∫ x7∕2 ____________________

3.9.51 $\int \frac {x^{7/2}}{(a+b x^2+c x^4)^3} \, dx$

Optimal. Leaf size=533 \[ \frac {c^{3/4} \left (36 b \sqrt {b^2-4 a c}+28 a c+41 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (-36 b \sqrt {b^2-4 a c}+28 a c+41 b^2\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {c^{3/4} \left (36 b \sqrt {b^2-4 a c}+28 a c+41 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-\sqrt {b^2-4 a c}-b}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (-36 b \sqrt {b^2-4 a c}+28 a c+41 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{\sqrt {b^2-4 a c}-b}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {\sqrt {x} \left (2 a+b x^2\right )}{4 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )^2}-\frac {\sqrt {x} \left (-4 a c+13 b^2+24 b c x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )} \]

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Rubi [A] time = 1.36, antiderivative size = 533, 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, 1430, 1422, 212, 208, 205} \begin {gather*} \frac {c^{3/4} \left (36 b \sqrt {b^2-4 a c}+28 a c+41 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 )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (-36 b \sqrt {b^2-4 a c}+28 a c+41 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 )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {c^{3/4} \left (36 b \sqrt {b^2-4 a c}+28 a c+41 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 )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-\sqrt {b^2-4 a c}-b\right )^{3/4}}-\frac {c^{3/4} \left (-36 b \sqrt {b^2-4 a c}+28 a c+41 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 )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (\sqrt {b^2-4 a c}-b\right )^{3/4}}+\frac {\sqrt {x} \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 {\sqrt {x} \left (-4 a c+13 b^2+24 b c x^2\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^(7/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

(Sqrt[x]*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (Sqrt[x]*(13*b^2 - 4*a*c + 24*b*c*x^2))/(16*

(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (c^(3/4)*(41*b^2 + 28*a*c + 36*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(

1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4))

- (c^(3/4)*(41*b^2 + 28*a*c - 36*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c

])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(41*b^2 + 28*a*c + 36*b*

Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c

)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(41*b^2 + 28*a*c - 36*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)

*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3

/4))

Rule 205

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

&& PosQ[a/b]

Rule 208

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

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

Rule 212

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

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

!GtQ[a/b, 0]

Rule 1115

Int[((d_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> With[{k = Denominator[m]}, Dist[

k/d, Subst[Int[x^(k*(m + 1) - 1)*(a + (b*x^(2*k))/d^2 + (c*x^(4*k))/d^4)^p, x], x, (d*x)^(1/k)], x]] /; FreeQ[

{a, b, c, d, p}, x] && NeQ[b^2 - 4*a*c, 0] && FractionQ[m] && IntegerQ[p]

Rule 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 1422

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

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

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

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

Rule 1430

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

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

[1/(a*n*(p + 1)*(b^2 - 4*a*c)), Int[Simp[(n*p + n + 1)*d*b^2 - a*b*e - 2*a*c*d*(2*n*p + 2*n + 1) + (2*n*p + 3*

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

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

Rubi steps

\begin {align*} \int \frac {x^{7/2}}{\left (a+b x^2+c x^4\right )^3} \, dx &=2 \operatorname {Subst}\left (\int \frac {x^8}{\left (a+b x^4+c x^8\right )^3} \, dx,x,\sqrt {x}\right )\\ &=\frac {\sqrt {x} \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 {2 a-11 b x^4}{\left (a+b x^4+c x^8\right )^2} \, dx,x,\sqrt {x}\right )}{4 \left (b^2-4 a c\right )}\\ &=\frac {\sqrt {x} \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 {\sqrt {x} \left (13 b^2-4 a c+24 b c 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 {a \left (5 b^2+28 a c\right )-72 a b c x^4}{a+b x^4+c x^8} \, dx,x,\sqrt {x}\right )}{16 a \left (b^2-4 a c\right )^2}\\ &=\frac {\sqrt {x} \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 {\sqrt {x} \left (13 b^2-4 a c+24 b c x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {\left (c \left (41 b^2+28 a c-36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2}}-\frac {\left (c \left (41 b^2+28 a c+36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^4} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2}}\\ &=\frac {\sqrt {x} \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 {\sqrt {x} \left (13 b^2-4 a c+24 b c x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}-\frac {\left (c \left (41 b^2+28 a c-36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2} \sqrt {-b+\sqrt {b^2-4 a c}}}-\frac {\left (c \left (41 b^2+28 a c-36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b+\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2} \sqrt {-b+\sqrt {b^2-4 a c}}}+\frac {\left (c \left (41 b^2+28 a c+36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}-\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2} \sqrt {-b-\sqrt {b^2-4 a c}}}+\frac {\left (c \left (41 b^2+28 a c+36 b \sqrt {b^2-4 a c}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {-b-\sqrt {b^2-4 a c}}+\sqrt {2} \sqrt {c} x^2} \, dx,x,\sqrt {x}\right )}{16 \left (b^2-4 a c\right )^{5/2} \sqrt {-b-\sqrt {b^2-4 a c}}}\\ &=\frac {\sqrt {x} \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 {\sqrt {x} \left (13 b^2-4 a c+24 b c x^2\right )}{16 \left (b^2-4 a c\right )^2 \left (a+b x^2+c x^4\right )}+\frac {c^{3/4} \left (41 b^2+28 a c+36 b \sqrt {b^2-4 a c}\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4}}-\frac {c^{3/4} \left (41 b^2+28 a c-36 b \sqrt {b^2-4 a c}\right ) \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4}}+\frac {c^{3/4} \left (41 b^2+28 a c+36 b \sqrt {b^2-4 a c}\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b-\sqrt {b^2-4 a c}}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-b-\sqrt {b^2-4 a c}\right )^{3/4}}-\frac {c^{3/4} \left (41 b^2+28 a c-36 b \sqrt {b^2-4 a c}\right ) \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{-b+\sqrt {b^2-4 a c}}}\right )}{16 \sqrt [4]{2} \left (b^2-4 a c\right )^{5/2} \left (-b+\sqrt {b^2-4 a c}\right )^{3/4}}\\ \end {align*}

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Mathematica [C] time = 0.44, size = 177, normalized size = 0.33 \begin {gather*} -\frac {\text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {72 \text {$\#$1}^4 b c \log \left (\sqrt {x}-\text {$\#$1}\right )-28 a c \log \left (\sqrt {x}-\text {$\#$1}\right )-5 b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\&\right ]+\frac {4 \sqrt {x} \left (28 a^2 c+a \left (5 b^2+36 b c x^2-4 c^2 x^4\right )+b x^2 \left (9 b^2+37 b c x^2+24 c^2 x^4\right )\right )}{\left (a+b x^2+c x^4\right )^2}}{64 \left (b^2-4 a c\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[x^(7/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

-1/64*((4*Sqrt[x]*(28*a^2*c + a*(5*b^2 + 36*b*c*x^2 - 4*c^2*x^4) + b*x^2*(9*b^2 + 37*b*c*x^2 + 24*c^2*x^4)))/(

a + b*x^2 + c*x^4)^2 + RootSum[a + b*#1^4 + c*#1^8 & , (-5*b^2*Log[Sqrt[x] - #1] - 28*a*c*Log[Sqrt[x] - #1] +

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

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IntegrateAlgebraic [C] time = 0.80, size = 350, normalized size = 0.66 \begin {gather*} -\frac {3 \text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {-8 \text {$\#$1}^4 a b c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )+8 \text {$\#$1}^4 b^3 c \log \left (\sqrt {x}-\text {$\#$1}\right )+140 a^2 c^2 \log \left (\sqrt {x}-\text {$\#$1}\right )-71 a b^2 c \log \left (\sqrt {x}-\text {$\#$1}\right )+8 b^4 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\&\right ]}{64 a c \left (4 a c-b^2\right )^2}-\frac {\text {RootSum}\left [\text {$\#$1}^8 c+\text {$\#$1}^4 b+a\&,\frac {3 \text {$\#$1}^4 b c \log \left (\sqrt {x}-\text {$\#$1}\right )-14 a c \log \left (\sqrt {x}-\text {$\#$1}\right )+3 b^2 \log \left (\sqrt {x}-\text {$\#$1}\right )}{2 \text {$\#$1}^7 c+\text {$\#$1}^3 b}\&\right ]}{8 a c \left (4 a c-b^2\right )}-\frac {\sqrt {x} \left (28 a^2 c+5 a b^2+36 a b c x^2-4 a c^2 x^4+9 b^3 x^2+37 b^2 c x^4+24 b c^2 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^(7/2)/(a + b*x^2 + c*x^4)^3,x]

[Out]

-1/16*(Sqrt[x]*(5*a*b^2 + 28*a^2*c + 9*b^3*x^2 + 36*a*b*c*x^2 + 37*b^2*c*x^4 - 4*a*c^2*x^4 + 24*b*c^2*x^6))/((

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

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

b*#1^4 + c*#1^8 & , (8*b^4*Log[Sqrt[x] - #1] - 71*a*b^2*c*Log[Sqrt[x] - #1] + 140*a^2*c^2*Log[Sqrt[x] - #1] +

8*b^3*c*Log[Sqrt[x] - #1]*#1^4 - 8*a*b*c^2*Log[Sqrt[x] - #1]*#1^4)/(b*#1^3 + 2*c*#1^7) & ])/(64*a*c*(-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^(7/2)/(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^(7/2)/(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: 191.21Unable to convert to real 1/4 Error: Bad Argument Value

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maple [C] time = 0.04, size = 237, normalized size = 0.44 \begin {gather*} \frac {\left (-72 \RootOf \left (c \,\textit {\_Z}^{8}+b \,\textit {\_Z}^{4}+a \right )^{4} b c +28 a c +5 b^{2}\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 {3 b \,c^{2} x^{\frac {13}{2}}}{2 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right )}+\frac {2 \left (4 a c -37 b^{2}\right ) c \,x^{\frac {9}{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 {5}{2}}}{16 \left (16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right )}-\frac {\left (28 a c +5 b^{2}\right ) a \sqrt {x}}{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^(7/2)/(c*x^4+b*x^2+a)^3,x)

[Out]

2*(-1/32*a*(28*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)-9/32*b*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(

5/2)+1/32*c*(4*a*c-37*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)-3/4*b*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(

c*x^4+b*x^2+a)^2+1/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((-72*_R^4*b*c+28*a*c+5*b^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 {{\left (5 \, b^{2} c^{2} + 28 \, a c^{3}\right )} x^{\frac {17}{2}} + 2 \, {\left (5 \, b^{3} c + 16 \, a b c^{2}\right )} x^{\frac {13}{2}} + {\left (5 \, b^{4} + a b^{2} c + 60 \, a^{2} c^{2}\right )} x^{\frac {9}{2}} + {\left (a b^{3} + 20 \, a^{2} b c\right )} x^{\frac {5}{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 {{\left (5 \, b^{2} c + 28 \, a c^{2}\right )} x^{\frac {7}{2}} + 5 \, {\left (b^{3} + 20 \, a b c\right )} x^{\frac {3}{2}}}{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^(7/2)/(c*x^4+b*x^2+a)^3,x, algorithm="maxima")

[Out]

1/16*((5*b^2*c^2 + 28*a*c^3)*x^(17/2) + 2*(5*b^3*c + 16*a*b*c^2)*x^(13/2) + (5*b^4 + a*b^2*c + 60*a^2*c^2)*x^(

9/2) + (a*b^3 + 20*a^2*b*c)*x^(5/2))/((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 + 1

6*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(1/32*((5*b^2*c + 28*a*c^2)*x^(7/2) + 5*(b^3 + 20*a*b*c)*x^(3

/2))/(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 = 8.38, size = 47803, normalized size = 89.69

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(x^(7/2)/(a + b*x^2 + c*x^4)^3,x)

[Out]

atan(((((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*b^

4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a

^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*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 - 27186

416*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 - 1688816578

560*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 + 7

0455242260480*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b

^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*

b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13

*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404

558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*

b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 17592186

04441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 8375186

227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9*c

^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800*a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(65536

*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344

064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) - (x^(1/2)*(209715200*b^27*c^4 - 629

145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 + 18

03886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^9 + 2330621053501440*a^6*b^15*c^10 - 15146459867381760*a

^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 180146733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b^7

*c^14 - 419309754368655360*a^11*b^5*c^15 + 296956100429742080*a^12*b^3*c^16))/(2097152*(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 + 890

00*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 + 416332644

3520*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*(a^3*b^40 + 10995116277

76*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^

30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*

c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280

*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16

- 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*((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 - 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*

a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 12

70087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 -

704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^1

7*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13

056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4) - (x^(1/2)*(481890304*a^6*c^13 + 441265825*b

^12*c^7 + 16718255400*a*b^10*c^8 + 151843979760*a^2*b^8*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^4*

c^11 + 7420127232*a^5*b^2*c^12))/(2097152*(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 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 134

2297600*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 + 666

4504147968*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*

c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*

a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299

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

14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579

840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*1i - (((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 172103

68*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*

a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6

- 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 12403

20*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*

b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 21134258995

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

15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 549755813888

0*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 67108

86400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 36

0777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9*c^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800

*a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*

b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*

c^8 - 36*a*b^16*c)) + (x^(1/2)*(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 94

623498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^

9 + 2330621053501440*a^6*b^15*c^10 - 15146459867381760*a^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 18014

6733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b^7*c^14 - 419309754368655360*a^11*b^5*c^15 + 29695610042

9742080*a^12*b^3*c^16))/(2097152*(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^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 + 666450414796

8*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 - 2

06669464207360*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 729

60*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26

*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*

b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 1664

7293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*

b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 151921046323

20*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 + 26745

9844112384*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*(a^

3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c

^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44

029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*

c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116

549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^

19)))^(1/4) + (x^(1/2)*(481890304*a^6*c^13 + 441265825*b^12*c^7 + 16718255400*a*b^10*c^8 + 151843979760*a^2*b^

8*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^4*c^11 + 7420127232*a^5*b^2*c^12))/(2097152*(b^24 + 1677

7216*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 + 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 + 2651

88833280*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 + 26745984411238

4*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 + 1

911000*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*(a^3*b^40 +

1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 1587

6096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240

*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 52

02279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^

19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/

4)*1i)/((((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*

b^4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256

*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*

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 - 271

86416*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 - 16888165

78560*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 - 15000911478784

0*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4

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

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

13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 104

04558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^2

0*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 175921

8604441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 83751

86227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9

*c^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800*a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(655

36*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 3

44064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) - (x^(1/2)*(209715200*b^27*c^4 - 6

29145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 +

1803886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^9 + 2330621053501440*a^6*b^15*c^10 - 15146459867381760

*a^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 180146733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b

^7*c^14 - 419309754368655360*a^11*b^5*c^15 + 296956100429742080*a^12*b^3*c^16))/(2097152*(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*(a^3*b^40 + 109951162

7776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*

b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^2

2*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 52022791372

80*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^

16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*((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^2

5*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^1

7*c^7 + 6664504147968*a^8*b^15*c^8 - 14462970429440*a^9*b^13*c^9 + 4163326443520*a^10*b^11*c^10 + 704552422604

80*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 304

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

1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10

- 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a

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

13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4) - (x^(1/2)*(481890304*a^6*c^13 + 441265825

*b^12*c^7 + 16718255400*a*b^10*c^8 + 151843979760*a^2*b^8*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^

4*c^11 + 7420127232*a^5*b^2*c^12))/(2097152*(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 + 89000*a^2*b^27*c^2 - 27186416*a^3*b^25*c^3 + 1

342297600*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 + 6

664504147968*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 - 3841

6*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^3

6*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 127008768

0*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 7044752

99840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*

c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 130567005

79840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4) + (((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 1721036

8*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*a

^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 -

589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*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 - 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 124032

0*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b

^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 211342589952

0*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^1

5 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880

*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 671088

6400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 360

777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9*c^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800*

a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b

^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c

^8 - 36*a*b^16*c)) + (x^(1/2)*(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 946

23498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^9

+ 2330621053501440*a^6*b^15*c^10 - 15146459867381760*a^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 180146

733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b^7*c^14 - 419309754368655360*a^11*b^5*c^15 + 296956100429

742080*a^12*b^3*c^16))/(2097152*(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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 7296

0*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*

c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b

^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647

293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b

^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*((625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 625*b^31 + 1519210463232

0*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 + 267459

844112384*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*(a^3

*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^

4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 440

29706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c

^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 208091165

49120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^1

9)))^(1/4) + (x^(1/2)*(481890304*a^6*c^13 + 441265825*b^12*c^7 + 16718255400*a*b^10*c^8 + 151843979760*a^2*b^8

*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^4*c^11 + 7420127232*a^5*b^2*c^12))/(2097152*(b^24 + 16777

216*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 - 5

0331648*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 + 26518

8833280*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 + 19

11000*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*(a^3*b^40 + 1

099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876

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

a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 520

2279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^1

9*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4

)))*((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 - 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^3

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

28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b

^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 1040455

8274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^

6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*2i - ((9*x^(5/2)*(b^3 + 4*a*b*c))

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

^(9/2)*(4*a*c^2 - 37*b^2*c))/(16*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*b*c^2*x^(13/2))/(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(((((171894580*a*b^8*c^7 - 48125

*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*c^10)/(655

36*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 3

44064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*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^11*c^10 - 70455242260480*a^11*b^9*c^11 + 20666

9464207360*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a

^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7

+ 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18

*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293

239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*

c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 1677721600*a

^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 6854767804416

0*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9*c^11 - 3051144767078400*a^9*b^7*c^12

+ 4727899999436800*a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b

^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^

7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) - (x^(1/2)*(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 916201049193185

28*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8 - 19723563

5650560*a^5*b^17*c^9 + 2330621053501440*a^6*b^15*c^10 - 15146459867381760*a^7*b^13*c^11 + 63613894492422144*a^

8*b^11*c^12 - 180146733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b^7*c^14 - 419309754368655360*a^11*b^5

*c^15 + 296956100429742080*a^12*b^3*c^16))/(2097152*(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 + 3244032

0*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^2

5*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^1

7*c^7 - 6664504147968*a^8*b^15*c^8 + 14462970429440*a^9*b^13*c^9 - 4163326443520*a^10*b^11*c^10 - 704552422604

80*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 304

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

1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10

- 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a

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

13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*(-(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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3

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

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

3425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18

*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497

558138880*a^22*b^2*c^19)))^(1/4) - (x^(1/2)*(481890304*a^6*c^13 + 441265825*b^12*c^7 + 16718255400*a*b^10*c^8

+ 151843979760*a^2*b^8*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^4*c^11 + 7420127232*a^5*b^2*c^12))/

(2097152*(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 + 6920

6016*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 + 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 12403

20*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*

b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 21134258995

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

15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 549755813888

0*a^22*b^2*c^19)))^(1/4)*1i - (((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*a^2*b^6

*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 537

6*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^

8*b^2*c^8 - 36*a*b^16*c)) + (((-(625*b^31 + 625*b^6*(-(4*a*c - b^2)^25)^(1/2) - 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*(a^3*b^40 + 109951162

7776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*

b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^2

2*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 52022791372

80*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^

16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*(83886

080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 5637144576

00*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c^10 + 1

278182267289600*a^8*b^9*c^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800*a^10*b^5*c^13 - 43100855808819

20*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 -

129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) + (x^(1/2)*

(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 + 129842

2300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^9 + 2330621053501440*a^6*b^15*c

^10 - 15146459867381760*a^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 180146733873889280*a^9*b^9*c^13 + 34

2651803680112640*a^10*b^7*c^14 - 419309754368655360*a^11*b^5*c^15 + 296956100429742080*a^12*b^3*c^16))/(209715

2*(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) - 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*

b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^

8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15

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

809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*

b^2*c^19)))^(3/4))*(-(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^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669464207360*a^12*b^7*c^12 - 267459844112384*a^13*b^5*c^13 + 15

0009114787840*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*(a^3*b^40 + 1099511627776*a^23*c

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

158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193

730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^1

4*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 195850

50869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4) + (x^(1/2)*(48189

0304*a^6*c^13 + 441265825*b^12*c^7 + 16718255400*a*b^10*c^8 + 151843979760*a^2*b^8*c^9 - 123896495360*a^3*b^6*

c^10 + 12295917312*a^4*b^4*c^11 + 7420127232*a^5*b^2*c^12))/(2097152*(b^24 + 16777216*a^12*c^12 + 1056*a^2*b^2

0*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 + 1688

816578560*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 + 1500091147

87840*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80

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

0*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 19373070745

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

10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760

*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*1i)/((((171894580*a*b^8*c

^7 - 48125*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*a^2*b^6*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*

c^10)/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b

^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*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 - 134229

7600*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 - 666450

4147968*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2

- 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^1

0*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840

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

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

*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)*(83886080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 16

77721600*a^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 563714457600*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 685

47678044160*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c^10 + 1278182267289600*a^8*b^9*c^11 - 3051144767078400*a^

9*b^7*c^12 + 4727899999436800*a^10*b^5*c^13 - 4310085580881920*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 +

576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*

a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) - (x^(1/2)*(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 91620

104919318528*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 + 1298422300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8

- 197235635650560*a^5*b^17*c^9 + 2330621053501440*a^6*b^15*c^10 - 15146459867381760*a^7*b^13*c^11 + 6361389449

2422144*a^8*b^11*c^12 - 180146733873889280*a^9*b^9*c^13 + 342651803680112640*a^10*b^7*c^14 - 41930975436865536

0*a^11*b^5*c^15 + 296956100429742080*a^12*b^3*c^16))/(2097152*(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 + 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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^

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

^28*c^6 - 1270087680*a^10*b^26*c^7 + 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*

b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 104045

58274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b

^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(3/4))*(-(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^11*c^10 - 70455242260480*a^11*b^9*c^11 + 206669

464207360*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*(a^3*b^40 + 1099511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^

6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7

+ 8255569920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*

c^11 + 2113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 166472932

39296*a^18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c

^18 - 5497558138880*a^22*b^2*c^19)))^(1/4) - (x^(1/2)*(481890304*a^6*c^13 + 441265825*b^12*c^7 + 16718255400*a

*b^10*c^8 + 151843979760*a^2*b^8*c^9 - 123896495360*a^3*b^6*c^10 + 12295917312*a^4*b^4*c^11 + 7420127232*a^5*b

^2*c^12))/(2097152*(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)^2

5)^(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^11*c^10 - 70455242260480*a^11*b^9*c^11 + 20666946420736

0*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)^2

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

^3 + 1240320*a^7*b^32*c^4 - 15876096*a^8*b^30*c^5 + 158760960*a^9*b^28*c^6 - 1270087680*a^10*b^26*c^7 + 825556

9920*a^11*b^24*c^8 - 44029706240*a^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2

113425899520*a^15*b^16*c^12 - 5202279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^

18*b^10*c^15 + 20809116549120*a^19*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 54

97558138880*a^22*b^2*c^19)))^(1/4) + (((171894580*a*b^8*c^7 - 48125*b^10*c^6 - 17210368*a^5*c^11 + 3520856800*

a^2*b^6*c^8 + 3512738432*a^3*b^4*c^9 + 167976704*a^4*b^2*c^10)/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^

2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 58

9824*a^8*b^2*c^8 - 36*a*b^16*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 - 265188

833280*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 + 191

1000*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*(a^3*b^40 + 10

99511627776*a^23*c^20 - 80*a^4*b^38*c + 3040*a^5*b^36*c^2 - 72960*a^6*b^34*c^3 + 1240320*a^7*b^32*c^4 - 158760

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

^12*b^22*c^9 + 193730707456*a^13*b^20*c^10 - 704475299840*a^14*b^18*c^11 + 2113425899520*a^15*b^16*c^12 - 5202

279137280*a^16*b^14*c^13 + 10404558274560*a^17*b^12*c^14 - 16647293239296*a^18*b^10*c^15 + 20809116549120*a^19

*b^8*c^16 - 19585050869760*a^20*b^6*c^17 + 13056700579840*a^21*b^4*c^18 - 5497558138880*a^22*b^2*c^19)))^(1/4)

*(83886080*a*b^23*c^4 + 1759218604441600*a^12*b*c^15 - 1677721600*a^2*b^21*c^5 - 6710886400*a^3*b^19*c^6 + 563

714457600*a^4*b^17*c^7 - 8375186227200*a^5*b^15*c^8 + 68547678044160*a^6*b^13*c^9 - 360777252864000*a^7*b^11*c

^10 + 1278182267289600*a^8*b^9*c^11 - 3051144767078400*a^9*b^7*c^12 + 4727899999436800*a^10*b^5*c^13 - 4310085

580881920*a^11*b^3*c^14))/(65536*(b^18 - 262144*a^9*c^9 + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^1

0*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 36*a*b^16*c)) + (x

^(1/2)*(209715200*b^27*c^4 - 629145600*a*b^25*c^5 - 91620104919318528*a^13*b*c^17 - 94623498240*a^2*b^23*c^6 +

1298422300672*a^3*b^21*c^7 + 1803886264320*a^4*b^19*c^8 - 197235635650560*a^5*b^17*c^9 + 2330621053501440*a^6

*b^15*c^10 - 15146459867381760*a^7*b^13*c^11 + 63613894492422144*a^8*b^11*c^12 - 180146733873889280*a^9*b^9*c^

13 + 342651803680112640*a^10*b^7*c^14 - 419309754368655360*a^11*b^5*c^15 + 296956100429742080*a^12*b^3*c^16))/