\(\int \frac {(d+e x^2)^4}{a+b x^2+c x^4} \, dx\) [263]

Optimal result

Integrand size = 24, antiderivative size = 459 \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right ) x}{c^3}+\frac {e^3 (4 c d-b e) x^3}{3 c^2}+\frac {e^4 x^5}{5 c}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )+\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )-\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b+\sqrt {b^2-4 a c}}} \]

[Out]

e^2*(6*c^2*d^2+b^2*e^2-c*e*(a*e+4*b*d))*x/c^3+1/3*e^3*(-b*e+4*c*d)*x^3/c^2+1/5*e^4*x^5/c+1/2*arctan(x*2^(1/2)*
c^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2))*(e*(-b*e+2*c*d)*(2*c^2*d^2+b^2*e^2-2*c*e*(a*e+b*d))+(2*c^4*d^4+b^4*e^4-4
*b^2*c*e^3*(a*e+b*d)-4*c^3*d^2*e*(3*a*e+b*d)+2*c^2*e^2*(a^2*e^2+6*a*b*d*e+3*b^2*d^2))/(-4*a*c+b^2)^(1/2))/c^(7
/2)*2^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)+1/2*arctan(x*2^(1/2)*c^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2))*(e*(-b*e+2
*c*d)*(2*c^2*d^2+b^2*e^2-2*c*e*(a*e+b*d))+(-2*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(a*e+b*d)+4*c^3*d^2*e*(3*a*e+b*d)-2*
c^2*e^2*(a^2*e^2+6*a*b*d*e+3*b^2*d^2))/(-4*a*c+b^2)^(1/2))/c^(7/2)*2^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2)

Rubi [A] (verified)

Time = 0.97 (sec) , antiderivative size = 459, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {1184, 1180, 211} \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\frac {\arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (\frac {2 c^2 e^2 \left (a^2 e^2+6 a b d e+3 b^2 d^2\right )-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\sqrt {b^2-4 a c}}+e (2 c d-b e) \left (-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right )\right )}{\sqrt {2} c^{7/2} \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (e (2 c d-b e) \left (-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right )-\frac {2 c^2 e^2 \left (a^2 e^2+6 a b d e+3 b^2 d^2\right )-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\sqrt {b^2-4 a c}}\right )}{\sqrt {2} c^{7/2} \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {e^2 x \left (-c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right )}{c^3}+\frac {e^3 x^3 (4 c d-b e)}{3 c^2}+\frac {e^4 x^5}{5 c} \]

[In]

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

[Out]

(e^2*(6*c^2*d^2 + b^2*e^2 - c*e*(4*b*d + a*e))*x)/c^3 + (e^3*(4*c*d - b*e)*x^3)/(3*c^2) + (e^4*x^5)/(5*c) + ((
e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)) + (2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4
*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqr
t[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((e*(2*c*d - b*e)*(2*c^2
*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)) - (2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*
e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[
b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])

Rule 211

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

Rule 1180

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

Rule 1184

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

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right )}{c^3}+\frac {e^3 (4 c d-b e) x^2}{c^2}+\frac {e^4 x^4}{c}+\frac {c^3 d^4-6 a c^2 d^2 e^2-a b^2 e^4+a c e^3 (4 b d+a e)+e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right ) x^2}{c^3 \left (a+b x^2+c x^4\right )}\right ) \, dx \\ & = \frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right ) x}{c^3}+\frac {e^3 (4 c d-b e) x^3}{3 c^2}+\frac {e^4 x^5}{5 c}+\frac {\int \frac {c^3 d^4-6 a c^2 d^2 e^2-a b^2 e^4+a c e^3 (4 b d+a e)+e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right ) x^2}{a+b x^2+c x^4} \, dx}{c^3} \\ & = \frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right ) x}{c^3}+\frac {e^3 (4 c d-b e) x^3}{3 c^2}+\frac {e^4 x^5}{5 c}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )-\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{2 c^3}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )+\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{2 c^3} \\ & = \frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right ) x}{c^3}+\frac {e^3 (4 c d-b e) x^3}{3 c^2}+\frac {e^4 x^5}{5 c}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )+\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\left (e (2 c d-b e) \left (2 c^2 d^2+b^2 e^2-2 c e (b d+a e)\right )-\frac {2 c^4 d^4+b^4 e^4-4 b^2 c e^3 (b d+a e)-4 c^3 d^2 e (b d+3 a e)+2 c^2 e^2 \left (3 b^2 d^2+6 a b d e+a^2 e^2\right )}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b+\sqrt {b^2-4 a c}}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.43 (sec) , antiderivative size = 570, normalized size of antiderivative = 1.24 \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\frac {e^2 \left (6 c^2 d^2+b^2 e^2-c e (4 b d+a e)\right ) x}{c^3}+\frac {e^3 (4 c d-b e) x^3}{3 c^2}+\frac {e^4 x^5}{5 c}+\frac {\left (2 c^4 d^4+b^3 \left (b-\sqrt {b^2-4 a c}\right ) e^4+4 c^3 d^2 e \left (-b d+\sqrt {b^2-4 a c} d-3 a e\right )+2 b c e^3 \left (-2 b^2 d+2 b \sqrt {b^2-4 a c} d-2 a b e+a \sqrt {b^2-4 a c} e\right )+2 c^2 e^2 \left (3 b^2 d^2-3 b d \left (\sqrt {b^2-4 a c} d-2 a e\right )+a e \left (-2 \sqrt {b^2-4 a c} d+a e\right )\right )\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b^2-4 a c} \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\left (2 c^4 d^4+b^3 \left (b+\sqrt {b^2-4 a c}\right ) e^4-4 c^3 d^2 e \left (b d+\sqrt {b^2-4 a c} d+3 a e\right )-2 b c e^3 \left (2 b^2 d+a \sqrt {b^2-4 a c} e+2 b \left (\sqrt {b^2-4 a c} d+a e\right )\right )+2 c^2 e^2 \left (3 b^2 d^2+a e \left (2 \sqrt {b^2-4 a c} d+a e\right )+3 b d \left (\sqrt {b^2-4 a c} d+2 a e\right )\right )\right ) \arctan \left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{\sqrt {2} c^{7/2} \sqrt {b^2-4 a c} \sqrt {b+\sqrt {b^2-4 a c}}} \]

[In]

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

[Out]

(e^2*(6*c^2*d^2 + b^2*e^2 - c*e*(4*b*d + a*e))*x)/c^3 + (e^3*(4*c*d - b*e)*x^3)/(3*c^2) + (e^4*x^5)/(5*c) + ((
2*c^4*d^4 + b^3*(b - Sqrt[b^2 - 4*a*c])*e^4 + 4*c^3*d^2*e*(-(b*d) + Sqrt[b^2 - 4*a*c]*d - 3*a*e) + 2*b*c*e^3*(
-2*b^2*d + 2*b*Sqrt[b^2 - 4*a*c]*d - 2*a*b*e + a*Sqrt[b^2 - 4*a*c]*e) + 2*c^2*e^2*(3*b^2*d^2 - 3*b*d*(Sqrt[b^2
- 4*a*c]*d - 2*a*e) + a*e*(-2*Sqrt[b^2 - 4*a*c]*d + a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a
*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((2*c^4*d^4 + b^3*(b + Sqrt[b^2 - 4*a
*c])*e^4 - 4*c^3*d^2*e*(b*d + Sqrt[b^2 - 4*a*c]*d + 3*a*e) - 2*b*c*e^3*(2*b^2*d + a*Sqrt[b^2 - 4*a*c]*e + 2*b*
(Sqrt[b^2 - 4*a*c]*d + a*e)) + 2*c^2*e^2*(3*b^2*d^2 + a*e*(2*Sqrt[b^2 - 4*a*c]*d + a*e) + 3*b*d*(Sqrt[b^2 - 4*
a*c]*d + 2*a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b^2 - 4*a*c]*
Sqrt[b + Sqrt[b^2 - 4*a*c]])

Maple [C] (verified)

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

Time = 0.24 (sec) , antiderivative size = 227, normalized size of antiderivative = 0.49

method	result	size
risch	\(\frac {e^{4} x^{5}}{5 c}-\frac {e^{4} b \,x^{3}}{3 c^{2}}+\frac {4 d \,e^{3} x^{3}}{3 c}-\frac {e^{4} a x}{c^{2}}+\frac {e^{4} b^{2} x}{c^{3}}-\frac {4 e^{3} b d x}{c^{2}}+\frac {6 e^{2} d^{2} x}{c}+\frac {\munderset {\textit {\_R} =\operatorname {RootOf}\left (c \,\textit {\_Z}^{4}+\textit {\_Z}^{2} b +a \right )}{\sum }\frac {\left (e \left (2 a b c \,e^{3}-4 a \,c^{2} d \,e^{2}-b^{3} e^{3}+4 b^{2} c d \,e^{2}-6 b \,c^{2} d^{2} e +4 c^{3} d^{3}\right ) \textit {\_R}^{2}+a^{2} c \,e^{4}-a \,b^{2} e^{4}+4 a b c d \,e^{3}-6 a \,c^{2} d^{2} e^{2}+c^{3} d^{4}\right ) \ln \left (x -\textit {\_R} \right )}{2 c \,\textit {\_R}^{3}+\textit {\_R} b}}{2 c^{3}}\)	\(227\)
default	\(-\frac {e^{2} \left (-\frac {1}{5} e^{2} x^{5} c^{2}+\frac {1}{3} b c \,e^{2} x^{3}-\frac {4}{3} c^{2} d e \,x^{3}+e^{2} a c x -b^{2} e^{2} x +4 b c d e x -6 c^{2} d^{2} x \right )}{c^{3}}+\frac {\frac {\left (2 a b c \,e^{4} \sqrt {-4 a c +b^{2}}-4 a \,c^{2} d \,e^{3} \sqrt {-4 a c +b^{2}}-b^{3} e^{4} \sqrt {-4 a c +b^{2}}+4 b^{2} c d \,e^{3} \sqrt {-4 a c +b^{2}}-6 b \,c^{2} d^{2} e^{2} \sqrt {-4 a c +b^{2}}+4 c^{3} d^{3} e \sqrt {-4 a c +b^{2}}-2 a^{2} c^{2} e^{4}+4 a \,b^{2} e^{4} c -12 a b \,c^{2} d \,e^{3}+12 a \,c^{3} d^{2} e^{2}-b^{4} e^{4}+4 b^{3} c d \,e^{3}-6 b^{2} c^{2} d^{2} e^{2}+4 b \,c^{3} e \,d^{3}-2 c^{4} d^{4}\right ) \sqrt {2}\, \arctan \left (\frac {c x \sqrt {2}}{\sqrt {\left (b +\sqrt {-4 a c +b^{2}}\right ) c}}\right )}{2 c \sqrt {-4 a c +b^{2}}\, \sqrt {\left (b +\sqrt {-4 a c +b^{2}}\right ) c}}-\frac {\left (2 a b c \,e^{4} \sqrt {-4 a c +b^{2}}-4 a \,c^{2} d \,e^{3} \sqrt {-4 a c +b^{2}}-b^{3} e^{4} \sqrt {-4 a c +b^{2}}+4 b^{2} c d \,e^{3} \sqrt {-4 a c +b^{2}}-6 b \,c^{2} d^{2} e^{2} \sqrt {-4 a c +b^{2}}+4 c^{3} d^{3} e \sqrt {-4 a c +b^{2}}+2 a^{2} c^{2} e^{4}-4 a \,b^{2} e^{4} c +12 a b \,c^{2} d \,e^{3}-12 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-4 b^{3} c d \,e^{3}+6 b^{2} c^{2} d^{2} e^{2}-4 b \,c^{3} e \,d^{3}+2 c^{4} d^{4}\right ) \sqrt {2}\, \operatorname {arctanh}\left (\frac {c x \sqrt {2}}{\sqrt {\left (-b +\sqrt {-4 a c +b^{2}}\right ) c}}\right )}{2 c \sqrt {-4 a c +b^{2}}\, \sqrt {\left (-b +\sqrt {-4 a c +b^{2}}\right ) c}}}{c^{2}}\)	\(621\)

[In]

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

[Out]

1/5*e^4*x^5/c-1/3*e^4/c^2*b*x^3+4/3*d*e^3*x^3/c-e^4/c^2*a*x+e^4/c^3*b^2*x-4*e^3/c^2*b*d*x+6*e^2/c*d^2*x+1/2/c^
3*sum((e*(2*a*b*c*e^3-4*a*c^2*d*e^2-b^3*e^3+4*b^2*c*d*e^2-6*b*c^2*d^2*e+4*c^3*d^3)*_R^2+a^2*c*e^4-a*b^2*e^4+4*
a*b*c*d*e^3-6*a*c^2*d^2*e^2+c^3*d^4)/(2*_R^3*c+_R*b)*ln(x-_R),_R=RootOf(_Z^4*c+_Z^2*b+a))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 16218 vs. \(2 (421) = 842\).

Time = 270.80 (sec) , antiderivative size = 16218, normalized size of antiderivative = 35.33 \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\text {Too large to display} \]

[In]

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

[Out]

Too large to include

Sympy [F(-1)]

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

[In]

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

[Out]

Timed out

Maxima [F]

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

[In]

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

[Out]

1/15*(3*c^2*e^4*x^5 + 5*(4*c^2*d*e^3 - b*c*e^4)*x^3 + 15*(6*c^2*d^2*e^2 - 4*b*c*d*e^3 + (b^2 - a*c)*e^4)*x)/c^
3 + integrate((c^3*d^4 - 6*a*c^2*d^2*e^2 + 4*a*b*c*d*e^3 - (a*b^2 - a^2*c)*e^4 + (4*c^3*d^3*e - 6*b*c^2*d^2*e^
2 + 4*(b^2*c - a*c^2)*d*e^3 - (b^3 - 2*a*b*c)*e^4)*x^2)/(c*x^4 + b*x^2 + a), x)/c^3

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 9306 vs. \(2 (421) = 842\).

Time = 1.30 (sec) , antiderivative size = 9306, normalized size of antiderivative = 20.27 \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\text {Too large to display} \]

[In]

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

[Out]

1/8*(4*(2*b^4*c^5 - 16*a*b^2*c^6 + 32*a^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*
c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 8
*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt
(b^2 - 4*a*c)*c)*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 2*(b^2 - 4*a*c)
*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6)*c^2*d^3*e - 6*(2*b^5*c^4 - 16*a*b^3*c^5 + 32*a^2*b*c^6 - sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a
*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*
sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*
c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d^2*e^2 + 4*(2*b^6*c^
3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6
*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3
- 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(
b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a
*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*c^2*d*e^3 - (2*b^7*c^2 - 20*a*b^5*c^3 + 64
*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(
b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c
)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 -
4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b
^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)
*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b
^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*
(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*c^2*e^4 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4
*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6
- 2*b^4*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*
a*b*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 + 16*a*b^2*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a
*c)*c)*a*c^8 - 32*a^2*c^8 + 2*(b^2 - 4*a*c)*b^2*c^6 - 8*(b^2 - 4*a*c)*a*c^7)*d^4*abs(c) - 12*(sqrt(2)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c
+ sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*a*b^4*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(
2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 16*a^2*b^2*
c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 - 32*a^3*c^7 + 2*(b^2 - 4*a*c)*a*b^2*c^5 - 8*(b^2 - 4*
a*c)*a^2*c^6)*d^2*e^2*abs(c) + 8*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 2*a*b^5*c^4 + 16*sqrt(2)
*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*s
qrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^
6 - 32*a^3*b*c^6 + 2*(b^2 - 4*a*c)*a*b^3*c^4 - 8*(b^2 - 4*a*c)*a^2*b*c^5)*d*e^3*abs(c) - 2*(sqrt(2)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sq
rt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 18*a^2
*b^4*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*
b*c^5 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2
- 4*a*c)*c)*a^3*c^6 + 32*a^4*c^6 + 2*(b^2 - 4*a*c)*a*b^4*c^3 - 10*(b^2 - 4*a*c)*a^2*b^2*c^4 + 8*(b^2 - 4*a*c)
*a^3*c^5)*e^4*abs(c) + 2*(2*b^3*c^8 - 8*a*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^
3*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt
(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^8 - 2*(b^2
- 4*a*c)*b*c^8)*d^4 - 4*(2*b^4*c^7 - 8*a*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*
b^4*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*
sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 -
2*(b^2 - 4*a*c)*b^2*c^7)*d^3*e + 6*(2*b^5*c^6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*
sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqr
t(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 -
4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6 + 4*(b^2 - 4*a*c)*a*b*c^7)*d^2*e^2 - 4*(2*b^6*c^5 - 14*a*b^4*c^6 +
24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a
*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^
5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)
*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5
+ 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 -
4*a*c)*a*b^2*c^6)*d*e^3 + (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c
)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*
c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4
- sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c +
sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*s
qrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sq
rt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6
)*e^4)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b
^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) - 1/8*(4*(2*b^4*c^5 - 16*a*b^2*c^6 + 32*a^2*c^
7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqr
t(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b
^2 - 4*a*c)*c)*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 4*sqrt(2)*sqrt(b^
2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^6 - 2*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6)*c^2*d^3*e
- 6*(2*b^5*c^4 - 16*a*b^3*c^5 + 32*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c
^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(
b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 -
8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - s
qrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4
*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d^2*e^2 + 4*(2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c
^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt
(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sq
rt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*
sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8
*(b^2 - 4*a*c)*a^2*c^5)*c^2*d*e^3 - (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b
^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)
*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4
*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3
+ 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*
c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a
^2*b*c^4)*c^2*e^4 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c
)*c)*a*b^2*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*b^4*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*a^2*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*b^2*c^7 - 16*a*b^2*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^8 + 32*a^2*c^8 - 2*(b^2 - 4*a*c)*
b^2*c^6 + 8*(b^2 - 4*a*c)*a*c^7)*d^4*abs(c) + 12*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2
)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*a*b^4*
c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6
+ sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 16*a^2*b^2*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)
*c)*a^2*c^7 + 32*a^3*c^7 - 2*(b^2 - 4*a*c)*a*b^2*c^5 + 8*(b^2 - 4*a*c)*a^2*c^6)*d^2*e^2*abs(c) - 8*(sqrt(2)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sq
rt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 +
8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 1
6*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 32*a^3*b*c^6 - 2*(b^2 - 4*a*c)*a*b^3*c^4
+ 8*(b^2 - 4*a*c)*a^2*b*c^5)*d*e^3*abs(c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*
sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*a*b^6*c^
3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^
3*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 -
4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*a^2*b^2*c^5 + 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 32*a^4*c^6 - 2*(b^2 -
4*a*c)*a*b^4*c^3 + 10*(b^2 - 4*a*c)*a^2*b^2*c^4 - 8*(b^2 - 4*a*c)*a^3*c^5)*e^4*abs(c) + 2*(2*b^3*c^8 - 8*a*b*
c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c
- sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^8 - 2*(b^2 - 4*a*c)*b*c^8)*d^4 - 4*(2*b^4*c^7 - 8*a*b^
2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b
*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - sq
rt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - 2*(b^2 - 4*a*c)*b^2*c^7)*d^3*e + 6*(2*b^5*c^
6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 6*sqrt(2
)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^
2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt
(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*
c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6
+ 4*(b^2 - 4*a*c)*a*b*c^7)*d^2*e^2 - 4*(2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*
sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^
4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*
c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 -
sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sq
rt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*d*e^3 + (2*b^7*c^4 - 16*a*
b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^2 +
8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c -
sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*s
qrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt
(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*s
qrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2
- 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*
c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*e^4)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 - sq
rt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^
7 - 4*a^2*c^8)*c^2) + 1/15*(3*c^4*e^4*x^5 + 20*c^4*d*e^3*x^3 - 5*b*c^3*e^4*x^3 + 90*c^4*d^2*e^2*x - 60*b*c^3*d
*e^3*x + 15*b^2*c^2*e^4*x - 15*a*c^3*e^4*x)/c^5

Mupad [B] (verification not implemented)

Time = 10.92 (sec) , antiderivative size = 29551, normalized size of antiderivative = 64.38 \[ \int \frac {\left (d+e x^2\right )^4}{a+b x^2+c x^4} \, dx=\text {Too large to display} \]

[In]

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

[Out]

x*((b*((b*e^4)/c^2 - (4*d*e^3)/c))/c - (a*e^4)/c^2 + (6*d^2*e^2)/c) - x^3*((b*e^4)/(3*c^2) - (4*d*e^3)/(3*c))
+ atan(((((16*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d
^2*e^2 - 16*a*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 - (2*x*(4*b^3*c^7 - 16*a*b*c^8)*(
-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7
*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^
4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e
^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*
b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^
4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*
c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6
*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 2
64*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/
2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*
d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a
*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^
(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3
*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2)
- a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e
^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 44
8*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2
*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*
d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c
- b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*
b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 +
80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^
4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c
^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*
a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)
^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2
*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (2*x*(b^8*e^8 + 2
*c^8*d^8 + 2*a^4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 -
56*a^3*c^5*d^2*e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^
6*c^2*d^2*e^6 - 8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3
+ 56*a*b^5*c^2*d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*
e^6 - 280*a^2*b*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2
)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*
a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d
^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) +
336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a
^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^
6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*
e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^
7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304
*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) +
24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^
3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*
c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) +
84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2)*1i - (((
16*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d^2*e^2 - 16
*a*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 + (2*x*(4*b^3*c^7 - 16*a*b*c^8)*(-(a*b^9*e^8
+ b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28
*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(
-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*
b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3
*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*
a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*
a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^
5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*
c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b
*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(
4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3
)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a
*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^
4*c^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8
*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3
*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d
^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^
3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 7
00*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(
1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5
*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6
*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 2
8*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-
(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^
3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32
*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^
6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) + (2*x*(b^8*e^8 + 2*c^8*d^8 +
2*a^4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 - 56*a^3*c^5*
d^2*e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^6*c^2*d^2*e
^6 - 8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3 + 56*a*b^5*
c^2*d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*e^6 - 280*a
^2*b*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2)
- a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e
^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 44
8*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2
*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*
d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c
- b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*
b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 +
80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^
4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c
^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*
a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)
^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2
*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2)*1i)/((((16*a*c^8*d^
4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d^2*e^2 - 16*a*b^3*c^5*
d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 - (2*x*(4*b^3*c^7 - 16*a*b*c^8)*(-(a*b^9*e^8 + b^3*c^7*
d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*
e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b
^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8
*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*
a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^
3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^
3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^
7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 -
560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^
3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2
)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 1
12*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^
7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a
^2*b^2*c^8)))^(1/2))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c -
b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^
8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*
a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2
*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*
c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a
*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a
*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7
+ 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6
*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^
2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) -
28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^
2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c
- b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (2*x*(b^8*e^8 + 2*c^8*d^8 + 2*a^4*c^4*e
^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 - 56*a^3*c^5*d^2*e^6 + 2
8*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^6*c^2*d^2*e^6 - 8*a*b^
6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3 + 56*a*b^5*c^2*d*e^7 +
56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*e^6 - 280*a^2*b*c^5*d^
3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8
*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3
*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d
^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^
3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 7
00*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(
1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5
*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6
*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 2
8*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-
(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^
3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32
*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^
6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (2*(a^4*b^3*e^12 - 4*c^7*d^1
1*e + b^7*d^4*e^8 - 4*a*b^6*d^3*e^9 - 4*a^3*b^4*d*e^11 - 12*a*c^6*d^9*e^3 + 4*a^5*c^2*d*e^11 + 22*b*c^6*d^10*e
^2 - 8*b^6*c*d^5*e^7 + 6*a^2*b^5*d^2*e^10 - 8*a^2*c^5*d^7*e^5 + 8*a^3*c^4*d^5*e^7 + 12*a^4*c^3*d^3*e^9 - 52*b^
2*c^5*d^9*e^3 + 69*b^3*c^4*d^8*e^4 - 56*b^4*c^3*d^7*e^5 + 28*b^5*c^2*d^6*e^6 - 2*a^5*b*c*e^12 - 48*a^2*b^2*c^3
*d^5*e^7 + 50*a^2*b^3*c^2*d^4*e^8 + 8*a^3*b^2*c^2*d^3*e^9 + 54*a*b*c^5*d^8*e^4 + 26*a*b^5*c*d^4*e^8 + 4*a^4*b^
2*c*d*e^11 - 104*a*b^2*c^4*d^7*e^5 + 112*a*b^3*c^3*d^6*e^6 - 72*a*b^4*c^2*d^5*e^7 + 28*a^2*b*c^4*d^6*e^6 - 28*
a^2*b^4*c*d^3*e^9 - 20*a^3*b*c^3*d^4*e^8 + 8*a^3*b^3*c*d^2*e^10 - 18*a^4*b*c^2*d^2*e^10))/c^5 + (((16*a*c^8*d^
4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d^2*e^2 - 16*a*b^3*c^5*
d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 + (2*x*(4*b^3*c^7 - 16*a*b*c^8)*(-(a*b^9*e^8 + b^3*c^7*
d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*
e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b
^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8
*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*
a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^
3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^
3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^
7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 -
560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^
3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2
)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 1
12*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^
7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a
^2*b^2*c^8)))^(1/2))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c -
b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^
8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*
a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2
*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*
c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a
*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a
*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7
+ 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6
*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^
2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) -
28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^
2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c
- b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) + (2*x*(b^8*e^8 + 2*c^8*d^8 + 2*a^4*c^4*e
^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 - 56*a^3*c^5*d^2*e^6 + 2
8*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^6*c^2*d^2*e^6 - 8*a*b^
6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3 + 56*a*b^5*c^2*d*e^7 +
56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*e^6 - 280*a^2*b*c^5*d^
3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*(-(a*b^9*e^8 + b^3*c^7*d^8 + c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8
*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 + 64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3
*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d
^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^
3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 7
00*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(
1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5
*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6
*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 2
8*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-
(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^
3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32
*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^
6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2)))*(-(a*b^9*e^8 + b^3*c^7*d^8 +
c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) - 11*a^2*b^7*c*e^8 + 28*a^5*b*c^4*e^8 +
64*a^2*c^8*d^7*e - 64*a^5*c^5*d*e^7 + 42*a^3*b^5*c^2*e^8 - 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3
)^(1/2) - 448*a^3*c^7*d^5*e^3 + 448*a^4*c^6*d^3*e^5 - 4*a*b*c^8*d^8 - 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4
*a*c - b^2)^3)^(1/2) + 336*a^2*b^2*c^6*d^5*e^3 - 490*a^2*b^3*c^5*d^4*e^4 + 448*a^2*b^4*c^4*d^3*e^5 - 252*a^2*b
^5*c^3*d^2*e^6 - 1008*a^3*b^2*c^5*d^3*e^5 + 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1
/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1
/2) + 28*a*b^3*c^6*d^6*e^2 - 56*a*b^4*c^5*d^5*e^3 + 70*a*b^5*c^4*d^4*e^4 - 56*a*b^6*c^3*d^3*e^5 + 28*a*b^7*c^2
*d^2*e^6 - 112*a^2*b*c^7*d^6*e^2 + 80*a^2*b^6*c^2*d*e^7 + 840*a^3*b*c^6*d^4*e^4 - 264*a^3*b^4*c^3*d*e^7 - 560*
a^4*b*c^5*d^2*e^6 + 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(
4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^
(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^
2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(
4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^
2*c^8)))^(1/2)*2i + atan(((((16*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*
e^4 - 96*a^2*c^7*d^2*e^2 - 16*a*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 - (2*x*(4*b^3*c
^7 - 16*a*b*c^8)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(
1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4
*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^
8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d
^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^
6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d
^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d
^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*
b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*
a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2
) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c
^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-
(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^
(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*
d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e
+ 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*
c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/
2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1
008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d
^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6
*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2
*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6
- 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1
/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c
^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-
(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1
/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (
2*x*(b^8*e^8 + 2*c^8*d^8 + 2*a^4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^
2*c^6*d^4*e^4 - 56*a^3*c^5*d^2*e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3
*d^3*e^5 + 28*b^6*c^2*d^2*e^6 - 8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*
a*b*c^6*d^5*e^3 + 56*a*b^5*c^2*d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 16
8*a*b^4*c^3*d^2*e^6 - 280*a^2*b*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2)
- b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*
c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2)
+ 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b
^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d
^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28
*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28
*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6
+ 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^
5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c -
b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) +
56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*
d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c -
b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))
^(1/2)*1i - (((16*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c
^7*d^2*e^2 - 16*a*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 + (2*x*(4*b^3*c^7 - 16*a*b*c^
8)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*
b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 +
a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*
d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a
^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5
*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b
^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*
b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4
+ 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^
(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c
^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(
4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^
3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*
a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^
8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d
*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 -
448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b
^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^
5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*
c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*
a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2
- 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*
c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b
*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(
4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^
3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b
^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) + (2*x*(b^8*e^8 +
2*c^8*d^8 + 2*a^4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4
- 56*a^3*c^5*d^2*e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*
b^6*c^2*d^2*e^6 - 8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^
3 + 56*a*b^5*c^2*d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^
2*e^6 - 280*a^2*b*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8
- a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64
*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*
d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) -
336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*
a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e
^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6
*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c
^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 30
4*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2)
+ 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d
^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a
*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2)
+ 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2)*1i)/(((
(16*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d^2*e^2 - 1
6*a*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 - (2*x*(4*b^3*c^7 - 16*a*b*c^8)*((c^7*d^8*(
-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28
*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(
-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*
b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3
*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*
a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*
a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^
5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*
c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b
*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(
4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3
)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a
*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^
4*c^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*
(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*
b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^
3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3
+ 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 70
0*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1
/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*
e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*
c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28
*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(
4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3
)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*
a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6
*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (2*x*(b^8*e^8 + 2*c^8*d^8 + 2
*a^4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 - 56*a^3*c^5*d
^2*e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^6*c^2*d^2*e^
6 - 8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3 + 56*a*b^5*c
^2*d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*e^6 - 280*a^
2*b*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 -
a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7
- 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*
a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c
^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^
3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c -
b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^
4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 8
0*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*
d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3
*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*
c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(
1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c
^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) - (2*(a^4*b^3*e^12 -
4*c^7*d^11*e + b^7*d^4*e^8 - 4*a*b^6*d^3*e^9 - 4*a^3*b^4*d*e^11 - 12*a*c^6*d^9*e^3 + 4*a^5*c^2*d*e^11 + 22*b*c
^6*d^10*e^2 - 8*b^6*c*d^5*e^7 + 6*a^2*b^5*d^2*e^10 - 8*a^2*c^5*d^7*e^5 + 8*a^3*c^4*d^5*e^7 + 12*a^4*c^3*d^3*e^
9 - 52*b^2*c^5*d^9*e^3 + 69*b^3*c^4*d^8*e^4 - 56*b^4*c^3*d^7*e^5 + 28*b^5*c^2*d^6*e^6 - 2*a^5*b*c*e^12 - 48*a^
2*b^2*c^3*d^5*e^7 + 50*a^2*b^3*c^2*d^4*e^8 + 8*a^3*b^2*c^2*d^3*e^9 + 54*a*b*c^5*d^8*e^4 + 26*a*b^5*c*d^4*e^8 +
4*a^4*b^2*c*d*e^11 - 104*a*b^2*c^4*d^7*e^5 + 112*a*b^3*c^3*d^6*e^6 - 72*a*b^4*c^2*d^5*e^7 + 28*a^2*b*c^4*d^6*
e^6 - 28*a^2*b^4*c*d^3*e^9 - 20*a^3*b*c^3*d^4*e^8 + 8*a^3*b^3*c*d^2*e^10 - 18*a^4*b*c^2*d^2*e^10))/c^5 + (((16
*a*c^8*d^4 + 16*a^3*c^6*e^4 - 4*b^2*c^7*d^4 + 4*a*b^4*c^4*e^4 - 20*a^2*b^2*c^5*e^4 - 96*a^2*c^7*d^2*e^2 - 16*a
*b^3*c^5*d*e^3 + 64*a^2*b*c^6*d*e^3 + 24*a*b^2*c^6*d^2*e^2)/c^5 + (2*x*(4*b^3*c^7 - 16*a*b*c^8)*((c^7*d^8*(-(4
*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^
5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4
*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2
*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^
5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c
- b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c
- b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 -
28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3
*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^
5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a
*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(
1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^
5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c
^7 - 8*a^2*b^2*c^8)))^(1/2))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(
4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5
*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e
^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 +
490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a
^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2)
+ 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3
- 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2
*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*
c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a
*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(
1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2
*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-
(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2) + (2*x*(b^8*e^8 + 2*c^8*d^8 + 2*a^
4*c^4*e^8 - 56*a*c^7*d^6*e^2 + 20*a^2*b^4*c^2*e^8 - 16*a^3*b^2*c^3*e^8 + 140*a^2*c^6*d^4*e^4 - 56*a^3*c^5*d^2*
e^6 + 28*b^2*c^6*d^6*e^2 - 56*b^3*c^5*d^5*e^3 + 70*b^4*c^4*d^4*e^4 - 56*b^5*c^3*d^3*e^5 + 28*b^6*c^2*d^2*e^6 -
8*a*b^6*c*e^8 - 8*b*c^7*d^7*e - 8*b^7*c*d*e^7 + 252*a^2*b^2*c^4*d^2*e^6 + 168*a*b*c^6*d^5*e^3 + 56*a*b^5*c^2*
d*e^7 + 56*a^3*b*c^4*d*e^7 - 280*a*b^2*c^5*d^4*e^4 + 280*a*b^3*c^4*d^3*e^5 - 168*a*b^4*c^3*d^2*e^6 - 280*a^2*b
*c^5*d^3*e^5 - 112*a^2*b^3*c^3*d*e^7))/c^5)*((c^7*d^8*(-(4*a*c - b^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b
^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 -
42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4
*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*
d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e
^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2
)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c
^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a
^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 + 560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e
^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*
e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c -
b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 112*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2
) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*
d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a^2*b^2*c^8)))^(1/2)))*((c^7*d^8*(-(4*a*c - b
^2)^3)^(1/2) - b^3*c^7*d^8 - a*b^9*e^8 - a*b^6*e^8*(-(4*a*c - b^2)^3)^(1/2) + 11*a^2*b^7*c*e^8 - 28*a^5*b*c^4*
e^8 - 64*a^2*c^8*d^7*e + 64*a^5*c^5*d*e^7 - 42*a^3*b^5*c^2*e^8 + 63*a^4*b^3*c^3*e^8 + a^4*c^3*e^8*(-(4*a*c - b
^2)^3)^(1/2) + 448*a^3*c^7*d^5*e^3 - 448*a^4*c^6*d^3*e^5 + 4*a*b*c^8*d^8 + 8*a*b^8*c*d*e^7 - 6*a^3*b^2*c^2*e^8
*(-(4*a*c - b^2)^3)^(1/2) - 336*a^2*b^2*c^6*d^5*e^3 + 490*a^2*b^3*c^5*d^4*e^4 - 448*a^2*b^4*c^4*d^3*e^5 + 252*
a^2*b^5*c^3*d^2*e^6 + 1008*a^3*b^2*c^5*d^3*e^5 - 700*a^3*b^3*c^4*d^2*e^6 + 70*a^2*c^5*d^4*e^4*(-(4*a*c - b^2)^
3)^(1/2) - 28*a^3*c^4*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) + 16*a*b^2*c^7*d^7*e + 5*a^2*b^4*c*e^8*(-(4*a*c - b^2)^
3)^(1/2) - 28*a*b^3*c^6*d^6*e^2 + 56*a*b^4*c^5*d^5*e^3 - 70*a*b^5*c^4*d^4*e^4 + 56*a*b^6*c^3*d^3*e^5 - 28*a*b^
7*c^2*d^2*e^6 + 112*a^2*b*c^7*d^6*e^2 - 80*a^2*b^6*c^2*d*e^7 - 840*a^3*b*c^6*d^4*e^4 + 264*a^3*b^4*c^3*d*e^7 +
560*a^4*b*c^5*d^2*e^6 - 304*a^4*b^2*c^4*d*e^7 - 28*a*c^6*d^6*e^2*(-(4*a*c - b^2)^3)^(1/2) + 56*a*b*c^5*d^5*e^
3*(-(4*a*c - b^2)^3)^(1/2) + 24*a^3*b*c^3*d*e^7*(-(4*a*c - b^2)^3)^(1/2) - 70*a*b^2*c^4*d^4*e^4*(-(4*a*c - b^2
)^3)^(1/2) + 56*a*b^3*c^3*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 28*a*b^4*c^2*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2) - 1
12*a^2*b*c^4*d^3*e^5*(-(4*a*c - b^2)^3)^(1/2) - 32*a^2*b^3*c^2*d*e^7*(-(4*a*c - b^2)^3)^(1/2) + 8*a*b^5*c*d*e^
7*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^2*c^3*d^2*e^6*(-(4*a*c - b^2)^3)^(1/2))/(8*(16*a^3*c^9 + a*b^4*c^7 - 8*a
^2*b^2*c^8)))^(1/2)*2i + (e^4*x^5)/(5*c)