∫ 1______√ x (a+bx2+cx4)2 dx

3.9.45 $\int \frac {1}{\sqrt {x} (a+b x^2+c x^4)^2} \, dx$

Optimal. Leaf size=503 \[ \frac {c^{3/4} \left (-3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {c^{3/4} \left (-3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {\sqrt {x} \left (-2 a c+b^2+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )} \]

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Rubi [A] time = 1.28, antiderivative size = 503, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 6, integrand size = 20, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.300, Rules used = {1115, 1345, 1422, 212, 208, 205} \begin {gather*} \frac {c^{3/4} \left (-3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {c^{3/4} \left (-3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (3 b \sqrt {b^2-4 a c}-28 a c+3 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {\sqrt {x} \left (-2 a c+b^2+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

(Sqrt[x]*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (c^(3/4)*(3*b^2 - 28*a*c - 3*b*Sqr

t[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(

3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(3*b^2 - 28*a*c + 3*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/

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

+ (c^(3/4)*(3*b^2 - 28*a*c - 3*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])

^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(3*b^2 - 28*a*c + 3*b*Sqr

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

(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))

Rule 205

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

&& PosQ[a/b]

Rule 208

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

b}, x] && NegQ[a/b]

Rule 212

Int[((a_) + (b_.)*(x_)^4)^(-1), x_Symbol] :> With[{r = Numerator[Rt[-(a/b), 2]], s = Denominator[Rt[-(a/b), 2]

]}, Dist[r/(2*a), Int[1/(r - s*x^2), x], x] + Dist[r/(2*a), Int[1/(r + s*x^2), x], x]] /; FreeQ[{a, b}, x] &&

!GtQ[a/b, 0]

Rule 1115

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 1345

Int[((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(b^2 - 2*a*c + b*c*x^n)*(a + b*x^

n + c*x^(2*n))^(p + 1))/(a*n*(p + 1)*(b^2 - 4*a*c)), x] + Dist[1/(a*n*(p + 1)*(b^2 - 4*a*c)), Int[(b^2 - 2*a*c

+ n*(p + 1)*(b^2 - 4*a*c) + b*c*(n*(2*p + 3) + 1)*x^n)*(a + b*x^n + c*x^(2*n))^(p + 1), x], x] /; FreeQ[{a, b

, c, n}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && ILtQ[p, -1]

Rule 1422

Int[((d_) + (e_.)*(x_)^(n_))/((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_)), x_Symbol] :> With[{q = Rt[b^2 - 4*a*

c, 2]}, Dist[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^n), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), In

t[1/(b/2 + q/2 + c*x^n), x], x]] /; FreeQ[{a, b, c, d, e, n}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && NeQ

[c*d^2 - b*d*e + a*e^2, 0] && (PosQ[b^2 - 4*a*c] || !IGtQ[n/2, 0])

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {x} \left (a+b x^2+c x^4\right )^2} \, dx &=2 \operatorname {Subst}\left (\int \frac {1}{\left (a+b x^4+c x^8\right )^2} \, dx,x,\sqrt {x}\right )\\ &=\frac {\sqrt {x} \left (b^2-2 a c+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\operatorname {Subst}\left (\int \frac {b^2-2 a c-4 \left (b^2-4 a c\right )-3 b c x^4}{a+b x^4+c x^8} \, dx,x,\sqrt {x}\right )}{2 a \left (b^2-4 a c\right )}\\ &=\frac {\sqrt {x} \left (b^2-2 a c+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\left (c \left (3 b^2-28 a c-3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2}}+\frac {\left (c \left (3 b^2-28 a c+3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2}}\\ &=\frac {\sqrt {x} \left (b^2-2 a c+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\left (c \left (3 b^2-28 a c-3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2} \sqrt {-b-\sqrt {b^2-4 a c}}}+\frac {\left (c \left (3 b^2-28 a c-3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2} \sqrt {-b-\sqrt {b^2-4 a c}}}-\frac {\left (c \left (3 b^2-28 a c+3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2} \sqrt {-b+\sqrt {b^2-4 a c}}}-\frac {\left (c \left (3 b^2-28 a c+3 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{4 a \left (b^2-4 a c\right )^{3/2} \sqrt {-b+\sqrt {b^2-4 a c}}}\\ &=\frac {\sqrt {x} \left (b^2-2 a c+b c x^2\right )}{2 a \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {c^{3/4} \left (3 b^2-28 a c-3 b \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 )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4}}-\frac {c^{3/4} \left (3 b^2-28 a c+3 b \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 )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4}}+\frac {c^{3/4} \left (3 b^2-28 a c-3 b \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 )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4}}-\frac {c^{3/4} \left (3 b^2-28 a c+3 b \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 )}{4 \sqrt [4]{2} a \left (b^2-4 a c\right )^{3/2} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4}}\\ \end {align*}

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Mathematica [C] time = 0.25, size = 153, normalized size = 0.30 \begin {gather*} -\frac {\left (a+b x^2+c x^4\right ) \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {3 \text {$\#$1}^4 b c \log \left (\sqrt {x}-\text {$\#$1}\right )-14 a c \log \left (\sqrt {x}-\text {$\#$1}\right )+3 b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\&\right ]+4 \sqrt {x} \left (-2 a c+b^2+b c x^2\right )}{8 a \left (4 a c-b^2\right ) \left (a+b x^2+c x^4\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

-1/8*(4*Sqrt[x]*(b^2 - 2*a*c + b*c*x^2) + (a + b*x^2 + c*x^4)*RootSum[a + b*#1^4 + c*#1^8 & , (3*b^2*Log[Sqrt[

x] - #1] - 14*a*c*Log[Sqrt[x] - #1] + 3*b*c*Log[Sqrt[x] - #1]*#1^4)/(b*#1^3 + 2*c*#1^7) & ])/(a*(-b^2 + 4*a*c)

*(a + b*x^2 + c*x^4))

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IntegrateAlgebraic [C] time = 0.30, size = 160, normalized size = 0.32 \begin {gather*} \frac {\sqrt {x} \left (2 a c-b^2-b c x^2\right )}{2 a \left (4 a c-b^2\right ) \left (a+b x^2+c x^4\right )}-\frac {\text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {3 \text {$\#$1}^4 b c \log \left (\sqrt {x}-\text {$\#$1}\right )-14 a c \log \left (\sqrt {x}-\text {$\#$1}\right )+3 b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\&\right ]}{8 a \left (4 a c-b^2\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

(3*b^2*Log[Sqrt[x] - #1] - 14*a*c*Log[Sqrt[x] - #1] + 3*b*c*Log[Sqrt[x] - #1]*#1^4)/(b*#1^3 + 2*c*#1^7) & ]/(8

*a*(-b^2 + 4*a*c))

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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Eval

uation time: 47.36Unable to convert to real 1/4 Error: Bad Argument Value

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maple [C] time = 0.02, size = 144, normalized size = 0.29 \begin {gather*} \frac {\left (-3 \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{4} b c +14 a c -3 b^{2}\right ) \ln \left (-\RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )+\sqrt {x}\right )}{8 \left (4 a c -b^{2}\right ) a \left (2 \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{7} c +\RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{3} b \right )}+\frac {-\frac {b c \,x^{\frac {5}{2}}}{2 \left (4 a c -b^{2}\right ) a}+\frac {\left (2 a c -b^{2}\right ) \sqrt {x}}{2 \left (4 a c -b^{2}\right ) a}}{c \,x^{4}+b \,x^{2}+a} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*(-1/4*b/a/(4*a*c-b^2)*c*x^(5/2)+1/4*(2*a*c-b^2)/(4*a*c-b^2)/a*x^(1/2))/(c*x^4+b*x^2+a)+1/8/a/(4*a*c-b^2)*sum

((-3*_R^4*b*c+14*a*c-3*b^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {{\left (3 \, b^{2} c - 14 \, a c^{2}\right )} x^{\frac {9}{2}} + {\left (3 \, b^{3} - 13 \, a b c\right )} x^{\frac {5}{2}} + 4 \, {\left (a b^{2} - 4 \, a^{2} c\right )} \sqrt {x}}{2 \, {\left (a^{3} b^{2} - 4 \, a^{4} c + {\left (a^{2} b^{2} c - 4 \, a^{3} c^{2}\right )} x^{4} + {\left (a^{2} b^{3} - 4 \, a^{3} b c\right )} x^{2}\right )}} - \int \frac {{\left (3 \, b^{2} c - 14 \, a c^{2}\right )} x^{\frac {7}{2}} + {\left (3 \, b^{3} - 17 \, a b c\right )} x^{\frac {3}{2}}}{4 \, {\left (a^{3} b^{2} - 4 \, a^{4} c + {\left (a^{2} b^{2} c - 4 \, a^{3} c^{2}\right )} x^{4} + {\left (a^{2} b^{3} - 4 \, a^{3} b c\right )} x^{2}\right )}}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*((3*b^2*c - 14*a*c^2)*x^(9/2) + (3*b^3 - 13*a*b*c)*x^(5/2) + 4*(a*b^2 - 4*a^2*c)*sqrt(x))/(a^3*b^2 - 4*a^4

*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2) - integrate(1/4*((3*b^2*c - 14*a*c^2)*x^(7/2) +

(3*b^3 - 17*a*b*c)*x^(3/2))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2), x)

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mupad [B] time = 7.29, size = 35171, normalized size = 69.92

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

((((((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^

17*c^3 - 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799

626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2

) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2)

- 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20

*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^

14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)

))^(1/4)*(285212672*a^11*b*c^11 - 12288*a^4*b^15*c^4 + 364544*a^5*b^13*c^5 - 4620288*a^6*b^11*c^6 + 32440320*a

^7*b^9*c^7 - 136314880*a^8*b^7*c^8 + 342884352*a^9*b^5*c^9 - 478150656*a^10*b^3*c^10))/(2*(a^4*b^8 + 256*a^8*c

^4 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)) - (x^(1/2)*(12683575296*a^11*b*c^13 - 36864*a^2*b^19*c^

4 + 1413120*a^3*b^17*c^5 - 23891968*a^4*b^15*c^6 + 233816064*a^5*b^13*c^7 - 1459421184*a^6*b^11*c^8 + 60238069

76*a^7*b^9*c^9 - 16436428800*a^8*b^7*c^10 + 28575793152*a^9*b^5*c^11 - 28705816576*a^10*b^3*c^12))/(16*(a^4*b^

12 + 4096*a^10*c^6 - 24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)

))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^1

7*c^3 - 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 17996

26752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2)

+ 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) -

1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*

c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^1

4*b^10*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11))

)^(3/4) - (537824*a^4*c^11 + 891*b^8*c^7 - 19548*a*b^6*c^8 + 155358*a^2*b^4*c^9 - 510384*a^3*b^2*c^10)/(2*(a^4

*b^8 + 256*a^8*c^4 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 8

1*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 64704576*

a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^

9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4

*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/

(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b

^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 5767

1680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4) + (x^(1/2)*(15059072*a^4*c^13 + 9

801*b^8*c^9 - 227502*a*b^6*c^10 + 2092104*a^2*b^4*c^11 - 8989344*a^3*b^2*c^12))/(16*(a^4*b^12 + 4096*a^10*c^6

- 24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*(-(4*a*

c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^

4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 +

2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c +

10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*

a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^

18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 324403

20*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*1i - ((((((

81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3

- 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752

*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 40

23*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593

*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 -

14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^1

0*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/

4)*(285212672*a^11*b*c^11 - 12288*a^4*b^15*c^4 + 364544*a^5*b^13*c^5 - 4620288*a^6*b^11*c^6 + 32440320*a^7*b^9

*c^7 - 136314880*a^8*b^7*c^8 + 342884352*a^9*b^5*c^9 - 478150656*a^10*b^3*c^10))/(2*(a^4*b^8 + 256*a^8*c^4 - 1

6*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)) + (x^(1/2)*(12683575296*a^11*b*c^13 - 36864*a^2*b^19*c^4 + 14

13120*a^3*b^17*c^5 - 23891968*a^4*b^15*c^6 + 233816064*a^5*b^13*c^7 - 1459421184*a^6*b^11*c^8 + 6023806976*a^7

*b^9*c^9 - 16436428800*a^8*b^7*c^10 + 28575793152*a^9*b^5*c^11 - 28705816576*a^10*b^3*c^12))/(16*(a^4*b^12 + 4

096*a^10*c^6 - 24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((8

1*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3

- 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*

a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 402

3*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*

a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 -

14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10

*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(3/4

) - (537824*a^4*c^11 + 891*b^8*c^7 - 19548*a*b^6*c^8 + 155358*a^2*b^4*c^9 - 510384*a^3*b^2*c^10)/(2*(a^4*b^8 +

256*a^8*c^4 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23

+ 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 64704576*a^5*b^

13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 20

38693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c -

b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*

(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^

4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a

^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4) - (x^(1/2)*(15059072*a^4*c^13 + 9801*b^

8*c^9 - 227502*a*b^6*c^10 + 2092104*a^2*b^4*c^11 - 8989344*a^3*b^2*c^12))/(16*(a^4*b^12 + 4096*a^10*c^6 - 24*a

^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*(-(4*a*c - b^

2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15

*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 24941

19936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*

a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c -

b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3

+ 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^1

5*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*1i)/(((((((81*b^8

*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 105

88384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b

^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b

^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6

*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080

*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7

+ 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*(28

5212672*a^11*b*c^11 - 12288*a^4*b^15*c^4 + 364544*a^5*b^13*c^5 - 4620288*a^6*b^11*c^6 + 32440320*a^7*b^9*c^7 -

136314880*a^8*b^7*c^8 + 342884352*a^9*b^5*c^9 - 478150656*a^10*b^3*c^10))/(2*(a^4*b^8 + 256*a^8*c^4 - 16*a^5*

b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)) - (x^(1/2)*(12683575296*a^11*b*c^13 - 36864*a^2*b^19*c^4 + 1413120*

a^3*b^17*c^5 - 23891968*a^4*b^15*c^6 + 233816064*a^5*b^13*c^7 - 1459421184*a^6*b^11*c^8 + 6023806976*a^7*b^9*c

^9 - 16436428800*a^8*b^7*c^10 + 28575793152*a^9*b^5*c^11 - 28705816576*a^10*b^3*c^12))/(16*(a^4*b^12 + 4096*a^

10*c^6 - 24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*

(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 1058

8384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^

7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^

21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*

c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*

a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 +

32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(3/4) - (5

37824*a^4*c^11 + 891*b^8*c^7 - 19548*a*b^6*c^8 + 155358*a^2*b^4*c^9 - 510384*a^3*b^2*c^10)/(2*(a^4*b^8 + 256*a

^8*c^4 - 16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741

801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5

- 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 20386938

88*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^

15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b

^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 81

1008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^

6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4) + (x^(1/2)*(15059072*a^4*c^13 + 9801*b^8*c^9

- 227502*a*b^6*c^10 + 2092104*a^2*b^4*c^11 - 8989344*a^3*b^2*c^12))/(16*(a^4*b^12 + 4096*a^10*c^6 - 24*a^5*b^1

0*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*(-(4*a*c - b^2)^15)

^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 +

64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*

a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^

4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^1

5)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126

720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*

c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4) + ((((((81*b^8*(-(4*a*c

- b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4

*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 +

2494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 1

0746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a

*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^1

8*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 3244032

0*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*(285212672*a

^11*b*c^11 - 12288*a^4*b^15*c^4 + 364544*a^5*b^13*c^5 - 4620288*a^6*b^11*c^6 + 32440320*a^7*b^9*c^7 - 13631488

0*a^8*b^7*c^8 + 342884352*a^9*b^5*c^9 - 478150656*a^10*b^3*c^10))/(2*(a^4*b^8 + 256*a^8*c^4 - 16*a^5*b^6*c + 9

6*a^6*b^4*c^2 - 256*a^7*b^2*c^3)) + (x^(1/2)*(12683575296*a^11*b*c^13 - 36864*a^2*b^19*c^4 + 1413120*a^3*b^17*

c^5 - 23891968*a^4*b^15*c^6 + 233816064*a^5*b^13*c^7 - 1459421184*a^6*b^11*c^8 + 6023806976*a^7*b^9*c^9 - 1643

6428800*a^8*b^7*c^10 + 28575793152*a^9*b^5*c^11 - 28705816576*a^10*b^3*c^12))/(16*(a^4*b^12 + 4096*a^10*c^6 -

24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*(-(4*a*c

- b^2)^15)^(1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*

b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2

494119936*a^9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10

746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*

c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18

*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320

*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(3/4) - (537824*a^4

*c^11 + 891*b^8*c^7 - 19548*a*b^6*c^8 + 155358*a^2*b^4*c^9 - 510384*a^3*b^2*c^10)/(2*(a^4*b^8 + 256*a^8*c^4 -

16*a^5*b^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 81*b^23 + 741801984*a^

11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 64704576*a^5*b^13*c^5 - 279571

968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c^9 - 2038693888*a^10*b

^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2)

- 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 167

77216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12

*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 6

9206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4) - (x^(1/2)*(15059072*a^4*c^13 + 9801*b^8*c^9 - 227502*

a*b^6*c^10 + 2092104*a^2*b^4*c^11 - 8989344*a^3*b^2*c^12))/(16*(a^4*b^12 + 4096*a^10*c^6 - 24*a^5*b^10*c + 240

*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*((81*b^8*(-(4*a*c - b^2)^15)^(1/2) -

81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 64704576

*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^9*b^5*c

^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*c^2*(-(

4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)^(1/2))

/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 126720*a^11*

b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^8 - 576

71680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)))*((81*b^8*(-(4*a*c - b^2)^15)^(

1/2) - 81*b^23 + 741801984*a^11*b*c^11 - 90126*a^2*b^19*c^2 + 1201623*a^3*b^17*c^3 - 10588384*a^4*b^15*c^4 + 6

4704576*a^5*b^13*c^5 - 279571968*a^6*b^11*c^6 + 853174784*a^7*b^9*c^7 - 1799626752*a^8*b^7*c^8 + 2494119936*a^

9*b^5*c^9 - 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) + 4023*a*b^21*c + 10746*a^2*b^4*

c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*c*(-(4*a*c - b^2)^15)

^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*a^10*b^18*c^3 + 12672

0*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 + 32440320*a^15*b^8*c^

8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*2i + atan(((((((-(81*b^23

+ 81*b^8*(-(4*a*c - b^2)^15)^(1/2) - 741801984*a^11*b*c^11 + 90126*a^2*b^19*c^2 - 1201623*a^3*b^17*c^3 + 1058

8384*a^4*b^15*c^4 - 64704576*a^5*b^13*c^5 + 279571968*a^6*b^11*c^6 - 853174784*a^7*b^9*c^7 + 1799626752*a^8*b^

7*c^8 - 2494119936*a^9*b^5*c^9 + 2038693888*a^10*b^3*c^10 + 9604*a^4*c^4*(-(4*a*c - b^2)^15)^(1/2) - 4023*a*b^

21*c + 10746*a^2*b^4*c^2*(-(4*a*c - b^2)^15)^(1/2) - 26313*a^3*b^2*c^3*(-(4*a*c - b^2)^15)^(1/2) - 1593*a*b^6*

c*(-(4*a*c - b^2)^15)^(1/2))/(8192*(a^7*b^24 + 16777216*a^19*c^12 - 48*a^8*b^22*c + 1056*a^9*b^20*c^2 - 14080*

a^10*b^18*c^3 + 126720*a^11*b^16*c^4 - 811008*a^12*b^14*c^5 + 3784704*a^13*b^12*c^6 - 12976128*a^14*b^10*c^7 +

32440320*a^15*b^8*c^8 - 57671680*a^16*b^6*c^9 + 69206016*a^17*b^4*c^10 - 50331648*a^18*b^2*c^11)))^(1/4)*(285

212672*a^11*b*c^11 - 12288*a^4*b^15*c^4 + 364544*a^5*b^13*c^5 - 4620288*a^6*b^11*c^6 + 32440320*a^7*b^9*c^7 -

136314880*a^8*b^7*c^8 + 342884352*a^9*b^5*c^9 - 478150656*a^10*b^3*c^10))/(2*(a^4*b^8 + 256*a^8*c^4 - 16*a^5*b

^6*c + 96*a^6*b^4*c^2 - 256*a^7*b^2*c^3)) - (x^(1/2)*(12683575296*a^11*b*c^13 - 36864*a^2*b^19*c^4 + 1413120*a

^3*b^17*c^5 - 23891968*a^4*b^15*c^6 + 233816064*a^5*b^13*c^7 - 1459421184*a^6*b^11*c^8 + 6023806976*a^7*b^9*c^

9 - 16436428800*a^8*b^7*c^10 + 28575793152*a^9*b^5*c^11 - 28705816576*a^10*b^3*c^12))/(16*(a^4*b^12 + 4096*a^1

0*c^6 - 24*a^5*b^10*c + 240*a^6*b^8*c^2 - 1280*a^7*b^6*c^3 + 3840*a^8*b^4*c^4 - 6144*a^9*b^2*c^5)))*(-(81*b^23