∫ x13∕2 ____________________

3.9.48 $\int \frac {x^{13/2}}{(a+b x^2+c x^4)^3} \, dx$

Optimal. Leaf size=569 \[ \frac {x^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (x^2 \left (28 a c+5 b^2\right )+24 a b\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\left (\sqrt {b^2-4 a c} \left (28 a c+5 b^2\right )+172 a b c+5 b^3\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-\sqrt {b^2-4 a c}-b}}+\frac {\left (-\frac {172 a b c+5 b^3}{\sqrt {b^2-4 a c}}+28 a c+5 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}}-\frac {\left (\sqrt {b^2-4 a c} \left (28 a c+5 b^2\right )+172 a b c+5 b^3\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-\sqrt {b^2-4 a c}-b}}-\frac {\left (-\frac {172 a b c+5 b^3}{\sqrt {b^2-4 a c}}+28 a c+5 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{32\ 2^{3/4} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}} \]

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Rubi [A] time = 1.91, antiderivative size = 569, 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, 1365, 1498, 1510, 298, 205, 208} \begin {gather*} \frac {\left (\sqrt {b^2-4 a c} \left (28 a c+5 b^2\right )+172 a b c+5 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} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-\sqrt {b^2-4 a c}-b}}+\frac {\left (-\frac {172 a b c+5 b^3}{\sqrt {b^2-4 a c}}+28 a c+5 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} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}}-\frac {\left (\sqrt {b^2-4 a c} \left (28 a c+5 b^2\right )+172 a b c+5 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} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-\sqrt {b^2-4 a c}-b}}-\frac {\left (-\frac {172 a b c+5 b^3}{\sqrt {b^2-4 a c}}+28 a c+5 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} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{\sqrt {b^2-4 a c}-b}}+\frac {x^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (x^2 \left (28 a c+5 b^2\right )+24 a b\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[x^(13/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

(x^(7/2)*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^(3/2)*(24*a*b + (5*b^2 + 28*a*c)*x^2))/(1

6*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((5*b^3 + 172*a*b*c + Sqrt[b^2 - 4*a*c]*(5*b^2 + 28*a*c))*ArcTan[(2^(

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

- 4*a*c])^(1/4)) + ((5*b^2 + 28*a*c - (5*b^3 + 172*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)*c^(3/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - ((5*b^3

+ 172*a*b*c + Sqrt[b^2 - 4*a*c]*(5*b^2 + 28*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^

(1/4)])/(32*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((5*b^2 + 28*a*c - (5*b^3 +

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

^(3/4)*(b^2 - 4*a*c)^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 1365

Int[((d_.)*(x_))^(m_.)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(d^(2*n - 1)*(d*x

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

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

Q[p, -1] && GtQ[m, 2*n - 1]

Rule 1498

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

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

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

*Simp[(n - m - 1)*(b*d - 2*a*e) + (2*n*p + 2*n + m + 1)*(b*e - 2*c*d)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e,

f}, x] && EqQ[n2, 2*n] && NeQ[b^2 - 4*a*c, 0] && IGtQ[n, 0] && LtQ[p, -1] && GtQ[m, n - 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^{13/2}}{\left (a+b x^2+c x^4\right )^3} \, dx &=2 \operatorname {Subst}\left (\int \frac {x^{14}}{\left (a+b x^4+c x^8\right )^3} \, dx,x,\sqrt {x}\right )\\ &=\frac {x^{7/2} \left (2 a+b 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^6 \left (14 a-5 b 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^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (24 a b+\left (5 b^2+28 a c\right ) x^2\right )}{16 \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 (-72 a b+\left (5 b^2+28 a c\right ) x^4\right )}{a+b x^4+c x^8} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^2}\\ &=\frac {x^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (24 a b+\left (5 b^2+28 a c\right ) x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\left (5 b^3+172 a b c+\sqrt {b^2-4 a c} \left (5 b^2+28 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 \left (b^2-4 a c\right )^{5/2}}+\frac {\left (5 b^2+28 a c-\frac {5 b^3+172 a b c}{\sqrt {b^2-4 a c}}\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 \left (b^2-4 a c\right )^2}\\ &=\frac {x^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (24 a b+\left (5 b^2+28 a c\right ) x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {\left (5 b^3+172 a b c+\sqrt {b^2-4 a c} \left (5 b^2+28 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} \sqrt {c} \left (b^2-4 a c\right )^{5/2}}+\frac {\left (5 b^3+172 a b c+\sqrt {b^2-4 a c} \left (5 b^2+28 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} \sqrt {c} \left (b^2-4 a c\right )^{5/2}}-\frac {\left (5 b^2+28 a c-\frac {5 b^3+172 a b c}{\sqrt {b^2-4 a c}}\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} \sqrt {c} \left (b^2-4 a c\right )^2}+\frac {\left (5 b^2+28 a c-\frac {5 b^3+172 a b c}{\sqrt {b^2-4 a c}}\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} \sqrt {c} \left (b^2-4 a c\right )^2}\\ &=\frac {x^{7/2} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}+\frac {x^{3/2} \left (24 a b+\left (5 b^2+28 a c\right ) x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\left (5 b^3+172 a b c+\sqrt {b^2-4 a c} \left (5 b^2+28 a c\right )\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} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-b-\sqrt {b^2-4 a c}}}+\frac {\left (5 b^2+28 a c-\frac {5 b^3+172 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} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}-\frac {\left (5 b^3+172 a b c+\sqrt {b^2-4 a c} \left (5 b^2+28 a c\right )\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} c^{3/4} \left (b^2-4 a c\right )^{5/2} \sqrt [4]{-b-\sqrt {b^2-4 a c}}}-\frac {\left (5 b^2+28 a c-\frac {5 b^3+172 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} c^{3/4} \left (b^2-4 a c\right )^2 \sqrt [4]{-b+\sqrt {b^2-4 a c}}}\\ \end {align*}

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Mathematica [C] time = 0.41, size = 216, normalized size = 0.38 \begin {gather*} \frac {c \left (a+b x^2+c x^4\right )^2 \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {28 \text {$\#$1}^4 a c \log \left (\sqrt {x}-\text {$\#$1}\right )+5 \text {$\#$1}^4 b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )-72 a b \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^5 c+\text {$\#$1} b}\&\right ]-16 x^{3/2} \left (b^2-4 a c\right ) \left (a \left (b-2 c x^2\right )+b^2 x^2\right )+4 x^{3/2} \left (8 a b c+28 a c^2 x^2+4 b^3+5 b^2 c x^2\right ) \left (a+b x^2+c x^4\right )}{64 c \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^(13/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

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

x^2 + a*(b - 2*c*x^2)) + c*(a + b*x^2 + c*x^4)^2*RootSum[a + b*#1^4 + c*#1^8 & , (-72*a*b*Log[Sqrt[x] - #1] +

5*b^2*Log[Sqrt[x] - #1]*#1^4 + 28*a*c*Log[Sqrt[x] - #1]*#1^4)/(b*#1 + 2*c*#1^5) & ])/(64*c*(b^2 - 4*a*c)^2*(a

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

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IntegrateAlgebraic [C] time = 1.12, size = 397, normalized size = 0.70 \begin {gather*} \frac {\text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {-36 \text {$\#$1}^4 a^2 c^3 \log \left (\sqrt {x}-\text {$\#$1}\right )-11 \text {$\#$1}^4 a b^2 c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )+8 \text {$\#$1}^4 b^4 c \log \left (\sqrt {x}-\text {$\#$1}\right )+344 a^2 b c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )-136 a b^3 c \log \left (\sqrt {x}-\text {$\#$1}\right )+8 b^5 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^5 c+\text {$\#$1} b}\&\right ]}{64 a c^2 \left (4 a c-b^2\right )^2}+\frac {\text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {2 \text {$\#$1}^4 a c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )+\text {$\#$1}^4 b^2 c \log \left (\sqrt {x}-\text {$\#$1}\right )-13 a b c \log \left (\sqrt {x}-\text {$\#$1}\right )+b^3 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^5 c+\text {$\#$1} b}\&\right ]}{8 a c^2 \left (4 a c-b^2\right )}+\frac {x^{3/2} \left (24 a^2 b-4 a^2 c x^2+37 a b^2 x^2+36 a b c x^4+28 a c^2 x^6+9 b^3 x^4+5 b^2 c x^6\right )}{16 \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]

IntegrateAlgebraic[x^(13/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

(x^(3/2)*(24*a^2*b + 37*a*b^2*x^2 - 4*a^2*c*x^2 + 9*b^3*x^4 + 36*a*b*c*x^4 + 5*b^2*c*x^6 + 28*a*c^2*x^6))/(16*

(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)^2) + RootSum[a + b*#1^4 + c*#1^8 & , (b^3*Log[Sqrt[x] - #1] - 13*a*b*c*Log

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

*(-b^2 + 4*a*c)) + RootSum[a + b*#1^4 + c*#1^8 & , (8*b^5*Log[Sqrt[x] - #1] - 136*a*b^3*c*Log[Sqrt[x] - #1] +

344*a^2*b*c^2*Log[Sqrt[x] - #1] + 8*b^4*c*Log[Sqrt[x] - #1]*#1^4 - 11*a*b^2*c^2*Log[Sqrt[x] - #1]*#1^4 - 36*a^

2*c^3*Log[Sqrt[x] - #1]*#1^4)/(b*#1 + 2*c*#1^5) & ]/(64*a*c^2*(-b^2 + 4*a*c)^2)

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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(x^(13/2)/(c*x^4+b*x^2+a)^3,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(x^(13/2)/(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: 191.18Unable to convert to real 1/4 Error: Bad Argument Value

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maple [C] time = 0.04, size = 242, normalized size = 0.43 \begin {gather*} \frac {\left (\left (28 a c +5 b^{2}\right ) \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{6}-72 \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{2} a 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 ) \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 {2 \left (28 a c +5 b^{2}\right ) c \,x^{\frac {15}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}+\frac {9 \left (4 a c +b^{2}\right ) b \,x^{\frac {11}{2}}}{16 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right )}+\frac {3 a^{2} b \,x^{\frac {3}{2}}}{2 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right )}-\frac {\left (4 a c -37 b^{2}\right ) a \,x^{\frac {7}{2}}}{16 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right )}}{\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^(13/2)/(c*x^4+b*x^2+a)^3,x)

[Out]

2*(3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b*x^(3/2)-1/32*a*(4*a*c-37*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)+9/32*

b*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)+1/32*c*(28*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(15/2))/(

c*x^4+b*x^2+a)^2+1/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum(((28*a*c+5*b^2)*_R^6-72*_R^2*a*b)/(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 (5 \, b^{2} c + 28 \, a c^{2}\right )} x^{\frac {15}{2}} + 9 \, {\left (b^{3} + 4 \, a b c\right )} x^{\frac {11}{2}} + 24 \, a^{2} b x^{\frac {3}{2}} + {\left (37 \, a b^{2} - 4 \, a^{2} c\right )} x^{\frac {7}{2}}}{16 \, {\left ({\left (b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right )} x^{8} + 2 \, {\left (b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right )} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left (b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right )} x^{4} + 2 \, {\left (a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right )} x^{2}\right )}} + \int \frac {{\left (5 \, b^{2} + 28 \, a c\right )} x^{\frac {5}{2}} - 72 \, a b \sqrt {x}}{32 \, {\left (a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left (b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right )} x^{4} + {\left (b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right )} x^{2}\right )}}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(13/2)/(c*x^4+b*x^2+a)^3,x, algorithm="maxima")

[Out]

1/16*((5*b^2*c + 28*a*c^2)*x^(15/2) + 9*(b^3 + 4*a*b*c)*x^(11/2) + 24*a^2*b*x^(3/2) + (37*a*b^2 - 4*a^2*c)*x^(

7/2))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3

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

rate(1/32*((5*b^2 + 28*a*c)*x^(5/2) - 72*a*b*sqrt(x))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2

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

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mupad [B] time = 8.01, size = 39697, normalized size = 69.77

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^(13/2)/(a + b*x^2 + c*x^4)^3,x)

[Out]

((9*x^(11/2)*(b^3 + 4*a*b*c))/(16*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x^(7/2)*(37*a*b^2 - 4*a^2*c))/(16*(b^4 +

16*a^2*c^2 - 8*a*b^2*c)) + (c*x^(15/2)*(28*a*c + 5*b^2))/(16*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*a^2*b*x^(3/2

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

386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22

*c^5 - 5154027327193088*a^6*b^20*c^6 + 52821290217635840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 1560

295235622273024*a^9*b^14*c^9 - 4628236966960300032*a^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 79240

26369753743360*a^12*b^8*c^12 - 1942353261163970560*a^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 841919

8028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 268435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 +

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

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

12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) - (x^(1/2)*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 1519

2104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^

5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429

440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12

- 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 2

3125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(3355

4432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^

4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c

^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^

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

20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^1

9*b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 758

24426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c^7 + 6133342147706880*a^7*b^16*c^8 - 31188471955587072*a^

8*b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 286537128244936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^

8*c^12 - 599365778533253120*a^12*b^6*c^13 + 436356582645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^1

5))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 81100

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

69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/

2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492

409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14

462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12

*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^

(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/

2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1

240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a

^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425

899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^1

0*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 54975581

38880*a^19*b^2*c^22)))^(3/4) - (x^(1/2)*(3705625*a^3*b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^2 +

7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 + 387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 - 117

420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*

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

71680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(

4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*

a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 66645041479

68*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 +

206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*

(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(

4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72

960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26

*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11

*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 166

47293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18

*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*1i - (((386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^

3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*c^5 - 5154027327193088*a^6*b^20*c^6 + 52821290217635

840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 1560295235622273024*a^9*b^14*c^9 - 4628236966960300032*a^

10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7924026369753743360*a^12*b^8*c^12 - 1942353261163970560*a^

13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 8419198028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 26843

5456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 256256*a^4*b^20*c^4 - 2050048*a^5*b^18*c^5 + 1230028

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

*c^10 - 1526726656*a^11*b^6*c^11 + 1526726656*a^12*b^4*c^12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) + (x^(1/

2)*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 2718641

6*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 168881657856

0*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 704

55242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^

14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^2

5)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*

c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^

28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b

^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 1040455

8274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^

6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99

891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 75824426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c

^7 + 6133342147706880*a^7*b^16*c^8 - 31188471955587072*a^8*b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 28653

7128244936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^8*c^12 - 599365778533253120*a^12*b^6*c^13 + 436356582

645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^15))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^

20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 811008*a^5*b^14*c^5 + 3784704*a^6*b^12*c^6 - 12976128*a^7*

b^10*c^7 + 32440320*a^8*b^8*c^8 - 57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*

a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2

+ 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 168

8816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c

^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114

787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c

- b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 8

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

60*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 1937307074

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

+ 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 1958505086976

0*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(3/4) + (x^(1/2)*(3705625*a^3*

b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^2 + 7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 +

387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 - 117420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^1

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

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

*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 -

89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 26518883328

0*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 41633

26443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*

b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*

a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20

*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^

5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^

22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 520227913

7280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*

c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*1i)/

((((386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*

b^22*c^5 - 5154027327193088*a^6*b^20*c^6 + 52821290217635840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 +

1560295235622273024*a^9*b^14*c^9 - 4628236966960300032*a^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7

924026369753743360*a^12*b^8*c^12 - 1942353261163970560*a^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 84

19198028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 268435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c

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

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

4*c^12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) - (x^(1/2)*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) -

15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 2549240960

0*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 1446297

0429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*

c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2)

+ 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(

33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 124032

0*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^

24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 211342589952

0*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^1

8 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880

*a^19*b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 +

75824426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c^7 + 6133342147706880*a^7*b^16*c^8 - 3118847195558707

2*a^8*b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 286537128244936704*a^10*b^10*c^11 + 507743474590679040*a^1

1*b^8*c^12 - 599365778533253120*a^12*b^6*c^13 + 436356582645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2

*c^15))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 8

11008*a^5*b^14*c^5 + 3784704*a^6*b^12*c^6 - 12976128*a^7*b^10*c^7 + 32440320*a^8*b^8*c^8 - 57671680*a^9*b^6*c^

9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)

^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 2

5492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8

+ 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*

a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^

25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)

^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6

+ 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 82555699

20*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 211

3425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15

*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497

558138880*a^19*b^2*c^22)))^(3/4) - (x^(1/2)*(3705625*a^3*b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c

^2 + 7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 + 387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 -

117420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126

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

57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6

*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297

600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504

147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^1

1 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*

c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c

*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5

- 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*

b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*

a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 -

16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*

a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4) + (((386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c

^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*c^5 - 5154027327193088*a^6*b^20*c^6 + 5282129021763

5840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 1560295235622273024*a^9*b^14*c^9 - 4628236966960300032*a

^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7924026369753743360*a^12*b^8*c^12 - 1942353261163970560*a

^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 8419198028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 2684

35456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 256256*a^4*b^20*c^4 - 2050048*a^5*b^18*c^5 + 123002

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

8*c^10 - 1526726656*a^11*b^6*c^11 + 1526726656*a^12*b^4*c^12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) + (x^(1

/2)*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2 + 271864

16*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 16888165785

60*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 70

455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009114787840*a

^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^

25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38

*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b

^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*

b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 104045

58274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b

^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 9

9891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 75824426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*

c^7 + 6133342147706880*a^7*b^16*c^8 - 31188471955587072*a^8*b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 2865

37128244936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^8*c^12 - 599365778533253120*a^12*b^6*c^13 + 43635658

2645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^15))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b

^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 811008*a^5*b^14*c^5 + 3784704*a^6*b^12*c^6 - 12976128*a^7

*b^10*c^7 + 32440320*a^8*b^8*c^8 - 57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48

*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c^2

+ 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 + 16

88816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*

c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 15000911

4787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*

c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 -

80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760

960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707

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

+ 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 195850508697

60*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(3/4) + (x^(1/2)*(3705625*a^3

*b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^2 + 7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 +

387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 - 117420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^

12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 811008*a^5*b^14*c^5 + 3784704*a^6*b^1

2*c^6 - 12976128*a^7*b^10*c^7 + 32440320*a^8*b^8*c^8 - 57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 5033164

8*a^11*b^2*c^11 - 48*a*b^22*c)))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15

- 89000*a^2*b^27*c^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 2651888332

80*a^6*b^19*c^6 + 1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163

326443520*a^10*b^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13

*b^5*c^13 + 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000

*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^2

0*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a

^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b

^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 52022791

37280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8

*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4) - (

285333125*a^4*b^15*c + 48189030400*a^11*b*c^8 + 22337507500*a^5*b^13*c^2 + 657473586000*a^6*b^11*c^3 + 8657411

576000*a^7*b^9*c^4 + 43867083462400*a^8*b^7*c^5 + 13299491251200*a^9*b^5*c^6 + 1381697515520*a^10*b^3*c^7)/(13

4217728*(b^28 + 268435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 256256*a^4*b^20*c^4 - 2050048*a

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

+ 1049624576*a^10*b^8*c^10 - 1526726656*a^11*b^6*c^11 + 1526726656*a^12*b^4*c^12 - 939524096*a^13*b^2*c^13 - 5

6*a*b^26*c))))*(-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 15192104632320*a^15*b*c^15 - 89000*a^2*b^27*c

^2 + 27186416*a^3*b^25*c^3 - 1342297600*a^4*b^23*c^4 + 25492409600*a^5*b^21*c^5 - 265188833280*a^6*b^19*c^6 +

1688816578560*a^7*b^17*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^1

1*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 150009

114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) + 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*

a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3

- 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 1587

60960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 1937307

07456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^

16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 1958505086

9760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*2i - 2*atan(((((38618

3668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*c^5

- 5154027327193088*a^6*b^20*c^6 + 52821290217635840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 156029523

5622273024*a^9*b^14*c^9 - 4628236966960300032*a^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7924026369

753743360*a^12*b^8*c^12 - 1942353261163970560*a^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 84191980283

92431616*a^15*b^2*c^15)/(268435456*(b^28 + 268435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 2562

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

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

939524096*a^13*b^2*c^13 - 56*a*b^26*c)) - (x^(1/2)*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 1519210463

2320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*b^21

*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^

9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 + 267

459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a

*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(

1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32

*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 -

44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^1

6*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 208091

16549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*

c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 758244263

85408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c^7 + 6133342147706880*a^7*b^16*c^8 - 31188471955587072*a^8*b^14

*c^9 + 112343150323826688*a^9*b^12*c^10 - 286537128244936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^8*c^12

- 599365778533253120*a^12*b^6*c^13 + 436356582645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^15)*1i)

/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 811008*a

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

06016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 +

15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 254924096

00*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 144629

70429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7

*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2

) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/

(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 12403

20*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b

^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 21134258995

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

18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 549755813888

0*a^19*b^2*c^22)))^(3/4)*1i + (x^(1/2)*(3705625*a^3*b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^2 +

7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 + 387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 - 1174

20369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a

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

1680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*((625*b^6*(-(4*a*c - b^2)^

25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^

4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968

*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 20

6669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-

(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*

a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 7296

0*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c

^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b

^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647

293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b

^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4) - (((386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^3 - 7

615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*c^5 - 5154027327193088*a^6*b^20*c^6 + 52821290217635840*a

^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 1560295235622273024*a^9*b^14*c^9 - 4628236966960300032*a^10*b^

12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7924026369753743360*a^12*b^8*c^12 - 1942353261163970560*a^13*b^

6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 8419198028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 268435456*

a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 256256*a^4*b^20*c^4 - 2050048*a^5*b^18*c^5 + 12300288*a^6

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

- 1526726656*a^11*b^6*c^11 + 1526726656*a^12*b^4*c^12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) + (x^(1/2)*((

625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*

b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*

b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 704552422

60480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3

*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/

2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 +

3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9

- 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^

13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 1040455827456

0*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20

+ 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99891544

064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 75824426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c^7 + 6

133342147706880*a^7*b^16*c^8 - 31188471955587072*a^8*b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 28653712824

4936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^8*c^12 - 599365778533253120*a^12*b^6*c^13 + 436356582645694

464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^15)*1i)/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*

c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 811008*a^5*b^14*c^5 + 3784704*a^6*b^12*c^6 - 12976128*a^7*b^1

0*c^7 + 32440320*a^8*b^8*c^8 - 57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b

^22*c)))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27

186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816

578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10

+ 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 1500091147878

40*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b

^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*

b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a

^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a

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

404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^

17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(3/4)*1i - (x^(1/2)*(3705625*a^3*b

^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^2 + 7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 + 3

87469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 - 117420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^12

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

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

a^11*b^2*c^11 - 48*a*b^22*c)))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 8

9000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*

a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326

443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^

5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^

2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c

^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*

b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22

*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 52022791372

80*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^

19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4))/((((3

86183668047020032*a^16*c^16 + 2097152000*a^3*b^26*c^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*

c^5 - 5154027327193088*a^6*b^20*c^6 + 52821290217635840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 15602

95235622273024*a^9*b^14*c^9 - 4628236966960300032*a^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 792402

6369753743360*a^12*b^8*c^12 - 1942353261163970560*a^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 8419198

028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 268435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 +

256256*a^4*b^20*c^4 - 2050048*a^5*b^18*c^5 + 12300288*a^6*b^16*c^6 - 56229888*a^7*b^14*c^7 + 196804608*a^8*b^1

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

2 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) - (x^(1/2)*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 151921

04632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*

b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 1446297042944

0*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 +

267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 231

25*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/2))/(335544

32*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1240320*a^4*

b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a^8*b^24*c^1

1 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425899520*a^12

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

809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 5497558138880*a^19*

b^2*c^22)))^(1/4)*(27584547717644288*a^15*c^16 + 99891544064*a^3*b^24*c^4 - 4092566962176*a^4*b^22*c^5 + 75824

426385408*a^5*b^20*c^6 - 837991069122560*a^6*b^18*c^7 + 6133342147706880*a^7*b^16*c^8 - 31188471955587072*a^8*

b^14*c^9 + 112343150323826688*a^9*b^12*c^10 - 286537128244936704*a^10*b^10*c^11 + 507743474590679040*a^11*b^8*

c^12 - 599365778533253120*a^12*b^6*c^13 + 436356582645694464*a^13*b^4*c^14 - 170573835886657536*a^14*b^2*c^15)

*1i)/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 126720*a^4*b^16*c^4 - 8110

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

69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^

31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492

409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14

462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11 - 206669464207360*a^12

*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^

(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(-(4*a*c - b^2)^25)^(1/

2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 - 72960*a^3*b^34*c^6 + 1

240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^26*c^10 + 8255569920*a

^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^11*b^18*c^14 + 2113425

899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 16647293239296*a^15*b^1

0*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^18*b^4*c^21 - 54975581

38880*a^19*b^2*c^22)))^(3/4)*1i + (x^(1/2)*(3705625*a^3*b^15*c - 6402256896*a^10*b*c^8 + 281098125*a^4*b^13*c^

2 + 7885779000*a^5*b^11*c^3 + 95525940400*a^6*b^9*c^4 + 387469862400*a^7*b^7*c^5 - 497953639680*a^8*b^5*c^6 -

117420369920*a^9*b^3*c^7))/(4194304*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^20*c^2 - 14080*a^3*b^18*c^3 + 1267

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

57671680*a^9*b^6*c^9 + 69206016*a^10*b^4*c^10 - 50331648*a^11*b^2*c^11 - 48*a*b^22*c)))*((625*b^6*(-(4*a*c - b

^2)^25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 134229760

0*a^4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 1688816578560*a^7*b^17*c^7 + 666450414

7968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70455242260480*a^11*b^9*c^11

- 206669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a^14*b^3*c^14 - 38416*a^3*c^

3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^25)^(1/2) + 54375*a*b^4*c*(

-(4*a*c - b^2)^25)^(1/2))/(33554432*(1099511627776*a^20*c^23 + b^40*c^3 - 80*a*b^38*c^4 + 3040*a^2*b^36*c^5 -

72960*a^3*b^34*c^6 + 1240320*a^4*b^32*c^7 - 15876096*a^5*b^30*c^8 + 158760960*a^6*b^28*c^9 - 1270087680*a^7*b^

26*c^10 + 8255569920*a^8*b^24*c^11 - 44029706240*a^9*b^22*c^12 + 193730707456*a^10*b^20*c^13 - 704475299840*a^

11*b^18*c^14 + 2113425899520*a^12*b^16*c^15 - 5202279137280*a^13*b^14*c^16 + 10404558274560*a^14*b^12*c^17 - 1

6647293239296*a^15*b^10*c^18 + 20809116549120*a^16*b^8*c^19 - 19585050869760*a^17*b^6*c^20 + 13056700579840*a^

18*b^4*c^21 - 5497558138880*a^19*b^2*c^22)))^(1/4)*1i + (((386183668047020032*a^16*c^16 + 2097152000*a^3*b^26*

c^3 - 7615312560128*a^4*b^24*c^4 + 295658569334784*a^5*b^22*c^5 - 5154027327193088*a^6*b^20*c^6 + 528212902176

35840*a^7*b^18*c^7 - 350572668266741760*a^8*b^16*c^8 + 1560295235622273024*a^9*b^14*c^9 - 4628236966960300032*

a^10*b^12*c^10 + 8604139182719238144*a^11*b^10*c^11 - 7924026369753743360*a^12*b^8*c^12 - 1942353261163970560*

a^13*b^6*c^13 + 11823215659242749952*a^14*b^4*c^14 - 8419198028392431616*a^15*b^2*c^15)/(268435456*(b^28 + 268

435456*a^14*c^14 + 1456*a^2*b^24*c^2 - 23296*a^3*b^22*c^3 + 256256*a^4*b^20*c^4 - 2050048*a^5*b^18*c^5 + 12300

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

^8*c^10 - 1526726656*a^11*b^6*c^11 + 1526726656*a^12*b^4*c^12 - 939524096*a^13*b^2*c^13 - 56*a*b^26*c)) + (x^(

1/2)*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 15192104632320*a^15*b*c^15 + 89000*a^2*b^27*c^2 - 271864

16*a^3*b^25*c^3 + 1342297600*a^4*b^23*c^4 - 25492409600*a^5*b^21*c^5 + 265188833280*a^6*b^19*c^6 - 16888165785

60*a^7*b^17*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 70

455242260480*a^11*b^9*c^11 - 206669464207360*a^12*b^7*c^12 + 267459844112384*a^13*b^5*c^13 - 150009114787840*a

^14*b^3*c^14 - 38416*a^3*c^3*(-(4*a*c - b^2)^25)^(1/2) - 23125*a*b^29*c + 1911000*a^2*b^2*c^2*(-(4*a*c - b^2)^