∫ 1_____________ (df+efx)2(a+b(d+ex)2+c(d+ex)4)3 dx

3.659 \(\int \frac {1}{(d f+e f x)^2 (a+b (d+e x)^2+c (d+e x)^4)^3} \, dx\)

Optimal. Leaf size=499 \[ -\frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )}{8 a^3 e f^2 \left (b^2-4 a c\right )^2 (d+e x)}+\frac {36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e f^2 \left (b^2-4 a c\right )^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \sqrt {c} \left (\frac {b \left (124 a^2 c^2-47 a b^2 c+5 b^4\right )}{\sqrt {b^2-4 a c}}+\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^2 \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {3 \sqrt {c} \left (\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )-\frac {124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^2 \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {-2 a c+b^2+b c (d+e x)^2}{4 a e f^2 \left (b^2-4 a c\right ) (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2} \]

[Out]

-3/8*(-12*a*c+5*b^2)*(-5*a*c+b^2)/a^3/(-4*a*c+b^2)^2/e/f^2/(e*x+d)+1/4*(b^2-2*a*c+b*c*(e*x+d)^2)/a/(-4*a*c+b^2

)/e/f^2/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2+1/8*(5*b^4-35*a*b^2*c+36*a^2*c^2+b*c*(-32*a*c+5*b^2)*(e*x+d)^2)/

a^2/(-4*a*c+b^2)^2/e/f^2/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)-3/16*arctan((e*x+d)*2^(1/2)*c^(1/2)/(b-(-4*a*c+b^

2)^(1/2))^(1/2))*c^(1/2)*((-12*a*c+5*b^2)*(-5*a*c+b^2)+b*(124*a^2*c^2-47*a*b^2*c+5*b^4)/(-4*a*c+b^2)^(1/2))/a^

3/(-4*a*c+b^2)^2/e/f^2*2^(1/2)/(b-(-4*a*c+b^2)^(1/2))^(1/2)-3/16*arctan((e*x+d)*2^(1/2)*c^(1/2)/(b+(-4*a*c+b^2

)^(1/2))^(1/2))*c^(1/2)*((-12*a*c+5*b^2)*(-5*a*c+b^2)+(-124*a^2*b*c^2+47*a*b^3*c-5*b^5)/(-4*a*c+b^2)^(1/2))/a^

3/(-4*a*c+b^2)^2/e/f^2*2^(1/2)/(b+(-4*a*c+b^2)^(1/2))^(1/2)

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Rubi [A] time = 1.09, antiderivative size = 499, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 6, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1142, 1121, 1277, 1281, 1166, 205} \[ \frac {36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e f^2 \left (b^2-4 a c\right )^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \sqrt {c} \left (\frac {b \left (124 a^2 c^2-47 a b^2 c+5 b^4\right )}{\sqrt {b^2-4 a c}}+\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^2 \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {3 \sqrt {c} \left (\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )-\frac {124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^2 \sqrt {\sqrt {b^2-4 a c}+b}}-\frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )}{8 a^3 e f^2 \left (b^2-4 a c\right )^2 (d+e x)}+\frac {-2 a c+b^2+b c (d+e x)^2}{4 a e f^2 \left (b^2-4 a c\right ) (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2} \]

Antiderivative was successfully veriﬁed.

[In]

Int[1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]

[Out]

(-3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(8*a^3*(b^2 - 4*a*c)^2*e*f^2*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/

(4*a*(b^2 - 4*a*c)*e*f^2*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 +

b*c*(5*b^2 - 32*a*c)*(d + e*x)^2)/(8*a^2*(b^2 - 4*a*c)^2*e*f^2*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4))

- (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) + (b*(5*b^4 - 47*a*b^2*c + 124*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcT

an[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2

- 4*a*c]]*e*f^2) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) - (5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2)/Sqrt[b^2

- 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt

[b + Sqrt[b^2 - 4*a*c]]*e*f^2)

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 1121

Int[((d_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> -Simp[((d*x)^(m + 1)*(b^2 - 2*a

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

c)), Int[(d*x)^m*(a + b*x^2 + c*x^4)^(p + 1)*Simp[b^2*(m + 2*p + 3) - 2*a*c*(m + 4*p + 5) + b*c*(m + 4*p + 7)*

x^2, x], x], x] /; FreeQ[{a, b, c, d, m}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && IntegerQ[2*p] && (Integer

Q[p] || IntegerQ[m])

Rule 1142

Int[(u_)^(m_.)*((a_.) + (b_.)*(v_)^2 + (c_.)*(v_)^4)^(p_.), x_Symbol] :> Dist[u^m/(Coefficient[v, x, 1]*v^m),

Subst[Int[x^m*(a + b*x^2 + c*x^(2*2))^p, x], x, v], x] /; FreeQ[{a, b, c, m, p}, x] && LinearPairQ[u, v, x]

Rule 1166

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

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

q/2 + c*x^2), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - a*e^2, 0] && PosQ[b^

2 - 4*a*c]

Rule 1277

Int[((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^2)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> -Simp[((f

*x)^(m + 1)*(a + b*x^2 + c*x^4)^(p + 1)*(d*(b^2 - 2*a*c) - a*b*e + (b*d - 2*a*e)*c*x^2))/(2*a*f*(p + 1)*(b^2 -

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

(p + 1) + 1) - 2*a*c*(m + 4*(p + 1) + 1)) - a*b*e*(m + 1) + c*(m + 2*(2*p + 3) + 1)*(b*d - 2*a*e)*x^2, x], x],

x] /; FreeQ[{a, b, c, d, e, f, m}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && IntegerQ[2*p] && (IntegerQ[p] |

| IntegerQ[m])

Rule 1281

Int[((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^2)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> Simp[(d*(

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

*x^2 + c*x^4)^p*Simp[a*e*(m + 1) - b*d*(m + 2*p + 3) - c*d*(m + 4*p + 5)*x^2, x], x], x] /; FreeQ[{a, b, c, d,

e, f, p}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[m, -1] && IntegerQ[2*p] && (IntegerQ[p] || IntegerQ[m])

Rubi steps

\begin {align*} \int \frac {1}{(d f+e f x)^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )^3} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{x^2 \left (a+b x^2+c x^4\right )^3} \, dx,x,d+e x\right )}{e f^2}\\ &=\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}-\frac {\operatorname {Subst}\left (\int \frac {-5 b^2+18 a c-7 b c x^2}{x^2 \left (a+b x^2+c x^4\right )^2} \, dx,x,d+e x\right )}{4 a \left (b^2-4 a c\right ) e f^2}\\ &=\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {5 b^4-35 a b^2 c+36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2}{8 a^2 \left (b^2-4 a c\right )^2 e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}+\frac {\operatorname {Subst}\left (\int \frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )+3 b c \left (5 b^2-32 a c\right ) x^2}{x^2 \left (a+b x^2+c x^4\right )} \, dx,x,d+e x\right )}{8 a^2 \left (b^2-4 a c\right )^2 e f^2}\\ &=-\frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )}{8 a^3 \left (b^2-4 a c\right )^2 e f^2 (d+e x)}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {5 b^4-35 a b^2 c+36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2}{8 a^2 \left (b^2-4 a c\right )^2 e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {\operatorname {Subst}\left (\int \frac {3 b \left (5 b^4-42 a b^2 c+92 a^2 c^2\right )+3 c \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right ) x^2}{a+b x^2+c x^4} \, dx,x,d+e x\right )}{8 a^3 \left (b^2-4 a c\right )^2 e f^2}\\ &=-\frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )}{8 a^3 \left (b^2-4 a c\right )^2 e f^2 (d+e x)}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {5 b^4-35 a b^2 c+36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2}{8 a^2 \left (b^2-4 a c\right )^2 e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}+\frac {\left (3 c \left (5 b^5-47 a b^3 c+124 a^2 b c^2-\sqrt {b^2-4 a c} \left (5 b^4-37 a b^2 c+60 a^2 c^2\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx,x,d+e x\right )}{16 a^3 \left (b^2-4 a c\right )^{5/2} e f^2}-\frac {\left (3 c \left (\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )+\frac {b \left (5 b^4-47 a b^2 c+124 a^2 c^2\right )}{\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^2} \, dx,x,d+e x\right )}{16 a^3 \left (b^2-4 a c\right )^2 e f^2}\\ &=-\frac {3 \left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )}{8 a^3 \left (b^2-4 a c\right )^2 e f^2 (d+e x)}+\frac {b^2-2 a c+b c (d+e x)^2}{4 a \left (b^2-4 a c\right ) e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}+\frac {5 b^4-35 a b^2 c+36 a^2 c^2+b c \left (5 b^2-32 a c\right ) (d+e x)^2}{8 a^2 \left (b^2-4 a c\right )^2 e f^2 (d+e x) \left (a+b (d+e x)^2+c (d+e x)^4\right )}-\frac {3 \sqrt {c} \left (\left (5 b^2-12 a c\right ) \left (b^2-5 a c\right )+\frac {b \left (5 b^4-47 a b^2 c+124 a^2 c^2\right )}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{8 \sqrt {2} a^3 \left (b^2-4 a c\right )^2 \sqrt {b-\sqrt {b^2-4 a c}} e f^2}+\frac {3 \sqrt {c} \left (5 b^5-47 a b^3 c+124 a^2 b c^2-\sqrt {b^2-4 a c} \left (5 b^4-37 a b^2 c+60 a^2 c^2\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{8 \sqrt {2} a^3 \left (b^2-4 a c\right )^{5/2} \sqrt {b+\sqrt {b^2-4 a c}} e f^2}\\ \end {align*}

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Mathematica [A] time = 6.21, size = 575, normalized size = 1.15 \[ -\frac {1}{a^3 e f^2 (d+e x)}+\frac {-3 a b c (d+e x)-2 a c^2 (d+e x)^3+b^3 (d+e x)+b^2 c (d+e x)^3}{4 a^2 e f^2 \left (4 a c-b^2\right ) \left (a+b (d+e x)^2+c (d+e x)^4\right )^2}-\frac {3 \sqrt {c} \left (60 a^2 c^2 \sqrt {b^2-4 a c}+124 a^2 b c^2-47 a b^3 c-37 a b^2 c \sqrt {b^2-4 a c}+5 b^4 \sqrt {b^2-4 a c}+5 b^5\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^{5/2} \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {3 \sqrt {c} \left (60 a^2 c^2 \sqrt {b^2-4 a c}-124 a^2 b c^2+47 a b^3 c-37 a b^2 c \sqrt {b^2-4 a c}+5 b^4 \sqrt {b^2-4 a c}-5 b^5\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} (d+e x)}{\sqrt {\sqrt {b^2-4 a c}+b}}\right )}{8 \sqrt {2} a^3 e f^2 \left (b^2-4 a c\right )^{5/2} \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {-84 a^2 b c^2 (d+e x)-52 a^2 c^3 (d+e x)^3+52 a b^3 c (d+e x)+47 a b^2 c^2 (d+e x)^3-7 b^5 (d+e x)-7 b^4 c (d+e x)^3}{8 a^3 e f^2 \left (4 a c-b^2\right )^2 \left (a+b (d+e x)^2+c (d+e x)^4\right )} \]

Antiderivative was successfully veriﬁed.

[In]

Integrate[1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]

[Out]

-(1/(a^3*e*f^2*(d + e*x))) + (b^3*(d + e*x) - 3*a*b*c*(d + e*x) + b^2*c*(d + e*x)^3 - 2*a*c^2*(d + e*x)^3)/(4*

a^2*(-b^2 + 4*a*c)*e*f^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (-7*b^5*(d + e*x) + 52*a*b^3*c*(d + e*x) - 8

4*a^2*b*c^2*(d + e*x) - 7*b^4*c*(d + e*x)^3 + 47*a*b^2*c^2*(d + e*x)^3 - 52*a^2*c^3*(d + e*x)^3)/(8*a^3*(-b^2

+ 4*a*c)^2*e*f^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (3*Sqrt[c]*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 + 5*b^4

*Sqrt[b^2 - 4*a*c] - 37*a*b^2*c*Sqrt[b^2 - 4*a*c] + 60*a^2*c^2*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d +

e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^2) - (

3*Sqrt[c]*(-5*b^5 + 47*a*b^3*c - 124*a^2*b*c^2 + 5*b^4*Sqrt[b^2 - 4*a*c] - 37*a*b^2*c*Sqrt[b^2 - 4*a*c] + 60*a

^2*c^2*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2

- 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^2)

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fricas [B] time = 2.63, size = 10518, normalized size = 21.08 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="fricas")

[Out]

-1/16*(6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*e^8*x^8 + 48*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d*e^7*x^

7 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3 + 84*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^2)*e^6*x^6 + 12

*(28*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^3 + (30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d)*e^5*x^5 + 6*(

5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^8 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3 + 210*(5*b^

4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^4 + 15*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^2)*e^4*x^4 + 2*(30*b^

5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^6 + 8*(42*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^5 + 5*(30*b^5*c - 2

27*a*b^3*c^2 + 392*a^2*b*c^3)*d^3 + (15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d)*e^3*x^3 + 16*a^2*b

^4 - 128*a^3*b^2*c + 256*a^4*c^2 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^4 + 2*(84*(5*b^4*c

^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^6 + 25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2 + 15*(30*b^5*c - 227*a*b^3*c^2

+ 392*a^2*b*c^3)*d^4 + 6*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^2)*e^2*x^2 + 2*(25*a*b^5 - 194

*a^2*b^3*c + 364*a^3*b*c^2)*d^2 + 4*(12*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^7 + 3*(30*b^5*c - 227*a*b^3*

c^2 + 392*a^2*b*c^3)*d^5 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^3 + (25*a*b^5 - 194*a^2*b^

3*c + 364*a^3*b*c^2)*d)*e*x - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^

4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*

c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a

^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c

^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(

a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6

- 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^

4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 3

2*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3

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

2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 1

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

*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8

*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^

6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2

- 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a

^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 -

351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 1

60*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c +

160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77

825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(412

5*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9

)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*

c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^1

2 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*

a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5

)*e^4*f^8)) - (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 446

3140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*

a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*

c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b

^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^

14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/

((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4)))

+ 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*

a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^

5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 +

16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5

*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3

+ 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3

)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6

+ 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3

+ 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 +

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

4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^

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

d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3

)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8

*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720

*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2

*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 59188

6*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*

b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10

*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*

b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^

5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^

7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 +

342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*

a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a

^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) - (125*b^17 - 3

775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*

a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2

- 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a

^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 -

351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 1

60*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c +

160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))) + 3*sqrt(1/2)*((a^3*b^4*c^

2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*

(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 1

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

6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c -

8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^

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

^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^

3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a

^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c +

32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^

2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(

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

c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^

4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)

*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*

c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f

^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*

b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4

- 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^

4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c

^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 19

57349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2

006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 3235

84*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^

6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^

2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^

13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b

^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720

*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2

*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 59188

6*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*

b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10

*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*

c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2

+ 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b

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

+ 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c

^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 1

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

*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 +

5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^

7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^

5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*

b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*

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

5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(

a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 49

5*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^

8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a

*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((

a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8))

)/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4)

)*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 -

810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000

*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^

10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^

15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4

- 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280

*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^

3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)

*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*

c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f

^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*

b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4

- 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^

4 - 1024*a^12*c^5)*e^2*f^4))))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a

^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4

*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c -

8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*

b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2

- 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^

4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 +

16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*

d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a

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

^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*

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

+ 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^

2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^

3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)

________________________________________________________________________________________

giac [B] time = 1.42, size = 1658, normalized size = 3.32 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="giac")

[Out]

-1/8*(7*b^4*c^2*e^(-1)/((f*x*e + d*f)*f) - 47*a*b^2*c^3*e^(-1)/((f*x*e + d*f)*f) + 52*a^2*c^4*e^(-1)/((f*x*e +

d*f)*f) + 14*b^5*c*f*e^(-1)/(f*x*e + d*f)^3 - 99*a*b^3*c^2*f*e^(-1)/(f*x*e + d*f)^3 + 136*a^2*b*c^3*f*e^(-1)/

(f*x*e + d*f)^3 + 7*b^6*f^3*e^(-1)/(f*x*e + d*f)^5 - 43*a*b^4*c*f^3*e^(-1)/(f*x*e + d*f)^5 + 25*a^2*b^2*c^2*f^

3*e^(-1)/(f*x*e + d*f)^5 + 68*a^3*c^3*f^3*e^(-1)/(f*x*e + d*f)^5 + 9*a*b^5*f^5*e^(-1)/(f*x*e + d*f)^7 - 66*a^2

*b^3*c*f^5*e^(-1)/(f*x*e + d*f)^7 + 108*a^3*b*c^2*f^5*e^(-1)/(f*x*e + d*f)^7)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5

*c^2)*(c + b*f^2/(f*x*e + d*f)^2 + a*f^4/(f*x*e + d*f)^4)^2) - e^(-1)/((f*x*e + d*f)*a^3*f) + 3/64*((5*a^6*b^1

3 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12

*b*c^6)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 + 2*(5*a^4*b^6*c - 57*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*

a^7*c^4)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 +

16*a^5*c^2*f^4*e^2)*e^2 - (a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)^2*(5*b^5 - 42*a*b^3*c

+ 92*a^2*b*c^2)*sqrt(2*a*b + 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e^(-1)/((f*x*e + d*f)*f*sqrt((a^3*b^5*

f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2 + sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*

c^2*f^4*e^2)^2 - 4*(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 1

6*a^5*c^3)))/(a^4*b^4*f^8*e^4 - 8*a^5*b^2*c*f^8*e^4 + 16*a^6*c^2*f^8*e^4))))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c

^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*f^6*abs(a^3*b^4*f^4*e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^

2*f^4*e^2)*abs(a)) - 3/64*((5*a^6*b^13 - 112*a^7*b^11*c + 1030*a^8*b^9*c^2 - 4928*a^9*b^7*c^3 + 12736*a^10*b^5

*c^4 - 16384*a^11*b^3*c^5 + 7680*a^12*b*c^6)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*f^8*e^4 - 2*(5*a^4*b^6*c - 57

*a^5*b^4*c^2 + 208*a^6*b^2*c^3 - 240*a^7*c^4)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*f^4*abs(a^

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

5*c^2*f^4*e^2)^2*(5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2)*sqrt(2*a*b - 2*sqrt(b^2 - 4*a*c)*a))*arctan(2*sqrt(1/2)*e

^(-1)/((f*x*e + d*f)*f*sqrt((a^3*b^5*f^4*e^2 - 8*a^4*b^3*c*f^4*e^2 + 16*a^5*b*c^2*f^4*e^2 - sqrt((a^3*b^5*f^4*

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

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

)))*e^(-3)/((a^7*b^6*c - 12*a^8*b^4*c^2 + 48*a^9*b^2*c^3 - 64*a^10*c^4)*sqrt(b^2 - 4*a*c)*f^6*abs(a^3*b^4*f^4*

e^2 - 8*a^4*b^2*c*f^4*e^2 + 16*a^5*c^2*f^4*e^2)*abs(a))

________________________________________________________________________________________

maple [C] time = 0.07, size = 7019, normalized size = 14.07 \[ \text {output too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)

[Out]

result too large to display

________________________________________________________________________________________

maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm="maxima")

[Out]

Timed out

________________________________________________________________________________________

mupad [B] time = 15.40, size = 20580, normalized size = 41.24 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x)

[Out]

- atan(((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*

a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 626

84160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*

c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*

c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^

12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^

4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f^6 - 230400

*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*b

^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 333226967040*a^15

*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 174731349196

8*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^

(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b

^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*

c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*

c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10

*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 -

1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^

2*f^4)))^(1/2)*((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 -

188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c

^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*

a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 10485

76*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 2

58048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^

8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10 -

11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^14*f^10 + 2

2145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*c^8*e^14*f^

10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a^24*b^5*c^1

1*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 1099511627776*a^2

6*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 230686720*a^17*

b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10 - 12401718

0672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^9*d*e^13*f^

10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 3023656976384*a^25*b^

3*c^12*d*e^13*f^10) - 245760*a^12*b^23*c^2*e^12*f^8 + 10911744*a^13*b^21*c^3*e^12*f^8 - 220397568*a^14*b^19*c^

4*e^12*f^8 + 2673082368*a^15*b^17*c^5*e^12*f^8 - 21630025728*a^16*b^15*c^6*e^12*f^8 + 122607894528*a^17*b^13*c

^7*e^12*f^8 - 496773365760*a^18*b^11*c^8*e^12*f^8 + 1438679826432*a^19*b^9*c^9*e^12*f^8 - 2918430277632*a^20*b

^7*c^10*e^12*f^8 + 3949222428672*a^21*b^5*c^11*e^12*f^8 - 3208340570112*a^22*b^3*c^12*e^12*f^8 + 1185410973696

*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^2

0*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 16878108672*a^13

*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6 + 86981581

2096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^12*d*e^11*f^

6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6)*1i + (-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a

^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600

*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2

)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)

))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4

+ 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*

c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*

(271790899200*a^20*c^14*e^12*f^6 - 230400*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*a

^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*b^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a

^14*b^12*c^8*e^12*f^6 - 333226967040*a^15*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 1543847804

928*a^17*b^6*c^11*e^12*f^6 + 1747313491968*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (-

(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c

^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*

b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a

*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f

^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^

5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 262144

0*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18

923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 +

19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a

*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^1

5)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*

e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a

^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(

1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10 - 11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10

- 2768240640*a^18*b^17*c^5*e^14*f^10 + 22145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14*

f^10 + 496068722688*a^21*b^11*c^8*e^14*f^10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^

10*e^14*f^10 - 3779571220480*a^24*b^5*c^11*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a

^26*b*c^13*e^14*f^10) - 1099511627776*a^26*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^

16*b^21*c^3*d*e^13*f^10 + 230686720*a^17*b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 2214592

5120*a^19*b^15*c^6*d*e^13*f^10 - 124017180672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^

10 - 1417339207680*a^22*b^9*c^9*d*e^13*f^10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5

*c^11*d*e^13*f^10 + 3023656976384*a^25*b^3*c^12*d*e^13*f^10) + 245760*a^12*b^23*c^2*e^12*f^8 - 10911744*a^13*b

^21*c^3*e^12*f^8 + 220397568*a^14*b^19*c^4*e^12*f^8 - 2673082368*a^15*b^17*c^5*e^12*f^8 + 21630025728*a^16*b^1

5*c^6*e^12*f^8 - 122607894528*a^17*b^13*c^7*e^12*f^8 + 496773365760*a^18*b^11*c^8*e^12*f^8 - 1438679826432*a^1

9*b^9*c^9*e^12*f^8 + 2918430277632*a^20*b^7*c^10*e^12*f^8 - 3949222428672*a^21*b^5*c^11*e^12*f^8 + 32083405701

12*a^22*b^3*c^12*e^12*f^8 - 1185410973696*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*a

^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^20*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^

12*b^16*c^6*d*e^11*f^6 - 16878108672*a^13*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 3332269

67040*a^15*b^10*c^9*d*e^11*f^6 + 869815812096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^

6 + 1747313491968*a^18*b^4*c^12*d*e^11*f^6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6)*1i)/((-(9*(25*b^21 - 25*b

^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b

^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680

*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2

) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*

c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160

*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2

*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f^6 - 230400*a^9*b^22*c^3*e^12*f^6 + 986

1120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*b^16*c^6*e^12*f^6 - 168781086

72*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 333226967040*a^15*b^10*c^9*e^12*f^6 + 8698158

12096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 1747313491968*a^18*b^4*c^12*e^12*f^6 - 1

101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10

+ 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c

^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2

) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a

^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^

11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^

4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^2

1 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 12998

60*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 -

52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^

15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a

^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4

+ 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2

*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10 - 11534336*a^16*b^21*c^3*e^14

*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^14*f^10 + 22145925120*a^19*b^15*c^6*e^1

4*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*c^8*e^14*f^10 - 1417339207680*a^22*b^9*

c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a^24*b^5*c^11*e^14*f^10 + 3023656976384*

a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 1099511627776*a^26*b*c^13*d*e^13*f^10 + 26214

4*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 230686720*a^17*b^19*c^4*d*e^13*f^10 - 27682

40640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10 - 124017180672*a^20*b^13*c^7*d*e^13*f^

10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^9*d*e^13*f^10 + 2834678415360*a^23*b^7*

c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 3023656976384*a^25*b^3*c^12*d*e^13*f^10) + 245760

*a^12*b^23*c^2*e^12*f^8 - 10911744*a^13*b^21*c^3*e^12*f^8 + 220397568*a^14*b^19*c^4*e^12*f^8 - 2673082368*a^15

*b^17*c^5*e^12*f^8 + 21630025728*a^16*b^15*c^6*e^12*f^8 - 122607894528*a^17*b^13*c^7*e^12*f^8 + 496773365760*a

^18*b^11*c^8*e^12*f^8 - 1438679826432*a^19*b^9*c^9*e^12*f^8 + 2918430277632*a^20*b^7*c^10*e^12*f^8 - 394922242

8672*a^21*b^5*c^11*e^12*f^8 + 3208340570112*a^22*b^3*c^12*e^12*f^8 - 1185410973696*a^23*b*c^13*e^12*f^8) + 271

790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^20*c^4*d*e^11*f^6 - 191038464

*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 16878108672*a^13*b^14*c^7*d*e^11*f^6 + 89374

851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6 + 869815812096*a^16*b^8*c^10*d*e^11*f^

6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^12*d*e^11*f^6 - 1101055131648*a^19*b^2*c

^13*d*e^11*f^6) - (-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2

- 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7

*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 69

4*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 104

8576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 -

258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*

c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f^

6 - 230400*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 2207803

392*a^12*b^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 3332269

67040*a^15*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 17

47313491968*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 - 25*b^6*(-(4*a*c -

b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 612

6640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9

+ 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4

*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 -

7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6

*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8

*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*

b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256

*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^1

9*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f

^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e

^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a

^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*e

^14*f^10 - 11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^1

4*f^10 + 22145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*c

^8*e^14*f^10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a^

24*b^5*c^11*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 1099511

627776*a^26*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 23068

6720*a^17*b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10

- 124017180672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^9

*d*e^13*f^10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 30236569763

84*a^25*b^3*c^12*d*e^13*f^10) - 245760*a^12*b^23*c^2*e^12*f^8 + 10911744*a^13*b^21*c^3*e^12*f^8 - 220397568*a^

14*b^19*c^4*e^12*f^8 + 2673082368*a^15*b^17*c^5*e^12*f^8 - 21630025728*a^16*b^15*c^6*e^12*f^8 + 122607894528*a

^17*b^13*c^7*e^12*f^8 - 496773365760*a^18*b^11*c^8*e^12*f^8 + 1438679826432*a^19*b^9*c^9*e^12*f^8 - 2918430277

632*a^20*b^7*c^10*e^12*f^8 + 3949222428672*a^21*b^5*c^11*e^12*f^8 - 3208340570112*a^22*b^3*c^12*e^12*f^8 + 118

5410973696*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 986112

0*a^10*b^20*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 168781

08672*a^13*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6

+ 869815812096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^12

*d*e^11*f^6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6) + 191102976000*a^17*c^14*e^10*f^4 + 2851200*a^9*b^16*c^6

*e^10*f^4 - 92568960*a^10*b^14*c^7*e^10*f^4 + 1312630272*a^11*b^12*c^8*e^10*f^4 - 10611136512*a^12*b^10*c^9*e^

10*f^4 + 53445353472*a^13*b^8*c^10*e^10*f^4 - 171591892992*a^14*b^6*c^11*e^10*f^4 + 342580396032*a^15*b^4*c^12

*e^10*f^4 - 388363714560*a^16*b^2*c^13*e^10*f^4))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*

a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 1990560

0*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^

2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2

)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4

+ 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6

*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*2i

- atan(((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095

*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62

684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2

*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17

*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a

^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f

^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f^6 - 23040

0*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*

b^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 333226967040*a^1

5*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 17473134919

68*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)

^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*

b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3

*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a

*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^1

0*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4

- 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e

^2*f^4)))^(1/2)*((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2

- 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*

c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694

*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048

576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 -

258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c

^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10

- 11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^14*f^10 +

22145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*c^8*e^14*f

^10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a^24*b^5*c^

11*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 1099511627776*a^

26*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 230686720*a^17

*b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10 - 1240171

80672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^9*d*e^13*f

^10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 3023656976384*a^25*b

^3*c^12*d*e^13*f^10) - 245760*a^12*b^23*c^2*e^12*f^8 + 10911744*a^13*b^21*c^3*e^12*f^8 - 220397568*a^14*b^19*c

^4*e^12*f^8 + 2673082368*a^15*b^17*c^5*e^12*f^8 - 21630025728*a^16*b^15*c^6*e^12*f^8 + 122607894528*a^17*b^13*

c^7*e^12*f^8 - 496773365760*a^18*b^11*c^8*e^12*f^8 + 1438679826432*a^19*b^9*c^9*e^12*f^8 - 2918430277632*a^20*

b^7*c^10*e^12*f^8 + 3949222428672*a^21*b^5*c^11*e^12*f^8 - 3208340570112*a^22*b^3*c^12*e^12*f^8 + 118541097369

6*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^

20*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 16878108672*a^1

3*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6 + 8698158

12096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^12*d*e^11*f

^6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6)*1i + (-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*

a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 1990560

0*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^

2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2

)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4

+ 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6

*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x

*(271790899200*a^20*c^14*e^12*f^6 - 230400*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*

a^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*b^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*

a^14*b^12*c^8*e^12*f^6 - 333226967040*a^15*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 154384780

4928*a^17*b^6*c^11*e^12*f^6 + 1747313491968*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (

-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*

c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8

*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*

a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*

f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c

^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 26214

40*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 1

8923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 +

19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*

a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^

15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3

*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*

a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^

(1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10 - 11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^1

0 - 2768240640*a^18*b^17*c^5*e^14*f^10 + 22145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14

*f^10 + 496068722688*a^21*b^11*c^8*e^14*f^10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c

^10*e^14*f^10 - 3779571220480*a^24*b^5*c^11*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*

a^26*b*c^13*e^14*f^10) - 1099511627776*a^26*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a

^16*b^21*c^3*d*e^13*f^10 + 230686720*a^17*b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 221459

25120*a^19*b^15*c^6*d*e^13*f^10 - 124017180672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f

^10 - 1417339207680*a^22*b^9*c^9*d*e^13*f^10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^

5*c^11*d*e^13*f^10 + 3023656976384*a^25*b^3*c^12*d*e^13*f^10) + 245760*a^12*b^23*c^2*e^12*f^8 - 10911744*a^13*

b^21*c^3*e^12*f^8 + 220397568*a^14*b^19*c^4*e^12*f^8 - 2673082368*a^15*b^17*c^5*e^12*f^8 + 21630025728*a^16*b^

15*c^6*e^12*f^8 - 122607894528*a^17*b^13*c^7*e^12*f^8 + 496773365760*a^18*b^11*c^8*e^12*f^8 - 1438679826432*a^

19*b^9*c^9*e^12*f^8 + 2918430277632*a^20*b^7*c^10*e^12*f^8 - 3949222428672*a^21*b^5*c^11*e^12*f^8 + 3208340570

112*a^22*b^3*c^12*e^12*f^8 - 1185410973696*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*

a^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^20*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a

^12*b^16*c^6*d*e^11*f^6 - 16878108672*a^13*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 333226

967040*a^15*b^10*c^9*d*e^11*f^6 + 869815812096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f

^6 + 1747313491968*a^18*b^4*c^12*d*e^11*f^6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6)*1i)/((-(9*(25*b^21 + 25*

b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*

b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 5203968

0*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/

2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16

*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 86016

0*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^

2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f^6 - 230400*a^9*b^22*c^3*e^12*f^6 + 98

61120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 2207803392*a^12*b^16*c^6*e^12*f^6 - 16878108

672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 333226967040*a^15*b^10*c^9*e^12*f^6 + 869815

812096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 1747313491968*a^18*b^4*c^12*e^12*f^6 -

1101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^1

0 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*

c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/

2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(

a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a

^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f

^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^

21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299

860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 -

52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)

^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*

a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4

+ 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^

2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*e^14*f^10 - 11534336*a^16*b^21*c^3*e^1

4*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^14*f^10 + 22145925120*a^19*b^15*c^6*e^

14*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*c^8*e^14*f^10 - 1417339207680*a^22*b^9

*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a^24*b^5*c^11*e^14*f^10 + 3023656976384

*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 1099511627776*a^26*b*c^13*d*e^13*f^10 + 2621

44*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 230686720*a^17*b^19*c^4*d*e^13*f^10 - 2768

240640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10 - 124017180672*a^20*b^13*c^7*d*e^13*f

^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^9*d*e^13*f^10 + 2834678415360*a^23*b^7

*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 3023656976384*a^25*b^3*c^12*d*e^13*f^10) + 24576

0*a^12*b^23*c^2*e^12*f^8 - 10911744*a^13*b^21*c^3*e^12*f^8 + 220397568*a^14*b^19*c^4*e^12*f^8 - 2673082368*a^1

5*b^17*c^5*e^12*f^8 + 21630025728*a^16*b^15*c^6*e^12*f^8 - 122607894528*a^17*b^13*c^7*e^12*f^8 + 496773365760*

a^18*b^11*c^8*e^12*f^8 - 1438679826432*a^19*b^9*c^9*e^12*f^8 + 2918430277632*a^20*b^7*c^10*e^12*f^8 - 39492224

28672*a^21*b^5*c^11*e^12*f^8 + 3208340570112*a^22*b^3*c^12*e^12*f^8 - 1185410973696*a^23*b*c^13*e^12*f^8) + 27

1790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 9861120*a^10*b^20*c^4*d*e^11*f^6 - 19103846

4*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 16878108672*a^13*b^14*c^7*d*e^11*f^6 + 8937

4851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6 + 869815812096*a^16*b^8*c^10*d*e^11*f

^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^12*d*e^11*f^6 - 1101055131648*a^19*b^2*

c^13*d*e^11*f^6) - (-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^

2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^

7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 6

94*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 10

48576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4

- 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4

*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(271790899200*a^20*c^14*e^12*f

^6 - 230400*a^9*b^22*c^3*e^12*f^6 + 9861120*a^10*b^20*c^4*e^12*f^6 - 191038464*a^11*b^18*c^5*e^12*f^6 + 220780

3392*a^12*b^16*c^6*e^12*f^6 - 16878108672*a^13*b^14*c^7*e^12*f^6 + 89374851072*a^14*b^12*c^8*e^12*f^6 - 333226

967040*a^15*b^10*c^9*e^12*f^6 + 869815812096*a^16*b^8*c^10*e^12*f^6 - 1543847804928*a^17*b^6*c^11*e^12*f^6 + 1

747313491968*a^18*b^4*c^12*e^12*f^6 - 1101055131648*a^19*b^2*c^13*e^12*f^6) - (-(9*(25*b^21 + 25*b^6*(-(4*a*c

- b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 61

26640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9

- 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^

4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4

- 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^

6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^

8*b^18*c*e^2*f^4)))^(1/2)*((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2

*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 4390425

6*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^

19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(512*(a^7*b^20*e^2*

f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^4 + 53760*a^11*b^12*c^4*

e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^6*c^7*e^2*f^4 + 2949120*

a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*(x*(262144*a^15*b^23*c^2*

e^14*f^10 - 11534336*a^16*b^21*c^3*e^14*f^10 + 230686720*a^17*b^19*c^4*e^14*f^10 - 2768240640*a^18*b^17*c^5*e^

14*f^10 + 22145925120*a^19*b^15*c^6*e^14*f^10 - 124017180672*a^20*b^13*c^7*e^14*f^10 + 496068722688*a^21*b^11*

c^8*e^14*f^10 - 1417339207680*a^22*b^9*c^9*e^14*f^10 + 2834678415360*a^23*b^7*c^10*e^14*f^10 - 3779571220480*a

^24*b^5*c^11*e^14*f^10 + 3023656976384*a^25*b^3*c^12*e^14*f^10 - 1099511627776*a^26*b*c^13*e^14*f^10) - 109951

1627776*a^26*b*c^13*d*e^13*f^10 + 262144*a^15*b^23*c^2*d*e^13*f^10 - 11534336*a^16*b^21*c^3*d*e^13*f^10 + 2306

86720*a^17*b^19*c^4*d*e^13*f^10 - 2768240640*a^18*b^17*c^5*d*e^13*f^10 + 22145925120*a^19*b^15*c^6*d*e^13*f^10

- 124017180672*a^20*b^13*c^7*d*e^13*f^10 + 496068722688*a^21*b^11*c^8*d*e^13*f^10 - 1417339207680*a^22*b^9*c^

9*d*e^13*f^10 + 2834678415360*a^23*b^7*c^10*d*e^13*f^10 - 3779571220480*a^24*b^5*c^11*d*e^13*f^10 + 3023656976

384*a^25*b^3*c^12*d*e^13*f^10) - 245760*a^12*b^23*c^2*e^12*f^8 + 10911744*a^13*b^21*c^3*e^12*f^8 - 220397568*a

^14*b^19*c^4*e^12*f^8 + 2673082368*a^15*b^17*c^5*e^12*f^8 - 21630025728*a^16*b^15*c^6*e^12*f^8 + 122607894528*

a^17*b^13*c^7*e^12*f^8 - 496773365760*a^18*b^11*c^8*e^12*f^8 + 1438679826432*a^19*b^9*c^9*e^12*f^8 - 291843027

7632*a^20*b^7*c^10*e^12*f^8 + 3949222428672*a^21*b^5*c^11*e^12*f^8 - 3208340570112*a^22*b^3*c^12*e^12*f^8 + 11

85410973696*a^23*b*c^13*e^12*f^8) + 271790899200*a^20*c^14*d*e^11*f^6 - 230400*a^9*b^22*c^3*d*e^11*f^6 + 98611

20*a^10*b^20*c^4*d*e^11*f^6 - 191038464*a^11*b^18*c^5*d*e^11*f^6 + 2207803392*a^12*b^16*c^6*d*e^11*f^6 - 16878

108672*a^13*b^14*c^7*d*e^11*f^6 + 89374851072*a^14*b^12*c^8*d*e^11*f^6 - 333226967040*a^15*b^10*c^9*d*e^11*f^6

+ 869815812096*a^16*b^8*c^10*d*e^11*f^6 - 1543847804928*a^17*b^6*c^11*d*e^11*f^6 + 1747313491968*a^18*b^4*c^1

2*d*e^11*f^6 - 1101055131648*a^19*b^2*c^13*d*e^11*f^6) + 191102976000*a^17*c^14*e^10*f^4 + 2851200*a^9*b^16*c^

6*e^10*f^4 - 92568960*a^10*b^14*c^7*e^10*f^4 + 1312630272*a^11*b^12*c^8*e^10*f^4 - 10611136512*a^12*b^10*c^9*e

^10*f^4 + 53445353472*a^13*b^8*c^10*e^10*f^4 - 171591892992*a^14*b^6*c^11*e^10*f^4 + 342580396032*a^15*b^4*c^1

2*e^10*f^4 - 388363714560*a^16*b^2*c^13*e^10*f^4))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520

*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 199056

00*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b

^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/

2)))/(512*(a^7*b^20*e^2*f^4 + 1048576*a^17*c^10*e^2*f^4 + 720*a^9*b^16*c^2*e^2*f^4 - 7680*a^10*b^14*c^3*e^2*f^

4 + 53760*a^11*b^12*c^4*e^2*f^4 - 258048*a^12*b^10*c^5*e^2*f^4 + 860160*a^13*b^8*c^6*e^2*f^4 - 1966080*a^14*b^

6*c^7*e^2*f^4 + 2949120*a^15*b^4*c^8*e^2*f^4 - 2621440*a^16*b^2*c^9*e^2*f^4 - 40*a^8*b^18*c*e^2*f^4)))^(1/2)*2

i - ((x^4*(15*b^6*e^3 + 324*a^3*c^3*e^3 + 450*b^5*c*d^2*e^3 + 25*a^2*b^2*c^2*e^3 + 12600*a^2*c^4*d^4*e^3 + 105

0*b^4*c^2*d^4*e^3 - 91*a*b^4*c*e^3 - 3405*a*b^3*c^2*d^2*e^3 + 5880*a^2*b*c^3*d^2*e^3 - 7770*a*b^2*c^3*d^4*e^3)

)/(8*a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)) + (x^6*(30*b^5*c*e^5 - 227*a*b^3*c^2*e^5 + 392*a^2*b*c^3*e^5 + 50

40*a^2*c^4*d^2*e^5 + 420*b^4*c^2*d^2*e^5 - 3108*a*b^2*c^3*d^2*e^5))/(8*a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c))

+ (x*(30*b^6*d^3 + 90*b^5*c*d^5 + 648*a^3*c^3*d^3 + 720*a^2*c^4*d^7 + 60*b^4*c^2*d^7 + 25*a*b^5*d - 681*a*b^3

*c^2*d^5 + 1176*a^2*b*c^3*d^5 - 444*a*b^2*c^3*d^7 + 50*a^2*b^2*c^2*d^3 - 194*a^2*b^3*c*d + 364*a^3*b*c^2*d - 1

82*a*b^4*c*d^3))/(4*a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)) + (3*x^5*(1680*a^2*c^4*d^3*e^4 + 140*b^4*c^2*d^3*e

^4 + 30*b^5*c*d*e^4 - 227*a*b^3*c^2*d*e^4 + 392*a^2*b*c^3*d*e^4 - 1036*a*b^2*c^3*d^3*e^4))/(4*a*(a^2*b^4 + 16*

a^4*c^2 - 8*a^3*b^2*c)) + (3*x^8*(60*a^2*c^4*e^7 + 5*b^4*c^2*e^7 - 37*a*b^2*c^3*e^7))/(8*a*(a^2*b^4 + 16*a^4*c

^2 - 8*a^3*b^2*c)) + (x^2*(90*b^6*d^2*e + 25*a*b^5*e + 1944*a^3*c^3*d^2*e + 5040*a^2*c^4*d^6*e + 420*b^4*c^2*d

^6*e - 194*a^2*b^3*c*e + 364*a^3*b*c^2*e + 450*b^5*c*d^4*e - 546*a*b^4*c*d^2*e - 3405*a*b^3*c^2*d^4*e + 5880*a

^2*b*c^3*d^4*e - 3108*a*b^2*c^3*d^6*e + 150*a^2*b^2*c^2*d^2*e))/(8*a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)) + (

x^3*(15*b^6*d*e^2 + 324*a^3*c^3*d*e^2 + 150*b^5*c*d^3*e^2 + 2520*a^2*c^4*d^5*e^2 + 210*b^4*c^2*d^5*e^2 - 91*a*

b^4*c*d*e^2 + 25*a^2*b^2*c^2*d*e^2 - 1135*a*b^3*c^2*d^3*e^2 + 1960*a^2*b*c^3*d^3*e^2 - 1554*a*b^2*c^3*d^5*e^2)

)/(2*a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)) + (3*x^7*(60*a^2*c^4*d*e^6 + 5*b^4*c^2*d*e^6 - 37*a*b^2*c^3*d*e^6

))/(a*(a^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)) + (8*a^2*b^4 + 128*a^4*c^2 + 15*b^6*d^4 - 64*a^3*b^2*c + 25*a*b^5*

d^2 + 30*b^5*c*d^6 + 324*a^3*c^3*d^4 + 180*a^2*c^4*d^8 + 15*b^4*c^2*d^8 - 194*a^2*b^3*c*d^2 + 364*a^3*b*c^2*d^

2 - 227*a*b^3*c^2*d^6 + 392*a^2*b*c^3*d^6 - 111*a*b^2*c^3*d^8 + 25*a^2*b^2*c^2*d^4 - 91*a*b^4*c*d^4)/(8*a*e*(a

^2*b^4 + 16*a^4*c^2 - 8*a^3*b^2*c)))/(x^3*(10*b^2*d^2*e^3*f^2 + 84*c^2*d^6*e^3*f^2 + 2*a*b*e^3*f^2 + 20*a*c*d^

2*e^3*f^2 + 70*b*c*d^4*e^3*f^2) + x^6*(84*c^2*d^3*e^6*f^2 + 14*b*c*d*e^6*f^2) + x^2*(10*b^2*d^3*e^2*f^2 + 36*c

^2*d^7*e^2*f^2 + 6*a*b*d*e^2*f^2 + 20*a*c*d^3*e^2*f^2 + 42*b*c*d^5*e^2*f^2) + x^4*(5*b^2*d*e^4*f^2 + 126*c^2*d

^5*e^4*f^2 + 10*a*c*d*e^4*f^2 + 70*b*c*d^3*e^4*f^2) + x^7*(36*c^2*d^2*e^7*f^2 + 2*b*c*e^7*f^2) + x^5*(b^2*e^5*

f^2 + 126*c^2*d^4*e^5*f^2 + 2*a*c*e^5*f^2 + 42*b*c*d^2*e^5*f^2) + x*(a^2*e*f^2 + 5*b^2*d^4*e*f^2 + 9*c^2*d^8*e

*f^2 + 6*a*b*d^2*e*f^2 + 10*a*c*d^4*e*f^2 + 14*b*c*d^6*e*f^2) + a^2*d*f^2 + b^2*d^5*f^2 + c^2*d^9*f^2 + c^2*e^

9*f^2*x^9 + 2*a*b*d^3*f^2 + 2*a*c*d^5*f^2 + 2*b*c*d^7*f^2 + 9*c^2*d*e^8*f^2*x^8)

________________________________________________________________________________________

sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)

[Out]

Timed out

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