\(\int \frac {1}{x^{7/2} (a+b x^2+c x^4)} \, dx\) [1070]

Optimal result

Integrand size = 20, antiderivative size = 412 \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=-\frac {2}{5 a x^{5/2}}+\frac {2 b}{a^2 \sqrt {x}}+\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \arctan \left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}+\frac {\sqrt [4]{c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \arctan \left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}-\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}-\frac {\sqrt [4]{c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}} \]

[Out]

-2/5/a/x^(5/2)+1/2*c^(1/4)*arctan(2^(1/4)*c^(1/4)*x^(1/2)/(-b-(-4*a*c+b^2)^(1/2))^(1/4))*(b+(2*a*c-b^2)/(-4*a*
c+b^2)^(1/2))*2^(1/4)/a^2/(-b-(-4*a*c+b^2)^(1/2))^(1/4)-1/2*c^(1/4)*arctanh(2^(1/4)*c^(1/4)*x^(1/2)/(-b-(-4*a*
c+b^2)^(1/2))^(1/4))*(b+(2*a*c-b^2)/(-4*a*c+b^2)^(1/2))*2^(1/4)/a^2/(-b-(-4*a*c+b^2)^(1/2))^(1/4)+1/2*c^(1/4)*
arctan(2^(1/4)*c^(1/4)*x^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(1/4))*(b+(-2*a*c+b^2)/(-4*a*c+b^2)^(1/2))*2^(1/4)/a^2/
(-b+(-4*a*c+b^2)^(1/2))^(1/4)-1/2*c^(1/4)*arctanh(2^(1/4)*c^(1/4)*x^(1/2)/(-b+(-4*a*c+b^2)^(1/2))^(1/4))*(b+(-
2*a*c+b^2)/(-4*a*c+b^2)^(1/2))*2^(1/4)/a^2/(-b+(-4*a*c+b^2)^(1/2))^(1/4)+2*b/a^2/x^(1/2)

Rubi [A] (verified)

Time = 0.59 (sec) , antiderivative size = 412, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.350, Rules used = {1129, 1382, 1518, 1524, 304, 211, 214} \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \arctan \left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{2^{3/4} a^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}+\frac {\sqrt [4]{c} \left (\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}+b\right ) \arctan \left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{2^{3/4} a^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}}-\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \text {arctanh}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{2^{3/4} a^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}-\frac {\sqrt [4]{c} \left (\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}+b\right ) \text {arctanh}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{2^{3/4} a^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}}+\frac {2 b}{a^2 \sqrt {x}}-\frac {2}{5 a x^{5/2}} \]

[In]

Int[1/(x^(7/2)*(a + b*x^2 + c*x^4)),x]

[Out]

-2/(5*a*x^(5/2)) + (2*b)/(a^2*Sqrt[x]) + (c^(1/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4
)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(b + (b^2
- 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b
+ Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x]
)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b + (b^2 - 2*a*c)/
Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b + Sqrt[
b^2 - 4*a*c])^(1/4))

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 214

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

Rule 304

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

Rule 1129

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

Rule 1382

Int[((d_.)*(x_))^(m_)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(d*x)^(m + 1)*((a +
b*x^n + c*x^(2*n))^(p + 1)/(a*d*(m + 1))), x] - Dist[1/(a*d^n*(m + 1)), Int[(d*x)^(m + n)*(b*(m + n*(p + 1) +
1) + c*(m + 2*n*(p + 1) + 1)*x^n)*(a + b*x^n + c*x^(2*n))^p, x], x] /; FreeQ[{a, b, c, d, p}, x] && EqQ[n2, 2
*n] && NeQ[b^2 - 4*a*c, 0] && IGtQ[n, 0] && LtQ[m, -1] && IntegerQ[p]

Rule 1518

Int[((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(n_))*((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_))^(p_), x_Symbol] :>
Simp[d*(f*x)^(m + 1)*((a + b*x^n + c*x^(2*n))^(p + 1)/(a*f*(m + 1))), x] + Dist[1/(a*f^n*(m + 1)), Int[(f*x)^
(m + n)*(a + b*x^n + c*x^(2*n))^p*Simp[a*e*(m + 1) - b*d*(m + n*(p + 1) + 1) - c*d*(m + 2*n*(p + 1) + 1)*x^n,
x], x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && IGtQ[n, 0] && LtQ[m, -
1] && IntegerQ[p]

Rule 1524

Int[(((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(n_)))/((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_)), x_Symbol] :> Wi
th[{q = Rt[b^2 - 4*a*c, 2]}, Dist[e/2 + (2*c*d - b*e)/(2*q), Int[(f*x)^m/(b/2 - q/2 + c*x^n), x], x] + Dist[e/
2 - (2*c*d - b*e)/(2*q), Int[(f*x)^m/(b/2 + q/2 + c*x^n), x], x]] /; FreeQ[{a, b, c, d, e, f, m}, x] && EqQ[n2
, 2*n] && NeQ[b^2 - 4*a*c, 0] && IGtQ[n, 0]

Rubi steps \begin{align*} \text {integral}& = 2 \text {Subst}\left (\int \frac {1}{x^6 \left (a+b x^4+c x^8\right )} \, dx,x,\sqrt {x}\right ) \\ & = -\frac {2}{5 a x^{5/2}}+\frac {2 \text {Subst}\left (\int \frac {-5 b-5 c x^4}{x^2 \left (a+b x^4+c x^8\right )} \, dx,x,\sqrt {x}\right )}{5 a} \\ & = -\frac {2}{5 a x^{5/2}}+\frac {2 b}{a^2 \sqrt {x}}-\frac {2 \text {Subst}\left (\int \frac {x^2 \left (-5 \left (b^2-a c\right )-5 b c x^4\right )}{a+b x^4+c x^8} \, dx,x,\sqrt {x}\right )}{5 a^2} \\ & = -\frac {2}{5 a x^{5/2}}+\frac {2 b}{a^2 \sqrt {x}}+\frac {\left (c \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {x^2}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{a^2}+\frac {\left (c \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {x^2}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{a^2} \\ & = -\frac {2}{5 a x^{5/2}}+\frac {2 b}{a^2 \sqrt {x}}-\frac {\left (\sqrt {c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{\sqrt {2} a^2}+\frac {\left (\sqrt {c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{\sqrt {2} a^2}-\frac {\left (\sqrt {c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{\sqrt {2} a^2}+\frac {\left (\sqrt {c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{\sqrt {2} a^2} \\ & = -\frac {2}{5 a x^{5/2}}+\frac {2 b}{a^2 \sqrt {x}}+\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}+\frac {\sqrt [4]{c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}-\frac {\sqrt [4]{c} \left (b-\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}-\frac {\sqrt [4]{c} \left (b+\frac {b^2-2 a c}{\sqrt {b^2-4 a c}}\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{2^{3/4} a^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}} \\ \end{align*}

Mathematica [C] (verified)

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

Time = 0.11 (sec) , antiderivative size = 106, normalized size of antiderivative = 0.26 \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\frac {-\frac {4 \left (a-5 b x^2\right )}{x^{5/2}}+5 \text {RootSum}\left [a+b \text {$\#$1}^4+c \text {$\#$1}^8\&,\frac {b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )-a c \log \left (\sqrt {x}-\text {$\#$1}\right )+b c \log \left (\sqrt {x}-\text {$\#$1}\right ) \text {$\#$1}^4}{b \text {$\#$1}+2 c \text {$\#$1}^5}\&\right ]}{10 a^2} \]

[In]

Integrate[1/(x^(7/2)*(a + b*x^2 + c*x^4)),x]

[Out]

((-4*(a - 5*b*x^2))/x^(5/2) + 5*RootSum[a + b*#1^4 + c*#1^8 & , (b^2*Log[Sqrt[x] - #1] - a*c*Log[Sqrt[x] - #1]
+ b*c*Log[Sqrt[x] - #1]*#1^4)/(b*#1 + 2*c*#1^5) & ])/(10*a^2)

Maple [C] (verified)

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

Time = 0.08 (sec) , antiderivative size = 81, normalized size of antiderivative = 0.20

method	result	size
risch	\(-\frac {2 \left (-5 b \,x^{2}+a \right )}{5 a^{2} x^{\frac {5}{2}}}+\frac {\munderset {\textit {\_R} =\operatorname {RootOf}\left (c \,\textit {\_Z}^{8}+\textit {\_Z}^{4} b +a \right )}{\sum }\frac {\left (b c \,\textit {\_R}^{6}+\left (-a c +b^{2}\right ) \textit {\_R}^{2}\right ) \ln \left (\sqrt {x}-\textit {\_R} \right )}{2 \textit {\_R}^{7} c +\textit {\_R}^{3} b}}{2 a^{2}}\)	\(81\)
derivativedivides	\(-\frac {2}{5 a \,x^{\frac {5}{2}}}+\frac {2 b}{a^{2} \sqrt {x}}-\frac {\munderset {\textit {\_R} =\operatorname {RootOf}\left (c \,\textit {\_Z}^{8}+\textit {\_Z}^{4} b +a \right )}{\sum }\frac {\left (-b c \,\textit {\_R}^{6}+\left (a c -b^{2}\right ) \textit {\_R}^{2}\right ) \ln \left (\sqrt {x}-\textit {\_R} \right )}{2 \textit {\_R}^{7} c +\textit {\_R}^{3} b}}{2 a^{2}}\)	\(84\)
default	\(-\frac {2}{5 a \,x^{\frac {5}{2}}}+\frac {2 b}{a^{2} \sqrt {x}}-\frac {\munderset {\textit {\_R} =\operatorname {RootOf}\left (c \,\textit {\_Z}^{8}+\textit {\_Z}^{4} b +a \right )}{\sum }\frac {\left (-b c \,\textit {\_R}^{6}+\left (a c -b^{2}\right ) \textit {\_R}^{2}\right ) \ln \left (\sqrt {x}-\textit {\_R} \right )}{2 \textit {\_R}^{7} c +\textit {\_R}^{3} b}}{2 a^{2}}\)	\(84\)

[In]

int(1/x^(7/2)/(c*x^4+b*x^2+a),x,method=_RETURNVERBOSE)

[Out]

-2/5*(-5*b*x^2+a)/a^2/x^(5/2)+1/2/a^2*sum((b*c*_R^6+(-a*c+b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(x^(1/2)-_R),_R=RootO
f(_Z^8*c+_Z^4*b+a))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 8376 vs. \(2 (328) = 656\).

Time = 7.04 (sec) , antiderivative size = 8376, normalized size of antiderivative = 20.33 \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\text {Too large to display} \]

[In]

integrate(1/x^(7/2)/(c*x^4+b*x^2+a),x, algorithm="fricas")

[Out]

Too large to include

Sympy [F(-1)]

Timed out. \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\text {Timed out} \]

[In]

integrate(1/x**(7/2)/(c*x**4+b*x**2+a),x)

[Out]

Timed out

Maxima [F]

\[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\int { \frac {1}{{\left (c x^{4} + b x^{2} + a\right )} x^{\frac {7}{2}}} \,d x } \]

[In]

integrate(1/x^(7/2)/(c*x^4+b*x^2+a),x, algorithm="maxima")

[Out]

2/5*(5*b/sqrt(x) - a/x^(5/2))/a^2 + integrate((b*c*x^(5/2) + (b^2 - a*c)*sqrt(x))/(a^2*c*x^4 + a^2*b*x^2 + a^3
), x)

Giac [F]

\[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\int { \frac {1}{{\left (c x^{4} + b x^{2} + a\right )} x^{\frac {7}{2}}} \,d x } \]

[In]

integrate(1/x^(7/2)/(c*x^4+b*x^2+a),x, algorithm="giac")

[Out]

integrate(1/((c*x^4 + b*x^2 + a)*x^(7/2)), x)

Mupad [B] (verification not implemented)

Time = 15.16 (sec) , antiderivative size = 15149, normalized size of antiderivative = 36.77 \[ \int \frac {1}{x^{7/2} \left (a+b x^2+c x^4\right )} \, dx=\text {Too large to display} \]

[In]

int(1/(x^(7/2)*(a + b*x^2 + c*x^4)),x)

[Out]

atan((((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^
5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(
1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c
^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/
2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c
- b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1
/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*
a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 69632
0*a^26*b^4*c^7 - 655360*a^27*b^2*c^8) - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a
^23*b^7*c^6 - 368640*a^24*b^5*c^7 + 393216*a^25*b^3*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b
^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552
*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a
^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^1
0*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i + ((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b
*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2
) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*
c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3))
)^(3/4)*(131072*a^26*b*c^9 + x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2
- 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^
2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1
/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^
9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)
- 2048*a^21*b^11*c^4 + 28672*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8)
+ x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*
a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^
11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c
- b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i)
/(256*a^20*c^12 - ((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3
+ 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c
- b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8
+ 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 + b^8*(-(4*a*c -
b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c
^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c
- b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^
4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6
*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8) - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^
5 + 151552*a^23*b^7*c^6 - 368640*a^24*b^5*c^7 + 393216*a^25*b^3*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3
*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b
^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^
(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*
c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4) + ((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) +
144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2
)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) -
7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*
b^2*c^3)))^(3/4)*(131072*a^26*b*c^9 + x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2
*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*
c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b
^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(13107
2*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27
*b^2*c^8) - 2048*a^21*b^11*c^4 + 28672*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*
b^3*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c
^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2)
- 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*
(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^
(1/4)))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b
^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^
(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*
c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*2i - (2/(5*a) - (2*b*x^2)/a^2)/x^(5/2) + ata
n((((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c
^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2
) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4
- 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2)
+ 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b
^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2)
+ 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^1
2*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a
^26*b^4*c^7 - 655360*a^27*b^2*c^8) - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a^23
*b^7*c^6 - 368640*a^24*b^5*c^7 + 393216*a^25*b^3*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13
- b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^
5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*
b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b
^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i + ((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^
6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) -
17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(
-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(
3/4)*(131072*a^26*b*c^9 + x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 3
90*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b
^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2)
)/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 -
4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8) -
2048*a^21*b^11*c^4 + 28672*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8) + x
^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2
*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*
c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b
^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i)/(2
56*a^20*c^12 - ((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 6
81*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c -
b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 2
56*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^
2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*
(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b
^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c
^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^
6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8) - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 +
151552*a^23*b^7*c^6 - 368640*a^24*b^5*c^7 + 393216*a^25*b^3*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^
10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*
c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/
2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4
- 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4) + ((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144
*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5
)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*
a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2
*c^3)))^(3/4)*(131072*a^26*b*c^9 + x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^
9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c -
15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)
^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a
^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^
2*c^8) - 2048*a^21*b^11*c^4 + 28672*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3
*c^8) + x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6
+ 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 1
7*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(
4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/
4)))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*
c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/
2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4
- 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*2i - 2*atan((((-(b^13 + b^8*(-(4*a*c - b^2)^5)^
(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a
*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)
^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 2
56*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 3
90*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b
^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2)
)/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 -
4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i
- 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a^23*b^7*c^6 - 368640*a^24*b^5*c^7 + 3
93216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2)
+ 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c -
b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2
) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^
12*b^2*c^3)))^(1/4) + ((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*
c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4
*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*
b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(131072*a^26*b*c^9 + x^(1/2)*
(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 -
552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) -
10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16
*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b
^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i - 2048*a^21*b^11*c^4 + 28672*a^22
*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 25
6*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 +
681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c
- b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 +
256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4))/(256*a^20*c^12 + ((-(b^13 + b^8*(
-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^
5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*
(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 9
6*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 1
15*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a
*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a
*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*
(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 65536
0*a^27*b^2*c^8)*1i - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a^23*b^7*c^6 - 36864
0*a^24*b^5*c^7 + 393216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a
*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a
^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*
a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^1
1*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i - ((-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b
^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c
+ 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2
)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(131072*
a^26*b*c^9 + x^(1/2)*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^
3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a
*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^
8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^
10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i - 2048*a^21*
b^11*c^4 + 28672*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8)*1i - x^(1/2)*
(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 + b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^
2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*
a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^
(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i))*(-(b^13
+ b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5
*b^3*c^5 + a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c + 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a^3*b
^2*c^3*(-(4*a*c - b^2)^5)^(1/2) - 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^
6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4) - 2*atan((((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*
b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/
2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6
*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)
))^(3/4)*(x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 +
681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c
- b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 +
256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*
c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i - 131072*a^26*b
*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a^23*b^7*c^6 - 368640*a^24*b^5*c^7 + 393216*a^25*b^3*c
^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6
+ 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) -
17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-
(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1
/4) + ((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^
5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(
1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c
^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(131072*a^26*b*c^9 + x^(1/2)*(-(b^13 - b^8*(-
(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5
- a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(
-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96
*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*
a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i - 2048*a^21*b^11*c^4 + 28672*a^22*b^9*c^5 - 15155
2*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10)
)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4
- 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2)
+ 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 -
16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4))/(256*a^20*c^12 + ((-(b^13 - b^8*(-(4*a*c - b^2)^5
)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4
*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^
5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 -
256*a^12*b^2*c^3)))^(3/4)*(x^(1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 -
390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2
*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/
2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9
- 4096*a^23*b^10*c^4 + 57344*a^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*
1i - 131072*a^26*b*c^9 + 2048*a^21*b^11*c^4 - 28672*a^22*b^9*c^5 + 151552*a^23*b^7*c^6 - 368640*a^24*b^5*c^7 +
393216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11 - 256*a^20*b^3*c^10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/
2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c
- b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1
/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*
a^12*b^2*c^3)))^(1/4)*1i - ((-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3
*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2
*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*
(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(3/4)*(131072*a^26*b*c^9 + x^(
1/2)*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*
c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/
2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4
- 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*(131072*a^28*c^9 - 4096*a^23*b^10*c^4 + 57344*a
^24*b^8*c^5 - 299008*a^25*b^6*c^6 + 696320*a^26*b^4*c^7 - 655360*a^27*b^2*c^8)*1i - 2048*a^21*b^11*c^4 + 28672
*a^22*b^9*c^5 - 151552*a^23*b^7*c^6 + 368640*a^24*b^5*c^7 - 393216*a^25*b^3*c^8)*1i - x^(1/2)*(768*a^21*b*c^11
- 256*a^20*b^3*c^10))*(-(b^13 - b^8*(-(4*a*c - b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*
c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4
*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c - b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*
b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^4*c^2 - 256*a^12*b^2*c^3)))^(1/4)*1i))*(-(b^13 - b^8*(-(4*a*c -
b^2)^5)^(1/2) + 144*a^6*b*c^6 + 115*a^2*b^9*c^2 - 390*a^3*b^7*c^3 + 681*a^4*b^5*c^4 - 552*a^5*b^3*c^5 - a^4*c
^4*(-(4*a*c - b^2)^5)^(1/2) - 17*a*b^11*c - 15*a^2*b^4*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a^3*b^2*c^3*(-(4*a*c
- b^2)^5)^(1/2) + 7*a*b^6*c*(-(4*a*c - b^2)^5)^(1/2))/(32*(a^9*b^8 + 256*a^13*c^4 - 16*a^10*b^6*c + 96*a^11*b^
4*c^2 - 256*a^12*b^2*c^3)))^(1/4)