^2*d^2))/(a^9*f^9*(4*a*c - b^2)^6) + (54*c^5*d*e^15*x*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)^3)
/(a^9*f^9*(4*a*c - b^2)^6))*((27*c^5*e^16*x^2*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)^3)/(a^9*f^9*(4*a*c - b^2)^6) - ((
3*b + 3*a^4*e*f^3*(-(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2/(a^8*e^2*f^6*(4*a*c - b^2)^5))^(1/2))*(
(9*c^3*e^15*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)*(4*b^6 - 10*a^3*c^3 + 6*b^5*c*d^2 + 71*a^2*b^2*c^2 - 33*a*b^4*c - 4
7*a*b^3*c^2*d^2 + 90*a^2*b*c^3*d^2))/(a^6*f^6*(4*a*c - b^2)^4) - ((3*b + 3*a^4*e*f^3*(-(b^6 - 20*a^3*c^3 + 30*
a^2*b^2*c^2 - 10*a*b^4*c)^2/(a^8*e^2*f^6*(4*a*c - b^2)^5))^(1/2))*((6*c^2*e^16*(2*b^7 - 20*a^3*b*c^3 + b^6*c*d
^2 + 46*a^2*b^3*c^2 + 100*a^3*c^4*d^2 - 18*a*b^5*c - 2*a*b^4*c^2*d^2 - 30*a^2*b^2*c^3*d^2))/(a^3*f^3*(4*a*c -
b^2)^2) + (b*c^2*e^16*(3*b + 3*a^4*e*f^3*(-(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2/(a^8*e^2*f^6*(4*
a*c - b^2)^5))^(1/2))*(a*b + 3*b^2*d^2 + 3*b^2*e^2*x^2 - 10*a*c*d^2 + 6*b^2*d*e*x - 10*a*c*e^2*x^2 - 20*a*c*d*
e*x))/(a^4*f^3) + (6*c^3*e^18*x^2*(b^6 + 100*a^3*c^3 - 30*a^2*b^2*c^2 - 2*a*b^4*c))/(a^3*f^3*(4*a*c - b^2)^2)
+ (12*c^3*d*e^17*x*(b^6 + 100*a^3*c^3 - 30*a^2*b^2*c^2 - 2*a*b^4*c))/(a^3*f^3*(4*a*c - b^2)^2)))/(4*a^4*e*f^3)
+ (9*b*c^4*e^17*x^2*(6*b^8 + 900*a^4*c^4 + 479*a^2*b^4*c^2 - 1100*a^3*b^2*c^3 - 89*a*b^6*c))/(a^6*f^6*(4*a*c
- b^2)^4) + (18*b*c^4*d*e^16*x*(6*b^8 + 900*a^4*c^4 + 479*a^2*b^4*c^2 - 1100*a^3*b^2*c^3 - 89*a*b^6*c))/(a^6*f
^6*(4*a*c - b^2)^4)))/(4*a^4*e*f^3) + (27*c^4*e^14*(b^4 + 10*a^2*c^2 - 7*a*b^2*c)^2*(b^5 + 16*a^2*b*c^2 + b^4*
c*d^2 + 10*a^2*c^3*d^2 - 8*a*b^3*c - 7*a*b^2*c^2*d^2))/(a^9*f^9*(4*a*c - b^2)^6) + (54*c^5*d*e^15*x*(b^4 + 10*
a^2*c^2 - 7*a*b^2*c)^3)/(a^9*f^9*(4*a*c - b^2)^6)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 +
960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c
^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*
f^6)) - ((x^4*(6*b^6*e^3 + 100*a^3*c^3*e^3 + 180*b^5*c*d^2*e^3 + 14*a^2*b^2*c^2*e^3 + 4200*a^2*c^4*d^4*e^3 + 4
20*b^4*c^2*d^4*e^3 - 36*a*b^4*c*e^3 - 1305*a*b^3*c^2*d^2*e^3 + 2070*a^2*b*c^3*d^2*e^3 - 2940*a*b^2*c^3*d^4*e^3
))/(4*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)) + (3*x^6*(4*b^5*c*e^5 - 29*a*b^3*c^2*e^5 + 46*a^2*b*c^3*e^5 + 560*
a^2*c^4*d^2*e^5 + 56*b^4*c^2*d^2*e^5 - 392*a*b^2*c^3*d^2*e^5))/(4*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)) + (x*(
12*b^6*d^3 + 36*b^5*c*d^5 + 200*a^3*c^3*d^3 + 240*a^2*c^4*d^7 + 24*b^4*c^2*d^7 + 9*a*b^5*d - 261*a*b^3*c^2*d^5
+ 414*a^2*b*c^3*d^5 - 168*a*b^2*c^3*d^7 + 28*a^2*b^2*c^2*d^3 - 68*a^2*b^3*c*d + 122*a^3*b*c^2*d - 72*a*b^4*c*
d^3))/(2*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)) + (3*x^5*(560*a^2*c^4*d^3*e^4 + 56*b^4*c^2*d^3*e^4 + 12*b^5*c*d
*e^4 - 87*a*b^3*c^2*d*e^4 + 138*a^2*b*c^3*d*e^4 - 392*a*b^2*c^3*d^3*e^4))/(2*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2
*c)) + (3*x^8*(10*a^2*c^4*e^7 + b^4*c^2*e^7 - 7*a*b^2*c^3*e^7))/(2*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)) + (x^
2*(36*b^6*d^2*e + 9*a*b^5*e + 600*a^3*c^3*d^2*e + 1680*a^2*c^4*d^6*e + 168*b^4*c^2*d^6*e - 68*a^2*b^3*c*e + 12
2*a^3*b*c^2*e + 180*b^5*c*d^4*e - 216*a*b^4*c*d^2*e - 1305*a*b^3*c^2*d^4*e + 2070*a^2*b*c^3*d^4*e - 1176*a*b^2
*c^3*d^6*e + 84*a^2*b^2*c^2*d^2*e))/(4*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)) + (x^3*(6*b^6*d*e^2 + 100*a^3*c^3
*d*e^2 + 60*b^5*c*d^3*e^2 + 840*a^2*c^4*d^5*e^2 + 84*b^4*c^2*d^5*e^2 - 36*a*b^4*c*d*e^2 + 14*a^2*b^2*c^2*d*e^2
- 435*a*b^3*c^2*d^3*e^2 + 690*a^2*b*c^3*d^3*e^2 - 588*a*b^2*c^3*d^5*e^2))/(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c
) + (12*x^7*(10*a^2*c^4*d*e^6 + b^4*c^2*d*e^6 - 7*a*b^2*c^3*d*e^6))/(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c) + (2*
a^2*b^4 + 32*a^4*c^2 + 6*b^6*d^4 - 16*a^3*b^2*c + 9*a*b^5*d^2 + 12*b^5*c*d^6 + 100*a^3*c^3*d^4 + 60*a^2*c^4*d^
8 + 6*b^4*c^2*d^8 - 68*a^2*b^3*c*d^2 + 122*a^3*b*c^2*d^2 - 87*a*b^3*c^2*d^6 + 138*a^2*b*c^3*d^6 - 42*a*b^2*c^3
*d^8 + 14*a^2*b^2*c^2*d^4 - 36*a*b^4*c*d^4)/(4*e*(a^3*b^4 + 16*a^5*c^2 - 8*a^4*b^2*c)))/(x^4*(15*b^2*d^2*e^4*f
^3 + 210*c^2*d^6*e^4*f^3 + 2*a*b*e^4*f^3 + 30*a*c*d^2*e^4*f^3 + 140*b*c*d^4*e^4*f^3) + x^7*(120*c^2*d^3*e^7*f^
3 + 16*b*c*d*e^7*f^3) + x*(6*b^2*d^5*e*f^3 + 10*c^2*d^9*e*f^3 + 2*a^2*d*e*f^3 + 8*a*b*d^3*e*f^3 + 12*a*c*d^5*e
*f^3 + 16*b*c*d^7*e*f^3) + x^3*(20*b^2*d^3*e^3*f^3 + 120*c^2*d^7*e^3*f^3 + 8*a*b*d*e^3*f^3 + 40*a*c*d^3*e^3*f^
3 + 112*b*c*d^5*e^3*f^3) + x^2*(a^2*e^2*f^3 + 15*b^2*d^4*e^2*f^3 + 45*c^2*d^8*e^2*f^3 + 12*a*b*d^2*e^2*f^3 + 3
0*a*c*d^4*e^2*f^3 + 56*b*c*d^6*e^2*f^3) + x^5*(6*b^2*d*e^5*f^3 + 252*c^2*d^5*e^5*f^3 + 12*a*c*d*e^5*f^3 + 112*
b*c*d^3*e^5*f^3) + x^8*(45*c^2*d^2*e^8*f^3 + 2*b*c*e^8*f^3) + x^6*(b^2*e^6*f^3 + 210*c^2*d^4*e^6*f^3 + 2*a*c*e
^6*f^3 + 56*b*c*d^2*e^6*f^3) + a^2*d^2*f^3 + b^2*d^6*f^3 + c^2*d^10*f^3 + c^2*e^10*f^3*x^10 + 2*a*b*d^4*f^3 +
2*a*c*d^6*f^3 + 2*b*c*d^8*f^3 + 10*c^2*d*e^9*f^3*x^9) - (3*b*log(d + e*x))/(a^4*e*f^3) + (3*atan((x^2*((((((54
*a^3*b^13*c^4*e^17*f^3 - 1233*a^4*b^11*c^5*e^17*f^3 + 11583*a^5*b^9*c^6*e^17*f^3 - 57204*a^6*b^7*c^7*e^17*f^3
+ 156276*a^7*b^5*c^8*e^17*f^3 - 223200*a^8*b^3*c^9*e^17*f^3 + 129600*a^9*b*c^10*e^17*f^3)/(a^9*b^12*f^9 + 4096
*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 61
44*a^14*b^2*c^5*f^9) - (((153600*a^13*c^10*e^18*f^6 + 6*a^6*b^14*c^3*e^18*f^6 - 108*a^7*b^12*c^4*e^18*f^6 + 58
8*a^8*b^10*c^5*e^18*f^6 + 792*a^9*b^8*c^6*e^18*f^6 - 22272*a^10*b^6*c^7*e^18*f^6 + 100608*a^11*b^4*c^8*e^18*f^
6 - 199680*a^12*b^2*c^9*e^18*f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^
9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^
3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^
15*c^2*e^19*f^9 - 328*a^10*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 972
80*a^13*b^7*c^6*e^19*f^9 - 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^1
9*f^9))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5
120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a
^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120
*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^
3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*
a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a
^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2
*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6))
- (27000*a^6*c^11*e^16 + 27*b^12*c^5*e^16 - 567*a*b^10*c^6*e^16 + 4779*a^2*b^8*c^7*e^16 - 20601*a^3*b^6*c^8*e^
16 + 47790*a^4*b^4*c^9*e^16 - 56700*a^5*b^2*c^10*e^16)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9
+ 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + (3*((3*((153
600*a^13*c^10*e^18*f^6 + 6*a^6*b^14*c^3*e^18*f^6 - 108*a^7*b^12*c^4*e^18*f^6 + 588*a^8*b^10*c^5*e^18*f^6 + 792
*a^9*b^8*c^6*e^18*f^6 - 22272*a^10*b^6*c^7*e^18*f^6 + 100608*a^11*b^4*c^8*e^18*f^6 - 199680*a^12*b^2*c^9*e^18*
f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3
840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 96
0*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^15*c^2*e^19*f^9 - 328*a^10*b^
13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13*b^7*c^6*e^19*f^9 - 22
7328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))/(2*(4*a^4*b^10*e^2*f^
6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*
a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b
^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)
)/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)*(6*b^11*e*f^3 - 120*
a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3
)*(12*a^9*b^15*c^2*e^19*f^9 - 328*a^10*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^
19*f^9 + 97280*a^13*b^7*c^6*e^19*f^9 - 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^
16*b*c^9*e^19*f^9))/(8*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*
c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096
*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 61
44*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (
9*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3
+ 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^15*c^2*e^19*f^9 - 328*a^1
0*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13*b^7*c^6*e^19*f^9
- 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))/(32*a^8*e^2*f^6*(
4*a*c - b^2)^5*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6
+ 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 2
40*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(3*b^8 + 10*a^4
*c^4 + 120*a^2*b^4*c^2 - 145*a^3*b^2*c^3 - 33*a*b^6*c))/(8*a^3*c^2*(4*a*c - b^2)^6*(100*a^6*c^6 - 6*b^12 - 960
*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 - 7675*a^4*b^4*c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)) + (b*((3*((54*a^3*b^13*
c^4*e^17*f^3 - 1233*a^4*b^11*c^5*e^17*f^3 + 11583*a^5*b^9*c^6*e^17*f^3 - 57204*a^6*b^7*c^7*e^17*f^3 + 156276*a
^7*b^5*c^8*e^17*f^3 - 223200*a^8*b^3*c^9*e^17*f^3 + 129600*a^9*b*c^10*e^17*f^3)/(a^9*b^12*f^9 + 4096*a^15*c^6*
f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^
2*c^5*f^9) - (((153600*a^13*c^10*e^18*f^6 + 6*a^6*b^14*c^3*e^18*f^6 - 108*a^7*b^12*c^4*e^18*f^6 + 588*a^8*b^10
*c^5*e^18*f^6 + 792*a^9*b^8*c^6*e^18*f^6 - 22272*a^10*b^6*c^7*e^18*f^6 + 100608*a^11*b^4*c^8*e^18*f^6 - 199680
*a^12*b^2*c^9*e^18*f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a
^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a
^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^15*c^2*e^1
9*f^9 - 328*a^10*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13*b^
7*c^6*e^19*f^9 - 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))/(2
*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^
2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^
2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e
*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*
a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^
4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^
2)^(5/2)) - (((3*((153600*a^13*c^10*e^18*f^6 + 6*a^6*b^14*c^3*e^18*f^6 - 108*a^7*b^12*c^4*e^18*f^6 + 588*a^8*b
^10*c^5*e^18*f^6 + 792*a^9*b^8*c^6*e^18*f^6 - 22272*a^10*b^6*c^7*e^18*f^6 + 100608*a^11*b^4*c^8*e^18*f^6 - 199
680*a^12*b^2*c^9*e^18*f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 128
0*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 614
4*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^15*c^2*
e^19*f^9 - 328*a^10*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13
*b^7*c^6*e^19*f^9 - 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))
/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8
*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8
*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2
*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c
)*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 +
7680*a^4*b^3*c^4*e*f^3)*(12*a^9*b^15*c^2*e^19*f^9 - 328*a^10*b^13*c^3*e^19*f^9 + 3840*a^11*b^11*c^4*e^19*f^9 -
24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13*b^7*c^6*e^19*f^9 - 227328*a^14*b^5*c^7*e^19*f^9 + 294912*a^15*b^3*c^
8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))/(8*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*
e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6
)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840
*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^
2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*
f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)) +
(27*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^3*(12*a^9*b^15*c^2*e^19*f^9 - 328*a^10*b^13*c^3*e^19*f^9
+ 3840*a^11*b^11*c^4*e^19*f^9 - 24960*a^12*b^9*c^5*e^19*f^9 + 97280*a^13*b^7*c^6*e^19*f^9 - 227328*a^14*b^5*c
^7*e^19*f^9 + 294912*a^15*b^3*c^8*e^19*f^9 - 163840*a^16*b*c^9*e^19*f^9))/(64*a^12*e^3*f^9*(4*a*c - b^2)^(15/2
)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840
*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(3*b^8 + 190*a^4*c^4 + 180*a^2*b^4*c^2 - 335*a^3*b^2*c^3 - 39*a*b
^6*c))/(8*a^3*c^2*(4*a*c - b^2)^(13/2)*(100*a^6*c^6 - 6*b^12 - 960*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 - 7675*a^4*b
^4*c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)))*(16*a^12*b^12*f^9*(4*a*c - b^2)^(15/2) + 65536*a^18*c^6*f^9*(4*a*c
- b^2)^(15/2) - 384*a^13*b^10*c*f^9*(4*a*c - b^2)^(15/2) + 3840*a^14*b^8*c^2*f^9*(4*a*c - b^2)^(15/2) - 20480
*a^15*b^6*c^3*f^9*(4*a*c - b^2)^(15/2) + 61440*a^16*b^4*c^4*f^9*(4*a*c - b^2)^(15/2) - 98304*a^17*b^2*c^5*f^9*
(4*a*c - b^2)^(15/2)))/(10800*a^6*c^8*e^14 + 27*b^12*c^2*e^14 - 540*a*b^10*c^3*e^14 + 4320*a^2*b^8*c^4*e^14 -
17280*a^3*b^6*c^5*e^14 + 35100*a^4*b^4*c^6*e^14 - 32400*a^5*b^2*c^7*e^14) - (x*((((2*(27000*a^6*c^11*d*e^15 +
27*b^12*c^5*d*e^15 - 567*a*b^10*c^6*d*e^15 + 4779*a^2*b^8*c^7*d*e^15 - 20601*a^3*b^6*c^8*d*e^15 + 47790*a^4*b^
4*c^9*d*e^15 - 56700*a^5*b^2*c^10*d*e^15))/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b
^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - (((2*(129600*a^9*b*c^10*
d*e^16*f^3 + 54*a^3*b^13*c^4*d*e^16*f^3 - 1233*a^4*b^11*c^5*d*e^16*f^3 + 11583*a^5*b^9*c^6*d*e^16*f^3 - 57204*
a^6*b^7*c^7*d*e^16*f^3 + 156276*a^7*b^5*c^8*d*e^16*f^3 - 223200*a^8*b^3*c^9*d*e^16*f^3))/(a^9*b^12*f^9 + 4096*
a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 614
4*a^14*b^2*c^5*f^9) - (((2*(153600*a^13*c^10*d*e^17*f^6 + 6*a^6*b^14*c^3*d*e^17*f^6 - 108*a^7*b^12*c^4*d*e^17*
f^6 + 588*a^8*b^10*c^5*d*e^17*f^6 + 792*a^9*b^8*c^6*d*e^17*f^6 - 22272*a^10*b^6*c^7*d*e^17*f^6 + 100608*a^11*b
^4*c^8*d*e^17*f^6 - 199680*a^12*b^2*c^9*d*e^17*f^6))/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 +
240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - ((6*b^11*e*f^3
- 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^
4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*d*e^18*f^9 + 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11
*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 97280*a^13*b^7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e
^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/((4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f
^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6
*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b
^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*
c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 -
2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f
^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^
4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*
e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)) - (3*((3*((2*(153600*a^13*c^10*d*e^17*f^6 + 6*a^6*b^14*c^3*d*e^17*f^6 - 108*a
^7*b^12*c^4*d*e^17*f^6 + 588*a^8*b^10*c^5*d*e^17*f^6 + 792*a^9*b^8*c^6*d*e^17*f^6 - 22272*a^10*b^6*c^7*d*e^17*
f^6 + 100608*a^11*b^4*c^8*d*e^17*f^6 - 199680*a^12*b^2*c^9*d*e^17*f^6))/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24
*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^
9) - ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^
3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*d*e^18*f^9 + 328*a^10*b^13*c^3*d*e
^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 97280*a^13*b^7*c^6*d*e^18*f^9 + 2273
28*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/((4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 64
0*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*
f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^
4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^
(5/2)) - (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^
5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f
^9 - 12*a^9*b^15*c^2*d*e^18*f^9 + 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^
9*c^5*d*e^18*f^9 - 97280*a^13*b^7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18
*f^9))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 -
2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9
- 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c
^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (9*(b^6 - 20*a
^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7
*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*
d*e^18*f^9 + 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 97
280*a^13*b^7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/(16*a^8*e^2*f^
6*(4*a*c - b^2)^5*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*
f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9
+ 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(3*b^8 + 10*
a^4*c^4 + 120*a^2*b^4*c^2 - 145*a^3*b^2*c^3 - 33*a*b^6*c))/(8*a^3*c^2*(4*a*c - b^2)^6*(100*a^6*c^6 - 6*b^12 -
960*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 - 7675*a^4*b^4*c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)) + (b*((((3*((2*(1536
00*a^13*c^10*d*e^17*f^6 + 6*a^6*b^14*c^3*d*e^17*f^6 - 108*a^7*b^12*c^4*d*e^17*f^6 + 588*a^8*b^10*c^5*d*e^17*f^
6 + 792*a^9*b^8*c^6*d*e^17*f^6 - 22272*a^10*b^6*c^7*d*e^17*f^6 + 100608*a^11*b^4*c^8*d*e^17*f^6 - 199680*a^12*
b^2*c^9*d*e^17*f^6))/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12
*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*
b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^
18*f^9 - 12*a^9*b^15*c^2*d*e^18*f^9 + 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^1
2*b^9*c^5*d*e^18*f^9 - 97280*a^13*b^7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*
e^18*f^9))/((4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 +
5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*
a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3
+ 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) - (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10
*a*b^4*c)*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*
e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*d*e^18*f^9 + 328*a^10*b^13*c^3
*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 97280*a^13*b^7*c^6*d*e^18*f^9 +
227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10
*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^
6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280
*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*
a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2
*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 -
80*a^5*b^8*c*e^2*f^6)) - (3*((2*(129600*a^9*b*c^10*d*e^16*f^3 + 54*a^3*b^13*c^4*d*e^16*f^3 - 1233*a^4*b^11*c^5
*d*e^16*f^3 + 11583*a^5*b^9*c^6*d*e^16*f^3 - 57204*a^6*b^7*c^7*d*e^16*f^3 + 156276*a^7*b^5*c^8*d*e^16*f^3 - 22
3200*a^8*b^3*c^9*d*e^16*f^3))/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 -
1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - (((2*(153600*a^13*c^10*d*e^17*f^6 + 6
*a^6*b^14*c^3*d*e^17*f^6 - 108*a^7*b^12*c^4*d*e^17*f^6 + 588*a^8*b^10*c^5*d*e^17*f^6 + 792*a^9*b^8*c^6*d*e^17*
f^6 - 22272*a^10*b^6*c^7*d*e^17*f^6 + 100608*a^11*b^4*c^8*d*e^17*f^6 - 199680*a^12*b^2*c^9*d*e^17*f^6))/(a^9*b
^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^
4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c
^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*d*
e^18*f^9 + 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 9728
0*a^13*b^7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/((4*a^4*b^10*e^2
*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 -
80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^1
2*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*
b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6
- 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a
^5*b^8*c*e^2*f^6)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (27*
(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^3*(163840*a^16*b*c^9*d*e^18*f^9 - 12*a^9*b^15*c^2*d*e^18*f^9
+ 328*a^10*b^13*c^3*d*e^18*f^9 - 3840*a^11*b^11*c^4*d*e^18*f^9 + 24960*a^12*b^9*c^5*d*e^18*f^9 - 97280*a^13*b^
7*c^6*d*e^18*f^9 + 227328*a^14*b^5*c^7*d*e^18*f^9 - 294912*a^15*b^3*c^8*d*e^18*f^9))/(32*a^12*e^3*f^9*(4*a*c -
b^2)^(15/2)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3
*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(3*b^8 + 190*a^4*c^4 + 180*a^2*b^4*c^2 - 335*a^3*b^2*c
^3 - 39*a*b^6*c))/(8*a^3*c^2*(4*a*c - b^2)^(13/2)*(100*a^6*c^6 - 6*b^12 - 960*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 -
7675*a^4*b^4*c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)))*(16*a^12*b^12*f^9*(4*a*c - b^2)^(15/2) + 65536*a^18*c^6
*f^9*(4*a*c - b^2)^(15/2) - 384*a^13*b^10*c*f^9*(4*a*c - b^2)^(15/2) + 3840*a^14*b^8*c^2*f^9*(4*a*c - b^2)^(15
/2) - 20480*a^15*b^6*c^3*f^9*(4*a*c - b^2)^(15/2) + 61440*a^16*b^4*c^4*f^9*(4*a*c - b^2)^(15/2) - 98304*a^17*b
^2*c^5*f^9*(4*a*c - b^2)^(15/2)))/(10800*a^6*c^8*e^14 + 27*b^12*c^2*e^14 - 540*a*b^10*c^3*e^14 + 4320*a^2*b^8*
c^4*e^14 - 17280*a^3*b^6*c^5*e^14 + 35100*a^4*b^4*c^6*e^14 - 32400*a^5*b^2*c^7*e^14) + (((((36*a^3*b^14*c^3*e^
15*f^3 - 14400*a^10*c^10*e^15*f^3 - 837*a^4*b^12*c^4*e^15*f^3 + 8046*a^5*b^10*c^5*e^15*f^3 - 40941*a^6*b^8*c^6
*e^15*f^3 + 116532*a^7*b^6*c^7*e^15*f^3 - 177588*a^8*b^4*c^8*e^15*f^3 + 119520*a^9*b^2*c^9*e^15*f^3 + 129600*a
^9*b*c^10*d^2*e^15*f^3 + 54*a^3*b^13*c^4*d^2*e^15*f^3 - 1233*a^4*b^11*c^5*d^2*e^15*f^3 + 11583*a^5*b^9*c^6*d^2
*e^15*f^3 - 57204*a^6*b^7*c^7*d^2*e^15*f^3 + 156276*a^7*b^5*c^8*d^2*e^15*f^3 - 223200*a^8*b^3*c^9*d^2*e^15*f^3
)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840
*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) - (((12*a^6*b^15*c^2*e^16*f^6 - 300*a^7*b^13*c^3*e^16*f^6 + 3156*a^
8*b^11*c^4*e^16*f^6 - 17976*a^9*b^9*c^5*e^16*f^6 + 59136*a^10*b^7*c^6*e^16*f^6 - 109824*a^11*b^5*c^7*e^16*f^6
+ 101376*a^12*b^3*c^8*e^16*f^6 + 153600*a^13*c^10*d^2*e^16*f^6 - 30720*a^13*b*c^9*e^16*f^6 + 6*a^6*b^14*c^3*d^
2*e^16*f^6 - 108*a^7*b^12*c^4*d^2*e^16*f^6 + 588*a^8*b^10*c^5*d^2*e^16*f^6 + 792*a^9*b^8*c^6*d^2*e^16*f^6 - 22
272*a^10*b^6*c^7*d^2*e^16*f^6 + 100608*a^11*b^4*c^8*d^2*e^16*f^6 - 199680*a^12*b^2*c^9*d^2*e^16*f^6)/(a^9*b^12
*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c
^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*
e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^12*c^3*e^17*f^9
+ 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 24576*a^15*b^4*c^7*
e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e^17*f^9 - 328*a
^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 + 97280*a^13*b^7
*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(2*(4*a^4*b^10*e^2*f
^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80
*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*
b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*
c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 -
4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5
*b^8*c*e^2*f^6)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*
b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f
^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)) - (27*b^13*c^4*e^14 - 594*a*
b^11*c^5*e^14 + 43200*a^6*b*c^10*e^14 + 5319*a^2*b^9*c^6*e^14 - 24732*a^3*b^7*c^7*e^14 + 62748*a^4*b^5*c^8*e^1
4 - 82080*a^5*b^3*c^9*e^14 + 27000*a^6*c^11*d^2*e^14 + 27*b^12*c^5*d^2*e^14 + 4779*a^2*b^8*c^7*d^2*e^14 - 2060
1*a^3*b^6*c^8*d^2*e^14 + 47790*a^4*b^4*c^9*d^2*e^14 - 56700*a^5*b^2*c^10*d^2*e^14 - 567*a*b^10*c^6*d^2*e^14)/(
a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^
13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + (3*((3*((12*a^6*b^15*c^2*e^16*f^6 - 300*a^7*b^13*c^3*e^16*f^6 + 3156
*a^8*b^11*c^4*e^16*f^6 - 17976*a^9*b^9*c^5*e^16*f^6 + 59136*a^10*b^7*c^6*e^16*f^6 - 109824*a^11*b^5*c^7*e^16*f
^6 + 101376*a^12*b^3*c^8*e^16*f^6 + 153600*a^13*c^10*d^2*e^16*f^6 - 30720*a^13*b*c^9*e^16*f^6 + 6*a^6*b^14*c^3
*d^2*e^16*f^6 - 108*a^7*b^12*c^4*d^2*e^16*f^6 + 588*a^8*b^10*c^5*d^2*e^16*f^6 + 792*a^9*b^8*c^6*d^2*e^16*f^6 -
22272*a^10*b^6*c^7*d^2*e^16*f^6 + 100608*a^11*b^4*c^8*d^2*e^16*f^6 - 199680*a^12*b^2*c^9*d^2*e^16*f^6)/(a^9*b
^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^
4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c
^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^12*c^3*e^17*
f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 24576*a^15*b^4*c
^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e^17*f^9 - 32
8*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 + 97280*a^13*
b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(2*(4*a^4*b^10*e^
2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 -
80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^
12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^
4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)*(6*b^11*e*f^3 -
120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e
*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e
^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 24576*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^1
6*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*
e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 + 97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^
9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(8*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2
*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(
a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^
13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*
c - b^2)^(5/2)) + (9*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^2*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 61
44*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2
*e^17*f^9 - 96*a^11*b^12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b
^6*c^6*e^17*f^9 - 24576*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 +
12*a^9*b^15*c^2*d^2*e^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*
b^9*c^5*d^2*e^17*f^9 + 97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^
8*d^2*e^17*f^9))/(32*a^8*e^2*f^6*(4*a*c - b^2)^5*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*
e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^1
5*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a
^14*b^2*c^5*f^9)))*(3*b^8 + 10*a^4*c^4 + 120*a^2*b^4*c^2 - 145*a^3*b^2*c^3 - 33*a*b^6*c)*(16*a^12*b^12*f^9*(4*
a*c - b^2)^(15/2) + 65536*a^18*c^6*f^9*(4*a*c - b^2)^(15/2) - 384*a^13*b^10*c*f^9*(4*a*c - b^2)^(15/2) + 3840*
a^14*b^8*c^2*f^9*(4*a*c - b^2)^(15/2) - 20480*a^15*b^6*c^3*f^9*(4*a*c - b^2)^(15/2) + 61440*a^16*b^4*c^4*f^9*(
4*a*c - b^2)^(15/2) - 98304*a^17*b^2*c^5*f^9*(4*a*c - b^2)^(15/2)))/(8*a^3*c^2*(4*a*c - b^2)^6*(10800*a^6*c^8*
e^14 + 27*b^12*c^2*e^14 - 540*a*b^10*c^3*e^14 + 4320*a^2*b^8*c^4*e^14 - 17280*a^3*b^6*c^5*e^14 + 35100*a^4*b^4
*c^6*e^14 - 32400*a^5*b^2*c^7*e^14)*(100*a^6*c^6 - 6*b^12 - 960*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 - 7675*a^4*b^4*
c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)) + (b*((3*((36*a^3*b^14*c^3*e^15*f^3 - 14400*a^10*c^10*e^15*f^3 - 837*a
^4*b^12*c^4*e^15*f^3 + 8046*a^5*b^10*c^5*e^15*f^3 - 40941*a^6*b^8*c^6*e^15*f^3 + 116532*a^7*b^6*c^7*e^15*f^3 -
177588*a^8*b^4*c^8*e^15*f^3 + 119520*a^9*b^2*c^9*e^15*f^3 + 129600*a^9*b*c^10*d^2*e^15*f^3 + 54*a^3*b^13*c^4*
d^2*e^15*f^3 - 1233*a^4*b^11*c^5*d^2*e^15*f^3 + 11583*a^5*b^9*c^6*d^2*e^15*f^3 - 57204*a^6*b^7*c^7*d^2*e^15*f^
3 + 156276*a^7*b^5*c^8*d^2*e^15*f^3 - 223200*a^8*b^3*c^9*d^2*e^15*f^3)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*
a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9
) - (((12*a^6*b^15*c^2*e^16*f^6 - 300*a^7*b^13*c^3*e^16*f^6 + 3156*a^8*b^11*c^4*e^16*f^6 - 17976*a^9*b^9*c^5*e
^16*f^6 + 59136*a^10*b^7*c^6*e^16*f^6 - 109824*a^11*b^5*c^7*e^16*f^6 + 101376*a^12*b^3*c^8*e^16*f^6 + 153600*a
^13*c^10*d^2*e^16*f^6 - 30720*a^13*b*c^9*e^16*f^6 + 6*a^6*b^14*c^3*d^2*e^16*f^6 - 108*a^7*b^12*c^4*d^2*e^16*f^
6 + 588*a^8*b^10*c^5*d^2*e^16*f^6 + 792*a^9*b^8*c^6*d^2*e^16*f^6 - 22272*a^10*b^6*c^7*d^2*e^16*f^6 + 100608*a^
11*b^4*c^8*d^2*e^16*f^6 - 199680*a^12*b^2*c^9*d^2*e^16*f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c
*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^1
1*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4
*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13
*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 24576*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 -
163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^1
1*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 + 97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d
^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c
^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*
a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 614
4*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*
a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e
^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)))*(b^6 - 20*a^3*c^3 + 30*
a^2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) - (((3*((12*a^6*b^15*c^2*e^16*f^6 - 300*a^7*b^13*
c^3*e^16*f^6 + 3156*a^8*b^11*c^4*e^16*f^6 - 17976*a^9*b^9*c^5*e^16*f^6 + 59136*a^10*b^7*c^6*e^16*f^6 - 109824*
a^11*b^5*c^7*e^16*f^6 + 101376*a^12*b^3*c^8*e^16*f^6 + 153600*a^13*c^10*d^2*e^16*f^6 - 30720*a^13*b*c^9*e^16*f
^6 + 6*a^6*b^14*c^3*d^2*e^16*f^6 - 108*a^7*b^12*c^4*d^2*e^16*f^6 + 588*a^8*b^10*c^5*d^2*e^16*f^6 + 792*a^9*b^8
*c^6*d^2*e^16*f^6 - 22272*a^10*b^6*c^7*d^2*e^16*f^6 + 100608*a^11*b^4*c^8*d^2*e^16*f^6 - 199680*a^12*b^2*c^9*d
^2*e^16*f^6)/(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^6*c^3
*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9) + ((6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*
f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*
a^11*b^12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9
- 24576*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^
2*d^2*e^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^1
7*f^9 + 97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9)
)/(2*(4*a^4*b^10*e^2*f^6 - 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^
8*b^2*c^4*e^2*f^6 - 80*a^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^
8*c^2*f^9 - 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(b^6 - 20*a^3*c^3 + 30*a^
2*b^2*c^2 - 10*a*b^4*c))/(4*a^4*e*f^3*(4*a*c - b^2)^(5/2)) + (3*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*
c)*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 +
7680*a^4*b^3*c^4*e*f^3)*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 -
5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 24576*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^
17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840
*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 + 97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*
b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(8*a^4*e*f^3*(4*a*c - b^2)^(5/2)*(4*a^4*b^10*e^2*f^6
- 4096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a
^5*b^8*c*e^2*f^6)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9 - 1280*a^12*b^
6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(6*b^11*e*f^3 - 120*a*b^9*c*e*f^3 - 6144*a^5*b*c^
5*e*f^3 + 960*a^2*b^7*c^2*e*f^3 - 3840*a^3*b^5*c^3*e*f^3 + 7680*a^4*b^3*c^4*e*f^3))/(2*(4*a^4*b^10*e^2*f^6 - 4
096*a^9*c^5*e^2*f^6 + 640*a^6*b^6*c^2*e^2*f^6 - 2560*a^7*b^4*c^3*e^2*f^6 + 5120*a^8*b^2*c^4*e^2*f^6 - 80*a^5*b
^8*c*e^2*f^6)) + (27*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c)^3*(4*a^10*b^14*c^2*e^17*f^9 - 96*a^11*b^
12*c^3*e^17*f^9 + 960*a^12*b^10*c^4*e^17*f^9 - 5120*a^13*b^8*c^5*e^17*f^9 + 15360*a^14*b^6*c^6*e^17*f^9 - 2457
6*a^15*b^4*c^7*e^17*f^9 + 16384*a^16*b^2*c^8*e^17*f^9 - 163840*a^16*b*c^9*d^2*e^17*f^9 + 12*a^9*b^15*c^2*d^2*e
^17*f^9 - 328*a^10*b^13*c^3*d^2*e^17*f^9 + 3840*a^11*b^11*c^4*d^2*e^17*f^9 - 24960*a^12*b^9*c^5*d^2*e^17*f^9 +
97280*a^13*b^7*c^6*d^2*e^17*f^9 - 227328*a^14*b^5*c^7*d^2*e^17*f^9 + 294912*a^15*b^3*c^8*d^2*e^17*f^9))/(64*a
^12*e^3*f^9*(4*a*c - b^2)^(15/2)*(a^9*b^12*f^9 + 4096*a^15*c^6*f^9 - 24*a^10*b^10*c*f^9 + 240*a^11*b^8*c^2*f^9
- 1280*a^12*b^6*c^3*f^9 + 3840*a^13*b^4*c^4*f^9 - 6144*a^14*b^2*c^5*f^9)))*(3*b^8 + 190*a^4*c^4 + 180*a^2*b^4
*c^2 - 335*a^3*b^2*c^3 - 39*a*b^6*c)*(16*a^12*b^12*f^9*(4*a*c - b^2)^(15/2) + 65536*a^18*c^6*f^9*(4*a*c - b^2)
^(15/2) - 384*a^13*b^10*c*f^9*(4*a*c - b^2)^(15/2) + 3840*a^14*b^8*c^2*f^9*(4*a*c - b^2)^(15/2) - 20480*a^15*b
^6*c^3*f^9*(4*a*c - b^2)^(15/2) + 61440*a^16*b^4*c^4*f^9*(4*a*c - b^2)^(15/2) - 98304*a^17*b^2*c^5*f^9*(4*a*c
- b^2)^(15/2)))/(8*a^3*c^2*(4*a*c - b^2)^(13/2)*(10800*a^6*c^8*e^14 + 27*b^12*c^2*e^14 - 540*a*b^10*c^3*e^14 +
4320*a^2*b^8*c^4*e^14 - 17280*a^3*b^6*c^5*e^14 + 35100*a^4*b^4*c^6*e^14 - 32400*a^5*b^2*c^7*e^14)*(100*a^6*c^
6 - 6*b^12 - 960*a^2*b^8*c^2 + 3840*a^3*b^6*c^3 - 7675*a^4*b^4*c^4 + 6100*a^5*b^2*c^5 + 120*a*b^10*c)))*(b^6 -
20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(2*a^4*e*f^3*(4*a*c - b^2)^(5/2))