∫ x5∕2 ____________________

3.9.52 $\int \frac {x^{5/2}}{(a+b x^2+c x^4)^3} \, dx$

Optimal. Leaf size=594 \[ \frac {3 x^{3/2} \left (c x^2 \left (12 a c+b^2\right )+b \left (4 a c+b^2\right )\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 \sqrt [4]{c} \left (\frac {68 a b c}{\sqrt {b^2-4 a c}}-\frac {b^3}{\sqrt {b^2-4 a c}}+12 a c+b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}+\frac {3 \sqrt [4]{c} \left (\sqrt {b^2-4 a c} \left (12 a c+b^2\right )-68 a b c+b^3\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^{5/2} \sqrt [4]{\sqrt {b^2-4 a c}-b}}-\frac {3 \sqrt [4]{c} \left (\frac {68 a b c}{\sqrt {b^2-4 a c}}-\frac {b^3}{\sqrt {b^2-4 a c}}+12 a c+b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}-\frac {3 \sqrt [4]{c} \left (\sqrt {b^2-4 a c} \left (12 a c+b^2\right )-68 a b c+b^3\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^{5/2} \sqrt [4]{\sqrt {b^2-4 a c}-b}} \]

________________________________________________________________________________________

Rubi [A] time = 2.31, antiderivative size = 594, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 7, integrand size = 20, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.350, Rules used = {1115, 1364, 1500, 1510, 298, 205, 208} \begin {gather*} \frac {3 x^{3/2} \left (c x^2 \left (12 a c+b^2\right )+b \left (4 a c+b^2\right )\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 \sqrt [4]{c} \left (-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b c}{\sqrt {b^2-4 a c}}+12 a c+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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}+\frac {3 \sqrt [4]{c} \left (\sqrt {b^2-4 a c} \left (12 a c+b^2\right )-68 a b c+b^3\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^{5/2} \sqrt [4]{\sqrt {b^2-4 a c}-b}}-\frac {3 \sqrt [4]{c} \left (-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b c}{\sqrt {b^2-4 a c}}+12 a c+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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-\sqrt {b^2-4 a c}-b}}-\frac {3 \sqrt [4]{c} \left (\sqrt {b^2-4 a c} \left (12 a c+b^2\right )-68 a b c+b^3\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^{5/2} \sqrt [4]{\sqrt {b^2-4 a c}-b}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[x^(5/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

-(x^(3/2)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*x^(3/2)*(b*(b^2 + 4*a*c) + c*(b^2 + 12*a

*c)*x^2))/(16*a*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*c^(1/4)*(b^2 + 12*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*

a*b*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)])/(32*2^(3/4)*a*(b^2

- 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (3*c^(1/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 12*a*c))*A

rcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[

b^2 - 4*a*c])^(1/4)) - (3*c^(1/4)*(b^2 + 12*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan

h[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*

a*c])^(1/4)) - (3*c^(1/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 12*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x]

)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))

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 298

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 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 1364

Int[((d_.)*(x_))^(m_.)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(d^(n - 1)*(d*x)^(

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

(b^2 - 4*a*c)), Int[(d*x)^(m - n)*(b*(m - n + 1) + 2*c*(m + 2*n*(p + 1) + 1)*x^n)*(a + b*x^n + c*x^(2*n))^(p +

1), x], x] /; FreeQ[{a, b, c, d}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && IGtQ[n, 0] && ILtQ[p, -1] && G

tQ[m, n - 1] && LeQ[m, 2*n - 1]

Rule 1500

Int[((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(n_))*((a_) + (b_.)*(x_)^(n_) + (c_.)*(x_)^(n2_))^(p_), x_Symbol] :>

-Simp[((f*x)^(m + 1)*(a + b*x^n + c*x^(2*n))^(p + 1)*(d*(b^2 - 2*a*c) - a*b*e + (b*d - 2*a*e)*c*x^n))/(a*f*n*

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

imp[d*(b^2*(m + n*(p + 1) + 1) - 2*a*c*(m + 2*n*(p + 1) + 1)) - a*b*e*(m + 1) + c*(m + n*(2*p + 3) + 1)*(b*d -

2*a*e)*x^n, x], 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

] && LtQ[p, -1] && IntegerQ[p]

Rule 1510

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*} \int \frac {x^{5/2}}{\left (a+b x^2+c x^4\right )^3} \, dx &=2 \operatorname {Subst}\left (\int \frac {x^6}{\left (a+b x^4+c x^8\right )^3} \, dx,x,\sqrt {x}\right )\\ &=-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (3 b-18 c x^4\right )}{\left (a+b x^4+c x^8\right )^2} \, dx,x,\sqrt {x}\right )}{4 \left (b^2-4 a c\right )}\\ &=-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 x^{3/2} \left (b \left (b^2+4 a c\right )+c \left (b^2+12 a c\right ) x^2\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-3 b \left (b^2-28 a c\right )-3 c \left (b^2+12 a c\right ) x^4\right )}{a+b x^4+c x^8} \, dx,x,\sqrt {x}\right )}{16 a \left (b^2-4 a c\right )^2}\\ &=-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 x^{3/2} \left (b \left (b^2+4 a c\right )+c \left (b^2+12 a c\right ) x^2\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\left (3 c \left (b^2+12 a c+\frac {b^3}{\sqrt {b^2-4 a c}}-\frac {68 a b c}{\sqrt {b^2-4 a c}}\right )\right ) \operatorname {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 )}{32 a \left (b^2-4 a c\right )^2}+\frac {\left (3 c \left (b^2+12 a c-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b c}{\sqrt {b^2-4 a c}}\right )\right ) \operatorname {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 )}{32 a \left (b^2-4 a c\right )^2}\\ &=-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 x^{3/2} \left (b \left (b^2+4 a c\right )+c \left (b^2+12 a c\right ) x^2\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {\left (3 \sqrt {c} \left (b^2+12 a c+\frac {b^3}{\sqrt {b^2-4 a c}}-\frac {68 a b c}{\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 )}{32 \sqrt {2} a \left (b^2-4 a c\right )^2}+\frac {\left (3 \sqrt {c} \left (b^2+12 a c+\frac {b^3}{\sqrt {b^2-4 a c}}-\frac {68 a b c}{\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 )}{32 \sqrt {2} a \left (b^2-4 a c\right )^2}-\frac {\left (3 \sqrt {c} \left (b^2+12 a c-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b c}{\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 )}{32 \sqrt {2} a \left (b^2-4 a c\right )^2}+\frac {\left (3 \sqrt {c} \left (b^2+12 a c-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b c}{\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 )}{32 \sqrt {2} a \left (b^2-4 a c\right )^2}\\ &=-\frac {x^{3/2} \left (b+2 c x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {3 x^{3/2} \left (b \left (b^2+4 a c\right )+c \left (b^2+12 a c\right ) x^2\right )}{16 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {3 \sqrt [4]{c} \left (b^2+12 a c-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b 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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}+\frac {3 \sqrt [4]{c} \left (b^2+12 a c+\frac {b^3}{\sqrt {b^2-4 a c}}-\frac {68 a b 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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}-\frac {3 \sqrt [4]{c} \left (b^2+12 a c-\frac {b^3}{\sqrt {b^2-4 a c}}+\frac {68 a b 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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-b-\sqrt {b^2-4 a c}}}-\frac {3 \sqrt [4]{c} \left (b^2+12 a c+\frac {b^3}{\sqrt {b^2-4 a c}}-\frac {68 a b 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 )}{32\ 2^{3/4} a \left (b^2-4 a c\right )^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}\\ \end {align*}

________________________________________________________________________________________

Mathematica [C] time = 0.41, size = 222, normalized size = 0.37 \begin {gather*} \frac {3 \left (a+b x^2+c x^4\right )^2 \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {12 \text {$\#$1}^4 a c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )+\text {$\#$1}^4 b^2 c \log \left (\sqrt {x}-\text {$\#$1}\right )-28 a b c \log \left (\sqrt {x}-\text {$\#$1}\right )+b^3 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^5 c+\text {$\#$1} b}\&\right ]-16 a x^{3/2} \left (b^2-4 a c\right ) \left (b+2 c x^2\right )+12 x^{3/2} \left (4 a b c+12 a c^2 x^2+b^3+b^2 c x^2\right ) \left (a+b x^2+c x^4\right )}{64 a \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[x^(5/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

(-16*a*(b^2 - 4*a*c)*x^(3/2)*(b + 2*c*x^2) + 12*x^(3/2)*(b^3 + 4*a*b*c + b^2*c*x^2 + 12*a*c^2*x^2)*(a + b*x^2

+ c*x^4) + 3*(a + b*x^2 + c*x^4)^2*RootSum[a + b*#1^4 + c*#1^8 & , (b^3*Log[Sqrt[x] - #1] - 28*a*b*c*Log[Sqrt[

x] - #1] + b^2*c*Log[Sqrt[x] - #1]*#1^4 + 12*a*c^2*Log[Sqrt[x] - #1]*#1^4)/(b*#1 + 2*c*#1^5) & ])/(64*a*(b^2 -

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

________________________________________________________________________________________

IntegrateAlgebraic [C] time = 0.56, size = 245, normalized size = 0.41 \begin {gather*} \frac {3 \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {12 \text {$\#$1}^4 a c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )+\text {$\#$1}^4 b^2 c \log \left (\sqrt {x}-\text {$\#$1}\right )-28 a b c \log \left (\sqrt {x}-\text {$\#$1}\right )+b^3 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^5 c+\text {$\#$1} b}\&\right ]}{64 a \left (4 a c-b^2\right )^2}+\frac {x^{3/2} \left (28 a^2 b c+68 a^2 c^2 x^2-a b^3+7 a b^2 c x^2+48 a b c^2 x^4+36 a c^3 x^6+3 b^4 x^2+6 b^3 c x^4+3 b^2 c^2 x^6\right )}{16 a \left (4 a c-b^2\right )^2 \left (a+b x^2+c x^4\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

IntegrateAlgebraic[x^(5/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

(x^(3/2)*(-(a*b^3) + 28*a^2*b*c + 3*b^4*x^2 + 7*a*b^2*c*x^2 + 68*a^2*c^2*x^2 + 6*b^3*c*x^4 + 48*a*b*c^2*x^4 +

3*b^2*c^2*x^6 + 36*a*c^3*x^6))/(16*a*(-b^2 + 4*a*c)^2*(a + b*x^2 + c*x^4)^2) + (3*RootSum[a + b*#1^4 + c*#1^8

& , (b^3*Log[Sqrt[x] - #1] - 28*a*b*c*Log[Sqrt[x] - #1] + b^2*c*Log[Sqrt[x] - #1]*#1^4 + 12*a*c^2*Log[Sqrt[x]

- #1]*#1^4)/(b*#1 + 2*c*#1^5) & ])/(64*a*(-b^2 + 4*a*c)^2)

________________________________________________________________________________________

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(x^(5/2)/(c*x^4+b*x^2+a)^3,x, algorithm="fricas")

[Out]

Timed out

________________________________________________________________________________________

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(x^(5/2)/(c*x^4+b*x^2+a)^3,x, algorithm="giac")

[Out]

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

uation time: 191.33Unable to convert to real 1/4 Error: Bad Argument Value

________________________________________________________________________________________

maple [C] time = 0.04, size = 277, normalized size = 0.47 \begin {gather*} \frac {3 \left (\left (12 a c +b^{2}\right ) \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{6} c +\left (-28 a c +b^{2}\right ) \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{2} b \right ) \ln \left (-\RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )+\sqrt {x}\right )}{64 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\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 {3 \left (12 a c +b^{2}\right ) c^{2} x^{\frac {15}{2}}}{16 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) a}+\frac {3 \left (8 a c +b^{2}\right ) b c \,x^{\frac {11}{2}}}{8 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) a}+\frac {\left (68 a^{2} c^{2}+7 a \,b^{2} c +3 b^{4}\right ) x^{\frac {7}{2}}}{16 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right ) a}+\frac {2 \left (28 a c -b^{2}\right ) b \,x^{\frac {3}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}}{\left (c \,x^{4}+b \,x^{2}+a \right )^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^(5/2)/(c*x^4+b*x^2+a)^3,x)

[Out]

2*(1/32*b*(28*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)+1/32*(68*a^2*c^2+7*a*b^2*c+3*b^4)/a/(16*a^2*c^2-8*a*

b^2*c+b^4)*x^(7/2)+3/16/a*c*b*(8*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)+3/32*c^2*(12*a*c+b^2)/a/(16*a^2*

c^2-8*a*b^2*c+b^4)*x^(15/2))/(c*x^4+b*x^2+a)^2+3/64/a/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((c*(12*a*c+b^2)*_R^6+b*(-

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

________________________________________________________________________________________

maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {3 \, {\left (b^{2} c^{2} + 12 \, a c^{3}\right )} x^{\frac {15}{2}} + 6 \, {\left (b^{3} c + 8 \, a b c^{2}\right )} x^{\frac {11}{2}} + {\left (3 \, b^{4} + 7 \, a b^{2} c + 68 \, a^{2} c^{2}\right )} x^{\frac {7}{2}} - {\left (a b^{3} - 28 \, a^{2} b c\right )} x^{\frac {3}{2}}}{16 \, {\left ({\left (a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right )} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left (a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right )} x^{6} + {\left (a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right )} x^{4} + 2 \, {\left (a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right )} x^{2}\right )}} + \int \frac {3 \, {\left ({\left (b^{2} c + 12 \, a c^{2}\right )} x^{\frac {5}{2}} + {\left (b^{3} - 28 \, a b c\right )} \sqrt {x}\right )}}{32 \, {\left (a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left (a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right )} x^{4} + {\left (a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right )} x^{2}\right )}}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(5/2)/(c*x^4+b*x^2+a)^3,x, algorithm="maxima")

[Out]

1/16*(3*(b^2*c^2 + 12*a*c^3)*x^(15/2) + 6*(b^3*c + 8*a*b*c^2)*x^(11/2) + (3*b^4 + 7*a*b^2*c + 68*a^2*c^2)*x^(7

/2) - (a*b^3 - 28*a^2*b*c)*x^(3/2))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16

*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^

5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2) + integrate(3/32*((b^2*c + 12*a*c^2)*x^(5/2) + (b^3 - 28*a*b*c)*sqrt(x))/

(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a

^3*b*c^2)*x^2), x)

________________________________________________________________________________________

mupad [B] time = 8.02, size = 42197, normalized size = 71.04

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^(5/2)/(a + b*x^2 + c*x^4)^3,x)

[Out]

((3*x^(11/2)*(b^3*c + 8*a*b*c^2))/(8*(a*b^4 + 16*a^3*c^2 - 8*a^2*b^2*c)) - (x^(3/2)*(b^3 - 28*a*b*c))/(16*(b^4

+ 16*a^2*c^2 - 8*a*b^2*c)) + (x^(7/2)*(3*b^4 + 68*a^2*c^2 + 7*a*b^2*c))/(16*a*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))

+ (3*c^2*x^(15/2)*(12*a*c + b^2))/(16*(a*b^4 + 16*a^3*c^2 - 8*a^2*b^2*c)))/(x^4*(2*a*c + b^2) + a^2 + c^2*x^8

+ 2*a*b*x^2 + 2*b*c*x^6) - atan(((((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5

+ 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*

c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35694

820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^11*b^8*c^15 - 512152516218

06080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28

+ 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 205004

8*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10

*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^1

3)) - (9*x^(1/2)*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 -

394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^

7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*

a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 421

3765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c -

b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554

432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9

*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24

*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a

^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 +

20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^

24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800

*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225

740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878101

504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15 + 67905838131445760*a^1

3*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*

a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 1297612

8*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^

11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3

*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7

+ 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c

^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*

a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(

1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^

40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 -

15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 4402

9706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^

12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 2080911654

9120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19

)))^(3/4) + (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^9*c

^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24 +

16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7

*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 692

06016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^1

6*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 14243688

96*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656

*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 82

12262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*

c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(

4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 7

2960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*

b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a

^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 -

16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a

^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*1i - (((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4

- 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 8

1637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 1372839910519603

2*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^11*

b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^1

8))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 25625

6*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^

8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 -

939524096*a^15*b^2*c^13)) + (9*x^(1/2)*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16

+ 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b

^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^

13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682

624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009

*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c -

b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8

*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7

+ 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18

*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293

239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*

c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2

*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273051

648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*b^1

2*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15

+ 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 16777216*a^14*c^12

- 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704

*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10

- 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^

2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9

732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 9

86354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^

5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^

2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1

/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 +

1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 82555699

20*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 211

3425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20

*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497

558138880*a^24*b^2*c^19)))^(3/4) - (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c^8

+ 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^13)

)/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^

6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 5767

1680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(

1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*

a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9

*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 756253143

8592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^

25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^

(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c

+ 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28

*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^2

0*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 104045582

74560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*

c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*1i)/((((27*(3799912185593856*a^15*c

^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549

334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*

c^11 + 13728399105196032*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 -

33767651356442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 7061503

4782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 232

96*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 +

196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 152

6726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) - (9*x^(1/2)*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 4

71104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23

*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^

9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^1

3*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2

) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) -

107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a

^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1

270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 -

704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^

19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 1

3056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^

28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*

b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19

380541706993664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 934145078

95848960*a^12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^2

4 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008

*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 +

69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280

*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424

368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 1315117

4656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13

- 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b

^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c

*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2

- 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a

^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 7044752998

40*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^1

4 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 130567005798

40*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(3/4) + (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11

*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44

937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a

^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440

320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^

8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^

4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17

*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^

12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a

^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c

^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^2

5*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^

5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9

+ 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^1

8*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 1

9585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4) - (27*(21141

29160*a*b^11*c^10 - 24024195*b^13*c^9 + 1209323520*a^6*b*c^15 - 61748341200*a^2*b^9*c^11 + 590751532800*a^3*b^

7*c^12 + 227993875200*a^4*b^5*c^13 + 28822210560*a^5*b^3*c^14))/(16777216*(a^2*b^28 + 268435456*a^16*c^14 - 56

*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a

^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*

c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) + (((27*(37999121855938

56*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7

+ 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*

a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^1

0*c^14 - 33767651356442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17

- 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*

c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b

^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c

^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) + (9*x^(1/2)*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^

(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728

*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^

9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 75625314

38592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)

^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)

^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c

+ 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^2

8*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^

20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558

274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6

*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 1677

7216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 2044082310

3488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*

c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 -

93414507895848960*a^12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304

*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4

- 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*

b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471

104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c

^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9

+ 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*

b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2)

- 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 10

7*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7

*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 127

0087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 7

04475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19

*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 130

56700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(3/4) - (9*x^(1/2)*(2982998016*a^6*b*c^14 - 1731384

72*a*b^11*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*

c^12 + 44937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2

- 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^

7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(

b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9

219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744

*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358

219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15

+ 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*

a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 10995116

27776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^1

0*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*

b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 52022791

37280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8

*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)))*(

-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c

^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376

799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3

840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^

3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) -

54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 10

99511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 158760

96*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240

*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 52

02279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^

21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/

4)*2i - atan(((((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^

26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 64533547922227

2*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35694820362027008*a^9*b^1

2*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16

+ 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^

14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 123

00288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^

12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) - (9*x^(1/2)*(-(

81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3

+ 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 4337679

9744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 384

0358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*

c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54

648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099

511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096

*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a

^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202

279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21

*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)

*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491

964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^1

6*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^13 +

80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 2758454

7717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080

*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 324

40320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 -

b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*

a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^

17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*

a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296

*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2

*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a

^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*

c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^

9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a

^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 -

19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(3/4) + (9*x^(1/

2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a

^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 -

48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*

a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10

- 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2

*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 97

32052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 98

6354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5

*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2

*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/

2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 +

1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 825556992

0*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113

425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*

b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 54975

58138880*a^24*b^2*c^19)))^(1/4)*1i - (((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c

^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^

20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35

694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^11*b^8*c^15 - 512152516

21806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b

^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 205

0048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b

^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*

c^13)) + (9*x^(1/2)*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^

2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992

*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 9863540244

48*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 +

4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*

c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33

554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*

a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b

^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 211342589952

0*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^1

5 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880

*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724

800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1

225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878

101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15 + 67905838131445760*

a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 10

56*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 1297

6128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2

*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*

a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c

^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^1

1*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 42137655705

60*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25

)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5

*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^

4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 4

4029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16

*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 2080911

6549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c

^19)))^(3/4) - (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^

9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24

+ 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*

a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 +

69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*

a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 14243

68896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174

656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 -

8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^

31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*

(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2

- 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^

12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 70447529984

0*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14

- 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 1305670057984

0*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*1i)/((((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c

^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8

- 81637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 1372839910519

6032*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^

11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*

c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 25

6256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12

*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^1

2 - 939524096*a^15*b^2*c^13)) - (9*x^(1/2)*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c

^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^

6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10

*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262

682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4

009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c

- b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*

a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*

c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b

^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647

293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b

^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*

a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273

051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*

b^12*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^

15 + 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 16777216*a^14*c^

12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784

704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c

^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509

*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6

- 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10

+ 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14

*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4

*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)

^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^

3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 82555

69920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 +

2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a

^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5

497558138880*a^24*b^2*c^19)))^(3/4) + (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c

^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^

13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720

*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 5

7671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25

)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 1402337

28*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*

a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 756253

1438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^

2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^2

5)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38

*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b

^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*

b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 104045

58274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b

^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4) - (27*(2114129160*a*b^11*c^10 -

24024195*b^13*c^9 + 1209323520*a^6*b*c^15 - 61748341200*a^2*b^9*c^11 + 590751532800*a^3*b^7*c^12 + 22799387520

0*a^4*b^5*c^13 + 28822210560*a^5*b^3*c^14))/(16777216*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a

^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 562298

88*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^

13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) + (((27*(3799912185593856*a^15*c^19 + 20971

52*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*

b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 1372

8399105196032*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356

442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*

a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22

*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*

a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^1

4*b^4*c^12 - 939524096*a^15*b^2*c^13)) + (9*x^(1/2)*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280

*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424

368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 1315117

4656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13

- 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b

^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c

*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2

- 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a

^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 7044752998

40*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^1

4 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 130567005798

40*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 16

77721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 -

188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 1938054170699

3664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^

12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*c^17))/(4194304*(a^2*b^24 + 1677721

6*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c

^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a

^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^1

6 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*

b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b

^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 821226268

2624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 400

9*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c -

b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^

8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^

7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^1

8*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 1664729

3239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4

*c^18 - 5497558138880*a^24*b^2*c^19)))^(3/4) - (9*x^(1/2)*(2982998016*a^6*b*c^14 - 173138472*a*b^11*c^9 - 1232

01*b^13*c^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 + 147581948160*a^4*b^5*c^12 + 44937566208*a

^5*b^3*c^13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3

+ 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^

8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 - b^8*(-(4*a*c

- b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4

- 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 1084

93078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12

+ 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^4*(-(4

*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-(4*a*c

- b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80

*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 1587609

60*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707

456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13

+ 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 195850508697

60*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)))*(-(81*(b^33 - b^8*(-(

4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^2

5*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8

- 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^

9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 - 1296*a^4*c^

4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c - 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54648*a^3*b^2*c^3*(-

(4*a*c - b^2)^25)^(1/2) + 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^2

0 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 1

58760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193

730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^1

4*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 195850

50869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*2i - 2*atan(((((2

7*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*a^2*b^26*c^6 - 402594463

744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 645335479222272*a^6*b^18*c^10 -

3564382621532160*a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35694820362027008*a^9*b^12*c^13 + 565296036

35707904*a^10*b^10*c^14 - 33767651356442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6*c^16 + 1145427233351925

76*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a^16*c^14 - 56*a^3*b^26*c

+ 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5 + 12300288*a^8*b^16*c^6

- 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624576*a^12*b^8*c^10 - 1526

726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) - (x^(1/2)*(-(81*(b^33 + b^8*(-(4*

a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*

c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 -

108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*

c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*

(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4

*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20

- 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158

760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 19373

0707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*

c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050

869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(1/4)*(5066549580791808*a

^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 - 1491964264448*a^4*b^22*c

^7 + 20440823103488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7*b^16*c^10 - 57270811911

78240*a^8*b^14*c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^13 + 80798711478747136*a

^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 27584547717644288*a^14*b^2*

c^17)*9i)/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 1

26720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 - 12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^

8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^13*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^

2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 14

0233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 43376799744*a^8*b^17*c^8 - 10849307

8528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7

562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c

- b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b

^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6

*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a

^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 44029706240*a^14*b^22*c^9 + 193730707456*

a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 1

0404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*a^21*b^8*c^16 - 19585050869760*a

^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(3/4)*1i - (9*x^(1/2)*(2982998016

*a^6*b*c^14 - 173138472*a*b^11*c^9 - 123201*b^13*c^8 + 10695194640*a^2*b^9*c^10 - 166726460160*a^3*b^7*c^11 +

147581948160*a^4*b^5*c^12 + 44937566208*a^5*b^3*c^13))/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c

+ 1056*a^4*b^20*c^2 - 14080*a^5*b^18*c^3 + 126720*a^6*b^16*c^4 - 811008*a^7*b^14*c^5 + 3784704*a^8*b^12*c^6 -

12976128*a^9*b^10*c^7 + 32440320*a^10*b^8*c^8 - 57671680*a^11*b^6*c^9 + 69206016*a^12*b^4*c^10 - 50331648*a^1

3*b^2*c^11)))*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 39

4248*a^3*b^27*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b

^19*c^7 + 43376799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^1

1*b^11*c^11 - 3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 421376

5570560*a^15*b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^

2)^25)^(1/2) - 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432

*(a^5*b^40 + 1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^

32*c^4 - 15876096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^

8 - 44029706240*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17

*b^16*c^12 - 5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20

809116549120*a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*

b^2*c^19)))^(1/4) - (((27*(3799912185593856*a^15*c^19 + 2097152*b^30*c^4 - 266338304*a*b^28*c^5 + 14019461120*

a^2*b^26*c^6 - 402594463744*a^3*b^24*c^7 + 7074549334016*a^4*b^22*c^8 - 81637933056000*a^5*b^20*c^9 + 64533547

9222272*a^6*b^18*c^10 - 3564382621532160*a^7*b^16*c^11 + 13728399105196032*a^8*b^14*c^12 - 35694820362027008*a

^9*b^12*c^13 + 56529603635707904*a^10*b^10*c^14 - 33767651356442624*a^11*b^8*c^15 - 51215251621806080*a^12*b^6

*c^16 + 114542723335192576*a^13*b^4*c^17 - 70615034782285824*a^14*b^2*c^18))/(33554432*(a^2*b^28 + 268435456*a

^16*c^14 - 56*a^3*b^26*c + 1456*a^4*b^24*c^2 - 23296*a^5*b^22*c^3 + 256256*a^6*b^20*c^4 - 2050048*a^7*b^18*c^5

+ 12300288*a^8*b^16*c^6 - 56229888*a^9*b^14*c^7 + 196804608*a^10*b^12*c^8 - 524812288*a^11*b^10*c^9 + 1049624

576*a^12*b^8*c^10 - 1526726656*a^13*b^6*c^11 + 1526726656*a^14*b^4*c^12 - 939524096*a^15*b^2*c^13)) + (x^(1/2)

*(-(81*(b^33 + b^8*(-(4*a*c - b^2)^25)^(1/2) - 471104225280*a^16*b*c^16 + 10509*a^2*b^29*c^2 - 394248*a^3*b^27

*c^3 + 9219696*a^4*b^25*c^4 - 140233728*a^5*b^23*c^5 + 1424368896*a^6*b^21*c^6 - 9732052992*a^7*b^19*c^7 + 433

76799744*a^8*b^17*c^8 - 108493078528*a^9*b^15*c^9 + 13151174656*a^10*b^13*c^10 + 986354024448*a^11*b^11*c^11 -

3840358219776*a^12*b^9*c^12 + 7562531438592*a^13*b^7*c^13 - 8212262682624*a^14*b^5*c^14 + 4213765570560*a^15*

b^3*c^15 + 1296*a^4*c^4*(-(4*a*c - b^2)^25)^(1/2) - 157*a*b^31*c + 4009*a^2*b^4*c^2*(-(4*a*c - b^2)^25)^(1/2)

- 54648*a^3*b^2*c^3*(-(4*a*c - b^2)^25)^(1/2) - 107*a*b^6*c*(-(4*a*c - b^2)^25)^(1/2)))/(33554432*(a^5*b^40 +

1099511627776*a^25*c^20 - 80*a^6*b^38*c + 3040*a^7*b^36*c^2 - 72960*a^8*b^34*c^3 + 1240320*a^9*b^32*c^4 - 1587

6096*a^10*b^30*c^5 + 158760960*a^11*b^28*c^6 - 1270087680*a^12*b^26*c^7 + 8255569920*a^13*b^24*c^8 - 440297062

40*a^14*b^22*c^9 + 193730707456*a^15*b^20*c^10 - 704475299840*a^16*b^18*c^11 + 2113425899520*a^17*b^16*c^12 -

5202279137280*a^18*b^14*c^13 + 10404558274560*a^19*b^12*c^14 - 16647293239296*a^20*b^10*c^15 + 20809116549120*

a^21*b^8*c^16 - 19585050869760*a^22*b^6*c^17 + 13056700579840*a^23*b^4*c^18 - 5497558138880*a^24*b^2*c^19)))^(

1/4)*(5066549580791808*a^15*c^18 + 16777216*a*b^28*c^4 - 1677721600*a^2*b^26*c^5 + 67947724800*a^3*b^24*c^6 -

1491964264448*a^4*b^22*c^7 + 20440823103488*a^5*b^20*c^8 - 188712273051648*a^6*b^18*c^9 + 1225740716605440*a^7

*b^16*c^10 - 5727081191178240*a^8*b^14*c^11 + 19380541706993664*a^9*b^12*c^12 - 47173446878101504*a^10*b^10*c^

13 + 80798711478747136*a^11*b^8*c^14 - 93414507895848960*a^12*b^6*c^15 + 67905838131445760*a^13*b^4*c^16 - 275

84547717644288*a^14*b^2*c^17)*9i)/(4194304*(a^2*b^24 + 16777216*a^14*c^12 - 48*a^3*b^22*c + 1056*a^4*b^20*c^2