3.795 \(\int \frac {1}{\sqrt {1-d x} \sqrt {1+d x} (a+b x+c x^2)} \, dx\)

Optimal. Leaf size=282 \[ \frac {\sqrt {2} c \tanh ^{-1}\left (\frac {d^2 x \left (\sqrt {b^2-4 a c}+b\right )+2 c}{\sqrt {2} \sqrt {1-d^2 x^2} \sqrt {-b d^2 \left (\sqrt {b^2-4 a c}+b\right )+2 a c d^2+2 c^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {-b d^2 \left (\sqrt {b^2-4 a c}+b\right )+2 a c d^2+2 c^2}}-\frac {\sqrt {2} c \tanh ^{-1}\left (\frac {d^2 x \left (b-\sqrt {b^2-4 a c}\right )+2 c}{\sqrt {2} \sqrt {1-d^2 x^2} \sqrt {-b d^2 \left (b-\sqrt {b^2-4 a c}\right )+2 a c d^2+2 c^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {-b d^2 \left (b-\sqrt {b^2-4 a c}\right )+2 a c d^2+2 c^2}} \]

[Out]

-c*arctanh(1/2*(2*c+d^2*x*(b-(-4*a*c+b^2)^(1/2)))*2^(1/2)/(-d^2*x^2+1)^(1/2)/(2*c^2+2*a*c*d^2-b*d^2*(b-(-4*a*c
+b^2)^(1/2)))^(1/2))*2^(1/2)/(-4*a*c+b^2)^(1/2)/(2*c^2+2*a*c*d^2-b*d^2*(b-(-4*a*c+b^2)^(1/2)))^(1/2)+c*arctanh
(1/2*(2*c+d^2*x*(b+(-4*a*c+b^2)^(1/2)))*2^(1/2)/(-d^2*x^2+1)^(1/2)/(2*c^2+2*a*c*d^2-b*d^2*(b+(-4*a*c+b^2)^(1/2
)))^(1/2))*2^(1/2)/(-4*a*c+b^2)^(1/2)/(2*c^2+2*a*c*d^2-b*d^2*(b+(-4*a*c+b^2)^(1/2)))^(1/2)

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Rubi [A]  time = 0.52, antiderivative size = 282, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {899, 985, 725, 206} \[ \frac {\sqrt {2} c \tanh ^{-1}\left (\frac {d^2 x \left (\sqrt {b^2-4 a c}+b\right )+2 c}{\sqrt {2} \sqrt {1-d^2 x^2} \sqrt {-b d^2 \left (\sqrt {b^2-4 a c}+b\right )+2 a c d^2+2 c^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {-b d^2 \left (\sqrt {b^2-4 a c}+b\right )+2 a c d^2+2 c^2}}-\frac {\sqrt {2} c \tanh ^{-1}\left (\frac {d^2 x \left (b-\sqrt {b^2-4 a c}\right )+2 c}{\sqrt {2} \sqrt {1-d^2 x^2} \sqrt {-b d^2 \left (b-\sqrt {b^2-4 a c}\right )+2 a c d^2+2 c^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {-b d^2 \left (b-\sqrt {b^2-4 a c}\right )+2 a c d^2+2 c^2}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 725

Int[1/(((d_) + (e_.)*(x_))*Sqrt[(a_) + (c_.)*(x_)^2]), x_Symbol] :> -Subst[Int[1/(c*d^2 + a*e^2 - x^2), x], x,
(a*e - c*d*x)/Sqrt[a + c*x^2]] /; FreeQ[{a, c, d, e}, x]

Rule 899

Int[((d_) + (e_.)*(x_))^(m_)*((f_) + (g_.)*(x_))^(n_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :>
Int[(d*f + e*g*x^2)^m*(a + b*x + c*x^2)^p, x] /; FreeQ[{a, b, c, d, e, f, g, m, n, p}, x] && EqQ[m - n, 0] &&
EqQ[e*f + d*g, 0] && (IntegerQ[m] || (GtQ[d, 0] && GtQ[f, 0]))

Rule 985

Int[1/(((a_) + (b_.)*(x_) + (c_.)*(x_)^2)*Sqrt[(d_) + (f_.)*(x_)^2]), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2
]}, Dist[(2*c)/q, Int[1/((b - q + 2*c*x)*Sqrt[d + f*x^2]), x], x] - Dist[(2*c)/q, Int[1/((b + q + 2*c*x)*Sqrt[
d + f*x^2]), x], x]] /; FreeQ[{a, b, c, d, f}, x] && NeQ[b^2 - 4*a*c, 0] && PosQ[b^2 - 4*a*c]

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {1-d x} \sqrt {1+d x} \left (a+b x+c x^2\right )} \, dx &=\int \frac {1}{\left (a+b x+c x^2\right ) \sqrt {1-d^2 x^2}} \, dx\\ &=\frac {(2 c) \int \frac {1}{\left (b-\sqrt {b^2-4 a c}+2 c x\right ) \sqrt {1-d^2 x^2}} \, dx}{\sqrt {b^2-4 a c}}-\frac {(2 c) \int \frac {1}{\left (b+\sqrt {b^2-4 a c}+2 c x\right ) \sqrt {1-d^2 x^2}} \, dx}{\sqrt {b^2-4 a c}}\\ &=-\frac {(2 c) \operatorname {Subst}\left (\int \frac {1}{4 c^2-\left (b-\sqrt {b^2-4 a c}\right )^2 d^2-x^2} \, dx,x,\frac {2 c+\left (b-\sqrt {b^2-4 a c}\right ) d^2 x}{\sqrt {1-d^2 x^2}}\right )}{\sqrt {b^2-4 a c}}+\frac {(2 c) \operatorname {Subst}\left (\int \frac {1}{4 c^2-\left (b+\sqrt {b^2-4 a c}\right )^2 d^2-x^2} \, dx,x,\frac {2 c+\left (b+\sqrt {b^2-4 a c}\right ) d^2 x}{\sqrt {1-d^2 x^2}}\right )}{\sqrt {b^2-4 a c}}\\ &=-\frac {\sqrt {2} c \tanh ^{-1}\left (\frac {2 c+\left (b-\sqrt {b^2-4 a c}\right ) d^2 x}{\sqrt {2} \sqrt {2 c^2+2 a c d^2-b \left (b-\sqrt {b^2-4 a c}\right ) d^2} \sqrt {1-d^2 x^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c^2+2 a c d^2-b \left (b-\sqrt {b^2-4 a c}\right ) d^2}}+\frac {\sqrt {2} c \tanh ^{-1}\left (\frac {2 c+\left (b+\sqrt {b^2-4 a c}\right ) d^2 x}{\sqrt {2} \sqrt {2 c^2+2 a c d^2-b \left (b+\sqrt {b^2-4 a c}\right ) d^2} \sqrt {1-d^2 x^2}}\right )}{\sqrt {b^2-4 a c} \sqrt {2 c^2+2 a c d^2-b \left (b+\sqrt {b^2-4 a c}\right ) d^2}}\\ \end {align*}

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Mathematica [A]  time = 0.56, size = 260, normalized size = 0.92 \[ \frac {2 \sqrt {2} c \left (\frac {\tanh ^{-1}\left (\frac {d^2 x \left (\sqrt {b^2-4 a c}+b\right )+2 c}{\sqrt {1-d^2 x^2} \sqrt {-2 b d^2 \left (\sqrt {b^2-4 a c}+b\right )+4 a c d^2+4 c^2}}\right )}{2 \sqrt {-b d^2 \left (\sqrt {b^2-4 a c}+b\right )+2 a c d^2+2 c^2}}-\frac {\tanh ^{-1}\left (\frac {d^2 x \left (b-\sqrt {b^2-4 a c}\right )+2 c}{\sqrt {1-d^2 x^2} \sqrt {2 b d^2 \left (\sqrt {b^2-4 a c}-b\right )+4 a c d^2+4 c^2}}\right )}{2 \sqrt {b d^2 \left (\sqrt {b^2-4 a c}-b\right )+2 a c d^2+2 c^2}}\right )}{\sqrt {b^2-4 a c}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [B]  time = 1.20, size = 4313, normalized size = 15.29 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c
+ 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4
- 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))
)/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt
(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 + 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4
*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^
2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 +
8*a^2*c^4)*d^2))*x + sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*
b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a
^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c
^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2
*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2
*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4
*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4
+ b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x) - 1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 -
((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*
a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2
- 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3
- (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c
*d^2 + 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^
4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c
+ 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - sqrt(2)*(((a^3*b^3 - 4*a^
4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^
3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5
+ (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + ((a*b^
3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 - ((a^2*b^2 - 4*a^3*c)*d^4 +
b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6
*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4
*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2
*c^2)*d^2)))/x) - 1/2*sqrt(2)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3
- (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*
c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3
+ 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*
sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2*c*d^2*x - 4*a*b*c*d^2 - 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a
^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^
3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^
2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x + sqrt(2)*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*
a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8
- 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c
^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*
x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*
c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^
5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b
^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)))/x) + 1/2*sqrt(2)*sqrt(-((b^2 - 2*
a*c)*d^2 - 2*c^2 + ((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*
d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*
c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 +
b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2))*log((4*sqrt(d*x + 1)*sqrt(-d*x + 1)*a*b*c*d^2 - 2*b^2
*c*d^2*x - 4*a*b*c*d^2 - 2*(b^2*c^3 - 4*a*c^4 + (a^2*b^2*c - 4*a^3*c^2)*d^4 - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3
)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 +
(b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2))*x - sqrt(2)
*(((a^3*b^3 - 4*a^4*b*c)*d^6 - b^3*c^3 + 4*a*b*c^4 - (a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^4 + (b^5*c - 5*a*b^
3*c^2 + 4*a^2*b*c^3)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 +
b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4
)*d^2))*x - ((a*b^3 - 4*a^2*b*c)*d^4 + (b^3*c - 4*a*b*c^2)*d^2)*x)*sqrt(-((b^2 - 2*a*c)*d^2 - 2*c^2 + ((a^2*b^
2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d^2)*sqrt(b^2*d^4/((a^4*b^2 - 4*a^5*c)*d^
8 - 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d^6 + b^2*c^4 - 4*a*c^5 + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3
*c^3)*d^4 - 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2)))/((a^2*b^2 - 4*a^3*c)*d^4 + b^2*c^2 - 4*a*c^3 - (b^4 -
6*a*b^2*c + 8*a^2*c^2)*d^2)))/x)

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giac [B]  time = 1.50, size = 684, normalized size = 2.43 \[ -\frac {{\left (a d^{2} - b d + c\right )} {\left (\frac {{\left (a d^{2} - c + \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}\right )} d}{a d^{2} - b d + c} - d\right )} \sqrt {\frac {a d^{2} - c + \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}}{a d^{2} - b d + c}} \arctan \left (-\frac {\frac {\sqrt {2} - \sqrt {-d x + 1}}{\sqrt {d x + 1}} - \frac {\sqrt {d x + 1}}{\sqrt {2} - \sqrt {-d x + 1}}}{2 \, \sqrt {\frac {a d^{2} - c + \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}}{a d^{2} - b d + c}}}\right )}{{\left (a d^{2} - c + \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}\right )} \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}} + \frac {{\left (a d^{2} - b d + c\right )} {\left (\frac {{\left (a d^{2} - c - \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}\right )} d}{a d^{2} - b d + c} - d\right )} \sqrt {\frac {a d^{2} - c - \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}}{a d^{2} - b d + c}} \arctan \left (-\frac {\frac {\sqrt {2} - \sqrt {-d x + 1}}{\sqrt {d x + 1}} - \frac {\sqrt {d x + 1}}{\sqrt {2} - \sqrt {-d x + 1}}}{2 \, \sqrt {\frac {a d^{2} - c - \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}}{a d^{2} - b d + c}}}\right )}{{\left (a d^{2} - c - \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}\right )} \sqrt {-{\left (a d^{2} + b d + c\right )} {\left (a d^{2} - b d + c\right )} + {\left (a d^{2} - c\right )}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(a*d^2 - b*d + c)*((a*d^2 - c + sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))*d/(a*d^2 - b*d +
c) - d)*sqrt((a*d^2 - c + sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))/(a*d^2 - b*d + c))*arcta
n(-1/2*((sqrt(2) - sqrt(-d*x + 1))/sqrt(d*x + 1) - sqrt(d*x + 1)/(sqrt(2) - sqrt(-d*x + 1)))/sqrt((a*d^2 - c +
sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))/(a*d^2 - b*d + c)))/((a*d^2 - c + sqrt(-(a*d^2 +
b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))*sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2)) + (a*
d^2 - b*d + c)*((a*d^2 - c - sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))*d/(a*d^2 - b*d + c) -
d)*sqrt((a*d^2 - c - sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))/(a*d^2 - b*d + c))*arctan(-1
/2*((sqrt(2) - sqrt(-d*x + 1))/sqrt(d*x + 1) - sqrt(d*x + 1)/(sqrt(2) - sqrt(-d*x + 1)))/sqrt((a*d^2 - c - sqr
t(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))/(a*d^2 - b*d + c)))/((a*d^2 - c - sqrt(-(a*d^2 + b*d
+ c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))*sqrt(-(a*d^2 + b*d + c)*(a*d^2 - b*d + c) + (a*d^2 - c)^2))

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maple [C]  time = 0.14, size = 1759, normalized size = 6.24 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-32*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*csgn(d)^2*c^2*(ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b
*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*
c+b^2)^(1/2)+b))*a^2*d^4*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2
)^(1/2)-ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^
2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*a^2*d^4*(-(b*(-4*a*c+b^2
)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+2*ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/
2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2
/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))*a*c*d^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a
*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c
+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(
1/2)+b))*b^2*d^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-
2*ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-
4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*a*c*d^2*(-(b*(-4*a*c+b^2)^(1/2
)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2
+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/
2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*b^2*d^2*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^
(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1
/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))
*c^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-ln(2*((-4*a*
c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/
2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*c^2*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a
^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2))/(-d^2*x^2+1)^(1/2)/(b*d-d*(-4*a*c+b^2)^(1/2)+2*c)/(d*(-
4*a*c+b^2)^(1/2)+b*d+2*c)/(b*d-d*(-4*a*c+b^2)^(1/2)-2*c)/(-4*a*c+b^2)^(1/2)/(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)
*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)/(d*(-4*a*c+b^2)^(1/2)+b*d-2*c)/(-(b*(-4*a*c+b^2)^(
1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (c x^{2} + b x + a\right )} \sqrt {d x + 1} \sqrt {-d x + 1}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/((c*x^2 + b*x + a)*sqrt(d*x + 1)*sqrt(-d*x + 1)), x)

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mupad [B]  time = 82.37, size = 33018, normalized size = 117.09 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- atan(((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*
(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^
4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^
(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3
*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2
*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^
6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 1
0*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*
a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4
- 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(
4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*
b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-
(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^
4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2
*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*
d^14 + 1073741824*a^5*b^6*d^16 - 36283883716608*a^3*c^8*d^6 + 36283883716608*a^4*c^7*d^8 + 210900074102784*a^5
*c^6*d^10 + 167812962189312*a^6*c^5*d^12 + 29480655519744*a^7*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 7602092
11392*a*b^6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 -
8589934592*a^6*b^4*c*d^16 + 18141941858304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^
3*b^2*c^6*d^8 - 21930103013376*a^2*b^6*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c
^5*d^10 - 4173634469888*a^3*b^6*c^2*d^12 + 39994735460352*a^4*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12
+ 2478196129792*a^5*b^4*c^2*d^14 - 16080357556224*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)
^(1/2) - 1)^2 + 1073741824*a*b^10*d^12 + (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*
a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 2
10453397504*a^3*b^7*c*d^13 + 32985348833280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c
^3*d^15 + 10720238370816*a^2*b^3*c^6*d^7 - 10136122818560*a^2*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 3
646427234304*a^2*b^7*c^2*d^11 + 23768349016064*a^3*b^5*c^3*d^11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482
112*a^4*b^5*c^2*d^13 - 19859928776704*a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*
d^11))/((d*x + 1)^(1/2) - 1) - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 -
4947802324992*a^4*c^7*d^8 - 1580547964928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4
*d^14 + 68719476736*a*b^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*
b^8*c*d^12 - 15032385536*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290
624*a^2*b^4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*
d^10 + 5738076307456*a^4*b^2*c^5*d^10 - 1081258016768*a^3*b^6*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 2149
2016349184*a^5*b^2*c^4*d^12 + 949187772416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7
*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1)^2*(1778116460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*d^8 - 176737
9042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 + 29618094473216*a^5*b*c^4
*d^12 + 47244640256*a^4*b^5*c*d^14 + 755914244096*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8 + 1772103506
3296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 15564961480704*a^4*
b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(3023656976384
0*a^3*c^7*d^7 + 57449482551296*a^4*c^6*d^9 + 24189255811072*a^5*c^5*d^11 - 3023656976384*a^6*c^4*d^13 + 188978
5610240*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6
*d^7 + 17815524343808*a^2*b^4*c^4*d^9 - 57174604644352*a^3*b^2*c^5*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 4260
607557632*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b^2*c^4*d^11 - 1219770712064*a^4*b^4*c^2*d^13 + 3573412790272*a
^5*b^2*c^3*d^13 - 128849018880*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1) + 77309411328*a*b^5*c^4*d^8 + 123695058124
8*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 254
2620639232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^
5*d^8 + 910533066752*a^2*b^5*c^3*d^10 - 3058016714752*a^3*b^3*c^4*d^10 + 399431958528*a^3*b^5*c^2*d^12 - 17523
46656768*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3*c^2*d^14) - 2147483648*a*b^8*d^12 + (((1 - d*x)^(1/2) - 1)*(2
680059592704*a*b^3*c^5*d^7 - 10720238370816*a^2*b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c
^5*d^9 + 17248588660736*a^4*b*c^4*d^11 + 64424509440*a^3*b^5*c*d^13 + 687194767360*a^5*b*c^3*d^13 + 2405181685
760*a^2*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*
c^2*d^13 - 188978561024*a*b^7*c*d^11))/((d*x + 1)^(1/2) - 1) + (((1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^
14 - 2147483648*a*b^8*d^12 - 18141941858304*a^2*c^7*d^6 + 44598940401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*
d^10 + 23055384444928*a^5*c^4*d^12 + 4535485464576*a*b^2*c^6*d^6 + 1267015352320*a*b^4*c^4*d^8 - 2045478174720
*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 2
1371757264896*a^2*b^4*c^3*d^10 - 74208444940288*a^3*b^2*c^4*d^10 + 2832530931712*a^3*b^4*c^2*d^12 - 1585701925
6832*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 + 2147483648*a^3*b^6*d^14 + 549
755813888*a^2*c^7*d^6 - 755914244096*a^3*c^6*d^8 + 6768868458496*a^4*c^5*d^10 + 8074538516480*a^5*c^4*d^12 - 1
37438953472*a*b^2*c^6*d^6 + 304942678016*a*b^4*c^4*d^8 - 164282499072*a*b^6*c^2*d^10 - 17179869184*a^2*b^6*c*d
^12 - 15032385536*a^4*b^4*c*d^14 - 1030792151040*a^2*b^2*c^5*d^8 + 1133871366144*a^2*b^4*c^3*d^10 - 3599182594
048*a^3*b^2*c^4*d^10 + 1028644667392*a^3*b^4*c^2*d^12 - 5720896438272*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c
^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(13950053777408*a^2*b*c^5*d^8 - 3487513444352*a*b^3*c^4*d^8 + 173087182028
8*a*b^5*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 -
10479720202240*a^2*b^3*c^3*d^10 - 279172874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2)
- 1)*(15118284881920*a^2*c^6*d^7 + 13606456393728*a^3*c^5*d^9 - 1511828488192*a^4*c^4*d^11 - 3779571220480*a*b
^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 209
5944040448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 +
893353197568*a^2*b*c^5*d^8 + 124554051584*a*b^5*c^2*d^10 + 1236950581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5
*c*d^12 + 257698037760*a^4*b*c^3*d^12 - 807453851648*a^2*b^3*c^3*d^10 - 184683593728*a^3*b^3*c^2*d^12) + 10737
41824*a*b^6*d^12 + 68719476736*a*c^6*d^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382993920*
a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7 - 2147
4836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 687194767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 + (((1 -
d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 600006931251
2*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 31525
05995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*c^4*d^8
+ 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^
2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)^2*(2147483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10 + 1709396983808
*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^
4*d^9 + 146028888064*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3
*d^10 + 146028888064*a*b*c^4*d^8)*1i + (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a
^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 +
16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(214
7483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 - (-
(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^
4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2
*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*(1073741824*a*b^6*d^12 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*
a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^
4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8
*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4
+ b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b
^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^
2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 1
6*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1778
116460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c
^5*d^10 - 47244640256*a^2*b^7*c*d^12 + 29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 7559142440
96*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*
c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 15564961480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/
((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 -
6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^
4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^1
0*d^12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 - 36283883716608*a^3*c^8*d^6 + 36283883716608*a^4*c
^7*d^8 + 210900074102784*a^5*c^6*d^10 + 167812962189312*a^6*c^5*d^12 + 29480655519744*a^7*c^4*d^14 - 226774273
2288*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 -
66571993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 + 18141941858304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^
4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 21930103013376*a^2*b^6*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10
- 263779711451136*a^4*b^2*c^5*d^10 - 4173634469888*a^3*b^6*c^2*d^12 + 39994735460352*a^4*b^4*c^3*d^12 - 14023
9272148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4*c^2*d^14 - 16080357556224*a^6*b^2*c^3*d^14 + 17179869184*a
^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741824*a*b^10*d^12 + (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b
^7*c^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 42193
758715904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d^13 + 32985348833280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c
*d^15 + 687194767360*a^7*b*c^3*d^15 + 10720238370816*a^2*b^3*c^6*d^7 - 10136122818560*a^2*b^5*c^4*d^9 + 246015
72671488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^2*d^11 + 23768349016064*a^3*b^5*c^3*d^11 - 57999238365184*a
^4*b^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 - 19859928776704*a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*
d^15 + 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2) - 1) - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 +
1099511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*d^8 - 1580547964928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d
^12 + 11613591568384*a^7*c^4*d^14 + 68719476736*a*b^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8
*c^2*d^10 + 23622320128*a^2*b^8*c*d^12 - 15032385536*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 - 549755813888
*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10
- 1799591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^4*b^2*c^5*d^10 - 1081258016768*a^3*b^6*c^2*d^12 + 824633720
8320*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*d^12 + 949187772416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^
2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 574494825512
96*a^4*c^6*d^9 + 24189255811072*a^5*c^5*d^11 - 3023656976384*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778
116460544*a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^
4*c^4*d^9 - 57174604644352*a^3*b^2*c^5*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 -
4672924418048*a^4*b^2*c^4*d^11 - 1219770712064*a^4*b^4*c^2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 1288490188
80*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1) + 77309411328*a*b^5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 8804682956
8*a*b^7*c^2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 +
30064771072*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5
*c^3*d^10 - 3058016714752*a^3*b^3*c^4*d^10 + 399431958528*a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 -
240518168576*a^5*b^3*c^2*d^14) + 2147483648*a*b^8*d^12 - (((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 -
10720238370816*a^2*b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*
b*c^4*d^11 + 64424509440*a^3*b^5*c*d^13 + 687194767360*a^5*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 322122
5472000*a^2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^
7*c*d^11))/((d*x + 1)^(1/2) - 1) - (((1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 -
18141941858304*a^2*c^7*d^6 + 44598940401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^
4*d^12 + 4535485464576*a*b^2*c^6*d^6 + 1267015352320*a*b^4*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 6871947673
6*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^
10 - 74208444940288*a^3*b^2*c^4*d^10 + 2832530931712*a^3*b^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 2576
9803776*a^5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 - 2147483648*a^3*b^6*d^14 - 549755813888*a^2*c^7*d^6 + 7559
14244096*a^3*c^6*d^8 - 6768868458496*a^4*c^5*d^10 - 8074538516480*a^5*c^4*d^12 + 137438953472*a*b^2*c^6*d^6 -
304942678016*a*b^4*c^4*d^8 + 164282499072*a*b^6*c^2*d^10 + 17179869184*a^2*b^6*c*d^12 + 15032385536*a^4*b^4*c*
d^14 + 1030792151040*a^2*b^2*c^5*d^8 - 1133871366144*a^2*b^4*c^3*d^10 + 3599182594048*a^3*b^2*c^4*d^10 - 10286
44667392*a^3*b^4*c^2*d^12 + 5720896438272*a^4*b^2*c^3*d^12 - 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2)
- 1)^2*(13950053777408*a^2*b*c^5*d^8 - 3487513444352*a*b^3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 142249316
84352*a^3*b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d
^10 - 279172874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6
*d^7 + 13606456393728*a^3*c^5*d^9 - 1511828488192*a^4*c^4*d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a
*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11
+ 128849018880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8
+ 124554051584*a*b^5*c^2*d^10 + 1236950581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b
*c^3*d^12 - 807453851648*a^2*b^3*c^3*d^10 - 184683593728*a^3*b^3*c^2*d^12) + 68719476736*a*c^6*d^6 - (((1 - d*
x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 124554
051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 68719
4767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 226774273
2288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 50573
2399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d
^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*
c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)*(1889785610240*
a*c^5*d^7 - 188978561024*a^2*c^4*d^9 + 146028888064*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c
^2*d^10 + 34359738368*a^2*b*c^3*d^10 + 146028888064*a*b*c^4*d^8)*1i)/((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2
*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 +
a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)
*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^
2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32
*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2)
+ 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d
^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 +
b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2
- 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^
4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*
c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^
3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c
- b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^
4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d
*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 - 36283883716608*
a^3*c^8*d^6 + 36283883716608*a^4*c^7*d^8 + 210900074102784*a^5*c^6*d^10 + 167812962189312*a^6*c^5*d^12 + 29480
655519744*a^7*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^
10 + 75161927680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 + 18141941858304*a^2*
b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 21930103013376*a^2*b^6*c^3*d^10
+ 116415088558080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c^5*d^10 - 4173634469888*a^3*b^6*c^2*d^12 + 39994
735460352*a^4*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4*c^2*d^14 - 1608035755622
4*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741824*a*b^10*d^12 + (((1 -
d*x)^(1/2) - 1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^5*d^7 - 11
544872091648*a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d^13 + 32985348833280*a^6*
b*c^4*d^13 + 42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c^3*d^15 + 10720238370816*a^2*b^3*c^6*d^7 - 10136
122818560*a^2*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^2*d^11 + 23768349016064*a
^3*b^5*c^3*d^11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 - 19859928776704*a^5*b^3*c^
3*d^13 - 343597383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2) - 1) - 2147483648*a^3*b^
8*d^14 + 1073741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*d^8 - 1580547964928*a^5*c
^6*d^10 + 16080357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4*d^14 + 68719476736*a*b^4*c^6*d^6 - 115964116992
*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*b^8*c*d^12 - 15032385536*a^4*b^6*c*d^14 - 858993
4592*a^6*b^4*c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d
^8 - 77309411328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^4*b^2*c^5*d^10 - 10812580
16768*a^3*b^6*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*d^12 + 949187772416*a^5*b
^4*c^2*d^14 - 6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1)^2*(17781
16460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c^
5*d^10 - 47244640256*a^2*b^7*c*d^12 + 29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 75591424409
6*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*c
^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 15564961480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/(
(d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 57449482551296*a^4*c^6*d^9 + 241
89255811072*a^5*c^5*d^11 - 3023656976384*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*
d^9 + 128849018880*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^4*c^4*d^9 - 57174604
644352*a^3*b^2*c^5*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b
^2*c^4*d^11 - 1219770712064*a^4*b^4*c^2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 128849018880*a*b^8*c*d^11))/((
d*x + 1)^(1/2) - 1) + 77309411328*a*b^5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3
298534883328*a^4*b*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*
c*d^14 + 481036337152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5*c^3*d^10 - 30580167
14752*a^3*b^3*c^4*d^10 + 399431958528*a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3
*c^2*d^14) - 2147483648*a*b^8*d^12 + (((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 - 10720238370816*a^2*
b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*b*c^4*d^11 + 6442450
9440*a^3*b^5*c*d^13 + 687194767360*a^5*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*
d^11 - 14173392076800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^7*c*d^11))/((d*x + 1
)^(1/2) - 1) + (((1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 - 18141941858304*a^2*
c^7*d^6 + 44598940401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^4*d^12 + 45354854645
76*a*b^2*c^6*d^6 + 1267015352320*a*b^4*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 1
5032385536*a^4*b^4*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^10 - 74208444940288*
a^3*b^2*c^4*d^10 + 2832530931712*a^3*b^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*
d^14))/((d*x + 1)^(1/2) - 1)^2 + 2147483648*a^3*b^6*d^14 + 549755813888*a^2*c^7*d^6 - 755914244096*a^3*c^6*d^8
+ 6768868458496*a^4*c^5*d^10 + 8074538516480*a^5*c^4*d^12 - 137438953472*a*b^2*c^6*d^6 + 304942678016*a*b^4*c
^4*d^8 - 164282499072*a*b^6*c^2*d^10 - 17179869184*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 1030792151040
*a^2*b^2*c^5*d^8 + 1133871366144*a^2*b^4*c^3*d^10 - 3599182594048*a^3*b^2*c^4*d^10 + 1028644667392*a^3*b^4*c^2
*d^12 - 5720896438272*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(13950053777
408*a^2*b*c^5*d^8 - 3487513444352*a*b^3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10
+ 47244640256*a^2*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d^10 - 279172874240*a
^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6*d^7 + 1360645639372
8*a^3*c^5*d^9 - 1511828488192*a^4*c^4*d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d^9 - 99299
64388352*a^2*b^2*c^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6
*c*d^11))/((d*x + 1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8 + 124554051584*a*b^5
*c^2*d^10 + 1236950581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b*c^3*d^12 - 80745385
1648*a^2*b^3*c^3*d^10 - 184683593728*a^3*b^3*c^2*d^12) + 1073741824*a*b^6*d^12 + 68719476736*a*c^6*d^6 - (((1
- d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 12
4554051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 6
87194767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 22677
42732288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 5
05732399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c
^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*
b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)^2*(21474836
48*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 + (((1 -
d*x)^(1/2) - 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^4*d^9 + 146028888064*a*b^2*c^3*d^9))/((d*x + 1)^
(1/2) - 1) - 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3*d^10 + 146028888064*a*b*c^4*d^8) - (-(8*a*c^3 -
2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^
2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d
^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(2147483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10
+ 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b
^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 +
32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*(1073741824*
a*b^6*d^12 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2
)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2
*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2
)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 3
2*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 -
2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2
- b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^
2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1778116460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*
d^8 - 1767379042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 + 296180944732
16*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 755914244096*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8
+ 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 1556496
1480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 +
b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 -
8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4
*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b
^6*d^16 - 36283883716608*a^3*c^8*d^6 + 36283883716608*a^4*c^7*d^8 + 210900074102784*a^5*c^6*d^10 + 16781296218
9312*a^6*c^5*d^12 + 29480655519744*a^7*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1
504312295424*a*b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d
^16 + 18141941858304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 2193010
3013376*a^2*b^6*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c^5*d^10 - 4173634469888
*a^3*b^6*c^2*d^12 + 39994735460352*a^4*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4
*c^2*d^14 - 16080357556224*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741
824*a*b^10*d^12 + (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029
796352*a*b^5*c^5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d
^13 + 32985348833280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c^3*d^15 + 1072023837081
6*a^2*b^3*c^6*d^7 - 10136122818560*a^2*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^
2*d^11 + 23768349016064*a^3*b^5*c^3*d^11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 -
19859928776704*a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2)
- 1) - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*
d^8 - 1580547964928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4*d^14 + 68719476736*a*b
^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*b^8*c*d^12 - 1503238553
6*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 6
18475290624*a^3*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^
4*b^2*c^5*d^10 - 1081258016768*a^3*b^6*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*
d^12 + 949187772416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 -
d*x)^(1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 57449482551296*a^4*c^6*d^9 + 24189255811072*a^5*c^5*d^11 - 3023
656976384*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^
13 - 15118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^4*c^4*d^9 - 57174604644352*a^3*b^2*c^5*d^9 + 149464
8619008*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b^2*c^4*d^11 - 1219770712064*a^4
*b^4*c^2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 128849018880*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1) + 773094113
28*a*b^5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 3
0064771072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3
*d^14 - 618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5*c^3*d^10 - 3058016714752*a^3*b^3*c^4*d^10 + 399431
958528*a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3*c^2*d^14) + 2147483648*a*b^8*d
^12 - (((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 - 10720238370816*a^2*b*c^6*d^7 - 962072674304*a*b^5*
c^3*d^9 + 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*b*c^4*d^11 + 64424509440*a^3*b^5*c*d^13 + 687194767
360*a^5*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c
^3*d^11 - 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^7*c*d^11))/((d*x + 1)^(1/2) - 1) - (((1 - d*x)^(1/2
) - 1)^2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 - 18141941858304*a^2*c^7*d^6 + 44598940401664*a^3*c^
6*d^8 + 85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^4*d^12 + 4535485464576*a*b^2*c^6*d^6 + 126701535232
0*a*b^4*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 162
17796509696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^10 - 74208444940288*a^3*b^2*c^4*d^10 + 283253093171
2*a^3*b^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2
- 2147483648*a^3*b^6*d^14 - 549755813888*a^2*c^7*d^6 + 755914244096*a^3*c^6*d^8 - 6768868458496*a^4*c^5*d^10 -
8074538516480*a^5*c^4*d^12 + 137438953472*a*b^2*c^6*d^6 - 304942678016*a*b^4*c^4*d^8 + 164282499072*a*b^6*c^2
*d^10 + 17179869184*a^2*b^6*c*d^12 + 15032385536*a^4*b^4*c*d^14 + 1030792151040*a^2*b^2*c^5*d^8 - 113387136614
4*a^2*b^4*c^3*d^10 + 3599182594048*a^3*b^2*c^4*d^10 - 1028644667392*a^3*b^4*c^2*d^12 + 5720896438272*a^4*b^2*c
^3*d^12 - 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(13950053777408*a^2*b*c^5*d^8 - 34875134443
52*a*b^3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 +
360777252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d^10 - 279172874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1
/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6*d^7 + 13606456393728*a^3*c^5*d^9 - 1511828488192*a
^4*c^4*d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c^4*d^9 - 9448
92805120*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1)
- 223338299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8 + 124554051584*a*b^5*c^2*d^10 + 1236950581248*a^3*b
*c^4*d^10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b*c^3*d^12 - 807453851648*a^2*b^3*c^3*d^10 - 1846835
93728*a^3*b^3*c^2*d^12) + 68719476736*a*c^6*d^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382
993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7
- 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 687194767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 +
(((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 60000
69312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12
- 3152505995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*
c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416
*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^4*d^9 + 146028888064
*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3*d^10 + 146028888064
*a*b*c^4*d^8) + 283467841536*a*c^4*d^8 + (2*((1 - d*x)^(1/2) - 1)^2*(519691042816*a*c^4*d^8 + 1073741824*a*b^2
*c^2*d^10))/((d*x + 1)^(1/2) - 1)^2 + 2147483648*a*b^2*c^2*d^10 + (34359738368*a*b*c^3*d^9*((1 - d*x)^(1/2) -
1))/((d*x + 1)^(1/2) - 1)))*(-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 + b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2
- 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*
d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*2i - atan(((-(8*a*c^3 - 2*b^2*c^2 + b^4*d
^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*
b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^
2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)
/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*
c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)
^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32
*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2
*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2
- b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2
+ 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2
- 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*
d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2
*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 +
a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)
*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 - 36283
883716608*a^3*c^8*d^6 + 36283883716608*a^4*c^7*d^8 + 210900074102784*a^5*c^6*d^10 + 167812962189312*a^6*c^5*d^
12 + 29480655519744*a^7*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1504312295424*a*
b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 + 181419418
58304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 21930103013376*a^2*b^6
*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c^5*d^10 - 4173634469888*a^3*b^6*c^2*d^
12 + 39994735460352*a^4*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4*c^2*d^14 - 160
80357556224*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741824*a*b^10*d^12
+ (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^
5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d^13 + 329853488
33280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c^3*d^15 + 10720238370816*a^2*b^3*c^6*d
^7 - 10136122818560*a^2*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^2*d^11 + 237683
49016064*a^3*b^5*c^3*d^11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 - 19859928776704*
a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2) - 1) - 2147483
648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*d^8 - 158054796
4928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4*d^14 + 68719476736*a*b^4*c^6*d^6 - 11
5964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*b^8*c*d^12 - 15032385536*a^4*b^6*c*d^1
4 - 8589934592*a^6*b^4*c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 618475290624*a^3
*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^4*b^2*c^5*d^10
- 1081258016768*a^3*b^6*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*d^12 + 94918777
2416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1
)^2*(1778116460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 5731204359782
4*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 + 29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 7
55914244096*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776
*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 15564961480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^
2*d^14))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 57449482551296*a^4*c^6
*d^9 + 24189255811072*a^5*c^5*d^11 - 3023656976384*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778116460544*
a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^4*c^4*d^9
- 57174604644352*a^3*b^2*c^5*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 - 467292441
8048*a^4*b^2*c^4*d^11 - 1219770712064*a^4*b^4*c^2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 128849018880*a*b^8*c
*d^11))/((d*x + 1)^(1/2) - 1) + 77309411328*a*b^5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^
2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 + 3006477107
2*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5*c^3*d^10
- 3058016714752*a^3*b^3*c^4*d^10 + 399431958528*a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 - 2405181685
76*a^5*b^3*c^2*d^14) - 2147483648*a*b^8*d^12 + (((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 - 107202383
70816*a^2*b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*b*c^4*d^11
+ 64424509440*a^3*b^5*c*d^13 + 687194767360*a^5*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 3221225472000*a^
2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^7*c*d^11))
/((d*x + 1)^(1/2) - 1) + (((1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 - 181419418
58304*a^2*c^7*d^6 + 44598940401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^4*d^12 + 4
535485464576*a*b^2*c^6*d^6 + 1267015352320*a*b^4*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*
c*d^12 - 15032385536*a^4*b^4*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^10 - 74208
444940288*a^3*b^2*c^4*d^10 + 2832530931712*a^3*b^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 25769803776*a^
5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 + 2147483648*a^3*b^6*d^14 + 549755813888*a^2*c^7*d^6 - 755914244096*a
^3*c^6*d^8 + 6768868458496*a^4*c^5*d^10 + 8074538516480*a^5*c^4*d^12 - 137438953472*a*b^2*c^6*d^6 + 3049426780
16*a*b^4*c^4*d^8 - 164282499072*a*b^6*c^2*d^10 - 17179869184*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 103
0792151040*a^2*b^2*c^5*d^8 + 1133871366144*a^2*b^4*c^3*d^10 - 3599182594048*a^3*b^2*c^4*d^10 + 1028644667392*a
^3*b^4*c^2*d^12 - 5720896438272*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(1
3950053777408*a^2*b*c^5*d^8 - 3487513444352*a*b^3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 14224931684352*a^3*
b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d^10 - 2791
72874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6*d^7 + 136
06456393728*a^3*c^5*d^9 - 1511828488192*a^4*c^4*d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d
^9 - 9929964388352*a^2*b^2*c^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11 + 12884901
8880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8 + 12455405
1584*a*b^5*c^2*d^10 + 1236950581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b*c^3*d^12
- 807453851648*a^2*b^3*c^3*d^10 - 184683593728*a^3*b^3*c^2*d^12) + 1073741824*a*b^6*d^12 + 68719476736*a*c^6*d
^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3
*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2
) - 1) + 687194767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^
12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c
^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 9663676416
*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 64424
50944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)^2
*(2147483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2
+ (((1 - d*x)^(1/2) - 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^4*d^9 + 146028888064*a*b^2*c^3*d^9))/(
(d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3*d^10 + 146028888064*a*b*c^4*d^8)*1i +
(-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2
*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*
a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(2147483648*a*b^3*c^2*d^10 + 42949672960*a
^2*b*c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2
*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 +
a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)
*(1073741824*a*b^6*d^12 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 -
6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^
4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(
-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^
2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*(
(-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*
c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a
^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1778116460544*a*b^5*c^4*d^8 + 284498633687
04*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 +
29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 755914244096*a^6*b*c^3*d^14 - 14224931684352*a^2
*b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d
^12 - 15564961480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 -
2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^
2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d
^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*d^14 + 107
3741824*a^5*b^6*d^16 - 36283883716608*a^3*c^8*d^6 + 36283883716608*a^4*c^7*d^8 + 210900074102784*a^5*c^6*d^10
+ 167812962189312*a^6*c^5*d^12 + 29480655519744*a^7*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 760209211392*a*b^
6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 - 858993459
2*a^6*b^4*c*d^16 + 18141941858304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*
d^8 - 21930103013376*a^2*b^6*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c^5*d^10 -
4173634469888*a^3*b^6*c^2*d^12 + 39994735460352*a^4*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12 + 24781961
29792*a^5*b^4*c^2*d^14 - 16080357556224*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1
)^2 + 1073741824*a*b^10*d^12 + (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*a^3*b*c^7*
d^7 - 1340029796352*a*b^5*c^5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 21045339750
4*a^3*b^7*c*d^13 + 32985348833280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c^3*d^15 +
10720238370816*a^2*b^3*c^6*d^7 - 10136122818560*a^2*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 36464272343
04*a^2*b^7*c^2*d^11 + 23768349016064*a^3*b^5*c^3*d^11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482112*a^4*b^
5*c^2*d^13 - 19859928776704*a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*d^11))/((d
*x + 1)^(1/2) - 1) - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 - 494780232
4992*a^4*c^7*d^8 - 1580547964928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4*d^14 + 68
719476736*a*b^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*b^8*c*d^12
- 15032385536*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^
4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*d^10 + 573
8076307456*a^4*b^2*c^5*d^10 - 1081258016768*a^3*b^6*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 21492016349184
*a^5*b^2*c^4*d^12 + 949187772416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d
^16) + (((1 - d*x)^(1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 57449482551296*a^4*c^6*d^9 + 24189255811072*a^5*c^
5*d^11 - 3023656976384*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*d^9 + 128849018880
*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^4*c^4*d^9 - 57174604644352*a^3*b^2*c^5
*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b^2*c^4*d^11 - 1219
770712064*a^4*b^4*c^2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 128849018880*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1
) + 77309411328*a*b^5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3298534883328*a^4*b
*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*c*d^14 + 481036337
152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5*c^3*d^10 - 3058016714752*a^3*b^3*c^4*
d^10 + 399431958528*a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3*c^2*d^14) + 21474
83648*a*b^8*d^12 - (((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 - 10720238370816*a^2*b*c^6*d^7 - 962072
674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*b*c^4*d^11 + 64424509440*a^3*b^5*c*d^1
3 + 687194767360*a^5*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*d^11 - 14173392076
800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^7*c*d^11))/((d*x + 1)^(1/2) - 1) - (((
1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 - 18141941858304*a^2*c^7*d^6 + 44598940
401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^4*d^12 + 4535485464576*a*b^2*c^6*d^6 +
1267015352320*a*b^4*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 15032385536*a^4*b^4
*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^10 - 74208444940288*a^3*b^2*c^4*d^10 +
2832530931712*a^3*b^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14))/((d*x + 1)^
(1/2) - 1)^2 - 2147483648*a^3*b^6*d^14 - 549755813888*a^2*c^7*d^6 + 755914244096*a^3*c^6*d^8 - 6768868458496*a
^4*c^5*d^10 - 8074538516480*a^5*c^4*d^12 + 137438953472*a*b^2*c^6*d^6 - 304942678016*a*b^4*c^4*d^8 + 164282499
072*a*b^6*c^2*d^10 + 17179869184*a^2*b^6*c*d^12 + 15032385536*a^4*b^4*c*d^14 + 1030792151040*a^2*b^2*c^5*d^8 -
1133871366144*a^2*b^4*c^3*d^10 + 3599182594048*a^3*b^2*c^4*d^10 - 1028644667392*a^3*b^4*c^2*d^12 + 5720896438
272*a^4*b^2*c^3*d^12 - 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(13950053777408*a^2*b*c^5*d^8
- 3487513444352*a*b^3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10 + 47244640256*a^2
*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d^10 - 279172874240*a^3*b^3*c^2*d^12))/
((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6*d^7 + 13606456393728*a^3*c^5*d^9 - 15
11828488192*a^4*c^4*d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c
^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6*c*d^11))/((d*x +
1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8 + 124554051584*a*b^5*c^2*d^10 + 123695
0581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b*c^3*d^12 - 807453851648*a^2*b^3*c^3*d
^10 - 184683593728*a^3*b^3*c^2*d^12) + 68719476736*a*c^6*d^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*
d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 134002979635
2*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 687194767360*a^2*c^5*d^8 + 1859720839168*a^
3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^2*c^
5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 6442450944*a^
2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712
481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10
+ 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^4*d^9 +
146028888064*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3*d^10 +
146028888064*a*b*c^4*d^8)*1i)/((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*
d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*
c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b
*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^
3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(
1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(1
6*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4
- 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1
/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c
^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c
^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*
d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*
a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*
b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 -
8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^10*d^
12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 - 36283883716608*a^3*c^8*d^6 + 36283883716608*a^4*c^7*d
^8 + 210900074102784*a^5*c^6*d^10 + 167812962189312*a^6*c^5*d^12 + 29480655519744*a^7*c^4*d^14 - 2267742732288
*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^10 + 75161927680*a^2*b^8*c*d^12 - 6657
1993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 + 18141941858304*a^2*b^2*c^7*d^6 - 3813930958848*a^2*b^4*c^
5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 21930103013376*a^2*b^6*c^3*d^10 + 116415088558080*a^3*b^4*c^4*d^10 - 2
63779711451136*a^4*b^2*c^5*d^10 - 4173634469888*a^3*b^6*c^2*d^12 + 39994735460352*a^4*b^4*c^3*d^12 - 140239272
148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4*c^2*d^14 - 16080357556224*a^6*b^2*c^3*d^14 + 17179869184*a^7*b
^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741824*a*b^10*d^12 + (((1 - d*x)^(1/2) - 1)*(1176821039104*a*b^7*c
^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^5*d^7 - 11544872091648*a^4*b*c^6*d^9 + 421937587
15904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d^13 + 32985348833280*a^6*b*c^4*d^13 + 42949672960*a^5*b^5*c*d^1
5 + 687194767360*a^7*b*c^3*d^15 + 10720238370816*a^2*b^3*c^6*d^7 - 10136122818560*a^2*b^5*c^4*d^9 + 2460157267
1488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^2*d^11 + 23768349016064*a^3*b^5*c^3*d^11 - 57999238365184*a^4*b
^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 - 19859928776704*a^5*b^3*c^3*d^13 - 343597383680*a^6*b^3*c^2*d^15
+ 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2) - 1) - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 + 109
9511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*d^8 - 1580547964928*a^5*c^6*d^10 + 16080357556224*a^6*c^5*d^12
+ 11613591568384*a^7*c^4*d^14 + 68719476736*a*b^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^8 + 48318382080*a*b^8*c^2
*d^10 + 23622320128*a^2*b^8*c*d^12 - 15032385536*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 - 549755813888*a^2
*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d^8 - 77309411328*a^2*b^6*c^3*d^10 - 17
99591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^4*b^2*c^5*d^10 - 1081258016768*a^3*b^6*c^2*d^12 + 8246337208320
*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*d^12 + 949187772416*a^5*b^4*c^2*d^14 - 6322191859712*a^6*b^2*c^
3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1)^2*(1778116460544*a*b^5*c^4*d^8 + 2844986336870
4*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 57312043597824*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 +
29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^5*c*d^14 + 755914244096*a^6*b*c^3*d^14 - 14224931684352*a^2*
b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56934086475776*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^
12 - 15564961480704*a^4*b^3*c^3*d^12 - 377957122048*a^5*b^3*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(
1/2) - 1)*(30236569763840*a^3*c^7*d^7 + 57449482551296*a^4*c^6*d^9 + 24189255811072*a^5*c^5*d^11 - 30236569763
84*a^6*c^4*d^13 + 1889785610240*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^13 - 15
118284881920*a^2*b^2*c^6*d^7 + 17815524343808*a^2*b^4*c^4*d^9 - 57174604644352*a^3*b^2*c^5*d^9 + 1494648619008
*a^2*b^6*c^2*d^11 - 4260607557632*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b^2*c^4*d^11 - 1219770712064*a^4*b^4*c^
2*d^13 + 3573412790272*a^5*b^2*c^3*d^13 - 128849018880*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1) + 77309411328*a*b^
5*c^4*d^8 + 1236950581248*a^3*b*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 30064771
072*a^2*b^7*c*d^12 + 2542620639232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3*d^14 -
618475290624*a^2*b^3*c^5*d^8 + 910533066752*a^2*b^5*c^3*d^10 - 3058016714752*a^3*b^3*c^4*d^10 + 399431958528*
a^3*b^5*c^2*d^12 - 1752346656768*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3*c^2*d^14) - 2147483648*a*b^8*d^12 + (
((1 - d*x)^(1/2) - 1)*(2680059592704*a*b^3*c^5*d^7 - 10720238370816*a^2*b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9
+ 5772436045824*a^3*b*c^5*d^9 + 17248588660736*a^4*b*c^4*d^11 + 64424509440*a^3*b^5*c*d^13 + 687194767360*a^5
*b*c^3*d^13 + 2405181685760*a^2*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c^3*d^11
- 429496729600*a^4*b^3*c^2*d^13 - 188978561024*a*b^7*c*d^11))/((d*x + 1)^(1/2) - 1) + (((1 - d*x)^(1/2) - 1)^
2*(2147483648*a^3*b^6*d^14 - 2147483648*a*b^8*d^12 - 18141941858304*a^2*c^7*d^6 + 44598940401664*a^3*c^6*d^8 +
85796266704896*a^4*c^5*d^10 + 23055384444928*a^5*c^4*d^12 + 4535485464576*a*b^2*c^6*d^6 + 1267015352320*a*b^4
*c^4*d^8 - 2045478174720*a*b^6*c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 1621779650
9696*a^2*b^2*c^5*d^8 + 21371757264896*a^2*b^4*c^3*d^10 - 74208444940288*a^3*b^2*c^4*d^10 + 2832530931712*a^3*b
^4*c^2*d^12 - 15857019256832*a^4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 + 21474
83648*a^3*b^6*d^14 + 549755813888*a^2*c^7*d^6 - 755914244096*a^3*c^6*d^8 + 6768868458496*a^4*c^5*d^10 + 807453
8516480*a^5*c^4*d^12 - 137438953472*a*b^2*c^6*d^6 + 304942678016*a*b^4*c^4*d^8 - 164282499072*a*b^6*c^2*d^10 -
17179869184*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 1030792151040*a^2*b^2*c^5*d^8 + 1133871366144*a^2*b
^4*c^3*d^10 - 3599182594048*a^3*b^2*c^4*d^10 + 1028644667392*a^3*b^4*c^2*d^12 - 5720896438272*a^4*b^2*c^3*d^12
+ 25769803776*a^5*b^2*c^2*d^14) + (((1 - d*x)^(1/2) - 1)^2*(13950053777408*a^2*b*c^5*d^8 - 3487513444352*a*b^
3*c^4*d^8 + 1730871820288*a*b^5*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 + 360777
252864*a^4*b*c^3*d^12 - 10479720202240*a^2*b^3*c^3*d^10 - 279172874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1
)^2 + (((1 - d*x)^(1/2) - 1)*(15118284881920*a^2*c^6*d^7 + 13606456393728*a^3*c^5*d^9 - 1511828488192*a^4*c^4*
d^11 - 3779571220480*a*b^2*c^5*d^7 + 1632087572480*a*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c^4*d^9 - 94489280512
0*a^2*b^4*c^2*d^11 + 2095944040448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1) - 2233
38299392*a*b^3*c^4*d^8 + 893353197568*a^2*b*c^5*d^8 + 124554051584*a*b^5*c^2*d^10 + 1236950581248*a^3*b*c^4*d^
10 + 30064771072*a^2*b^5*c*d^12 + 257698037760*a^4*b*c^3*d^12 - 807453851648*a^2*b^3*c^3*d^10 - 184683593728*a
^3*b^3*c^2*d^12) + 1073741824*a*b^6*d^12 + 68719476736*a*c^6*d^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*
c^3*d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^3*b*c^3*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 13400297
96352*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x + 1)^(1/2) - 1) + 687194767360*a^2*c^5*d^8 + 185972083916
8*a^3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a*b^6*d^12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^
2*c^5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*a*b^2*c^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 644245094
4*a^2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 33
0712481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*
d^10 + 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2) - 1)^2*(2147483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*
c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(1889785610240*a*c^5*d
^7 - 188978561024*a^2*c^4*d^9 + 146028888064*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1) - 2147483648*a*b^3*c^2*d^10
+ 34359738368*a^2*b*c^3*d^10 + 146028888064*a*b*c^4*d^8) - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c
- b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^
4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d
*x)^(1/2) - 1)^2*(2147483648*a*b^3*c^2*d^10 + 42949672960*a^2*b*c^3*d^10 + 1709396983808*a*b*c^4*d^8))/((d*x +
1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2
*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a
^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*(1073741824*a*b^6*d^12 - (-(8*a*c^3 - 2*b^2*c^2 +
b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 -
8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4
*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c
*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3
*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c -
b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4
+ 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*
x)^(1/2) - 1)^2*(1778116460544*a*b^5*c^4*d^8 + 28449863368704*a^3*b*c^6*d^8 - 1767379042304*a*b^7*c^2*d^10 + 5
7312043597824*a^4*b*c^5*d^10 - 47244640256*a^2*b^7*c*d^12 + 29618094473216*a^5*b*c^4*d^12 + 47244640256*a^4*b^
5*c*d^14 + 755914244096*a^6*b*c^3*d^14 - 14224931684352*a^2*b^3*c^5*d^8 + 17721035063296*a^2*b^5*c^3*d^10 - 56
934086475776*a^3*b^3*c^4*d^10 + 2229088026624*a^3*b^5*c^2*d^12 - 15564961480704*a^4*b^3*c^3*d^12 - 37795712204
8*a^5*b^3*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 - (-(8*a*c^3 - 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/
2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^
3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2*d^2 + 10*a*b^4*c*d^2)))^(1/2)*((((1 - d*x)^(1/2) - 1
)^2*(1073741824*a*b^10*d^12 - 2147483648*a^3*b^8*d^14 + 1073741824*a^5*b^6*d^16 - 36283883716608*a^3*c^8*d^6 +
36283883716608*a^4*c^7*d^8 + 210900074102784*a^5*c^6*d^10 + 167812962189312*a^6*c^5*d^12 + 29480655519744*a^7
*c^4*d^14 - 2267742732288*a*b^4*c^6*d^6 + 760209211392*a*b^6*c^4*d^8 + 1504312295424*a*b^8*c^2*d^10 + 75161927
680*a^2*b^8*c*d^12 - 66571993088*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*c*d^16 + 18141941858304*a^2*b^2*c^7*d^6 -
3813930958848*a^2*b^4*c^5*d^8 - 5978594476032*a^3*b^2*c^6*d^8 - 21930103013376*a^2*b^6*c^3*d^10 + 11641508855
8080*a^3*b^4*c^4*d^10 - 263779711451136*a^4*b^2*c^5*d^10 - 4173634469888*a^3*b^6*c^2*d^12 + 39994735460352*a^4
*b^4*c^3*d^12 - 140239272148992*a^5*b^2*c^4*d^12 + 2478196129792*a^5*b^4*c^2*d^14 - 16080357556224*a^6*b^2*c^3
*d^14 + 17179869184*a^7*b^2*c^2*d^16))/((d*x + 1)^(1/2) - 1)^2 + 1073741824*a*b^10*d^12 + (((1 - d*x)^(1/2) -
1)*(1176821039104*a*b^7*c^3*d^9 - 21440476741632*a^3*b*c^7*d^7 - 1340029796352*a*b^5*c^5*d^7 - 11544872091648*
a^4*b*c^6*d^9 + 42193758715904*a^5*b*c^5*d^11 - 210453397504*a^3*b^7*c*d^13 + 32985348833280*a^6*b*c^4*d^13 +
42949672960*a^5*b^5*c*d^15 + 687194767360*a^7*b*c^3*d^15 + 10720238370816*a^2*b^3*c^6*d^7 - 10136122818560*a^2
*b^5*c^4*d^9 + 24601572671488*a^3*b^3*c^5*d^9 - 3646427234304*a^2*b^7*c^2*d^11 + 23768349016064*a^3*b^5*c^3*d^
11 - 57999238365184*a^4*b^3*c^4*d^11 + 3745211482112*a^4*b^5*c^2*d^13 - 19859928776704*a^5*b^3*c^3*d^13 - 3435
97383680*a^6*b^3*c^2*d^15 + 167503724544*a*b^9*c*d^11))/((d*x + 1)^(1/2) - 1) - 2147483648*a^3*b^8*d^14 + 1073
741824*a^5*b^6*d^16 + 1099511627776*a^3*c^8*d^6 - 4947802324992*a^4*c^7*d^8 - 1580547964928*a^5*c^6*d^10 + 160
80357556224*a^6*c^5*d^12 + 11613591568384*a^7*c^4*d^14 + 68719476736*a*b^4*c^6*d^6 - 115964116992*a*b^6*c^4*d^
8 + 48318382080*a*b^8*c^2*d^10 + 23622320128*a^2*b^8*c*d^12 - 15032385536*a^4*b^6*c*d^14 - 8589934592*a^6*b^4*
c*d^16 - 549755813888*a^2*b^2*c^7*d^6 + 618475290624*a^2*b^4*c^5*d^8 + 618475290624*a^3*b^2*c^6*d^8 - 77309411
328*a^2*b^6*c^3*d^10 - 1799591297024*a^3*b^4*c^4*d^10 + 5738076307456*a^4*b^2*c^5*d^10 - 1081258016768*a^3*b^6
*c^2*d^12 + 8246337208320*a^4*b^4*c^3*d^12 - 21492016349184*a^5*b^2*c^4*d^12 + 949187772416*a^5*b^4*c^2*d^14 -
6322191859712*a^6*b^2*c^3*d^14 + 17179869184*a^7*b^2*c^2*d^16) + (((1 - d*x)^(1/2) - 1)*(30236569763840*a^3*c
^7*d^7 + 57449482551296*a^4*c^6*d^9 + 24189255811072*a^5*c^5*d^11 - 3023656976384*a^6*c^4*d^13 + 1889785610240
*a*b^4*c^5*d^7 - 1778116460544*a*b^6*c^3*d^9 + 128849018880*a^3*b^6*c*d^13 - 15118284881920*a^2*b^2*c^6*d^7 +
17815524343808*a^2*b^4*c^4*d^9 - 57174604644352*a^3*b^2*c^5*d^9 + 1494648619008*a^2*b^6*c^2*d^11 - 42606075576
32*a^3*b^4*c^3*d^11 - 4672924418048*a^4*b^2*c^4*d^11 - 1219770712064*a^4*b^4*c^2*d^13 + 3573412790272*a^5*b^2*
c^3*d^13 - 128849018880*a*b^8*c*d^11))/((d*x + 1)^(1/2) - 1) + 77309411328*a*b^5*c^4*d^8 + 1236950581248*a^3*b
*c^6*d^8 - 88046829568*a*b^7*c^2*d^10 + 3298534883328*a^4*b*c^5*d^10 - 30064771072*a^2*b^7*c*d^12 + 2542620639
232*a^5*b*c^4*d^12 + 30064771072*a^4*b^5*c*d^14 + 481036337152*a^6*b*c^3*d^14 - 618475290624*a^2*b^3*c^5*d^8 +
910533066752*a^2*b^5*c^3*d^10 - 3058016714752*a^3*b^3*c^4*d^10 + 399431958528*a^3*b^5*c^2*d^12 - 175234665676
8*a^4*b^3*c^3*d^12 - 240518168576*a^5*b^3*c^2*d^14) + 2147483648*a*b^8*d^12 - (((1 - d*x)^(1/2) - 1)*(26800595
92704*a*b^3*c^5*d^7 - 10720238370816*a^2*b*c^6*d^7 - 962072674304*a*b^5*c^3*d^9 + 5772436045824*a^3*b*c^5*d^9
+ 17248588660736*a^4*b*c^4*d^11 + 64424509440*a^3*b^5*c*d^13 + 687194767360*a^5*b*c^3*d^13 + 2405181685760*a^2
*b^3*c^4*d^9 + 3221225472000*a^2*b^5*c^2*d^11 - 14173392076800*a^3*b^3*c^3*d^11 - 429496729600*a^4*b^3*c^2*d^1
3 - 188978561024*a*b^7*c*d^11))/((d*x + 1)^(1/2) - 1) - (((1 - d*x)^(1/2) - 1)^2*(2147483648*a^3*b^6*d^14 - 21
47483648*a*b^8*d^12 - 18141941858304*a^2*c^7*d^6 + 44598940401664*a^3*c^6*d^8 + 85796266704896*a^4*c^5*d^10 +
23055384444928*a^5*c^4*d^12 + 4535485464576*a*b^2*c^6*d^6 + 1267015352320*a*b^4*c^4*d^8 - 2045478174720*a*b^6*
c^2*d^10 - 68719476736*a^2*b^6*c*d^12 - 15032385536*a^4*b^4*c*d^14 - 16217796509696*a^2*b^2*c^5*d^8 + 21371757
264896*a^2*b^4*c^3*d^10 - 74208444940288*a^3*b^2*c^4*d^10 + 2832530931712*a^3*b^4*c^2*d^12 - 15857019256832*a^
4*b^2*c^3*d^12 + 25769803776*a^5*b^2*c^2*d^14))/((d*x + 1)^(1/2) - 1)^2 - 2147483648*a^3*b^6*d^14 - 5497558138
88*a^2*c^7*d^6 + 755914244096*a^3*c^6*d^8 - 6768868458496*a^4*c^5*d^10 - 8074538516480*a^5*c^4*d^12 + 13743895
3472*a*b^2*c^6*d^6 - 304942678016*a*b^4*c^4*d^8 + 164282499072*a*b^6*c^2*d^10 + 17179869184*a^2*b^6*c*d^12 + 1
5032385536*a^4*b^4*c*d^14 + 1030792151040*a^2*b^2*c^5*d^8 - 1133871366144*a^2*b^4*c^3*d^10 + 3599182594048*a^3
*b^2*c^4*d^10 - 1028644667392*a^3*b^4*c^2*d^12 + 5720896438272*a^4*b^2*c^3*d^12 - 25769803776*a^5*b^2*c^2*d^14
) + (((1 - d*x)^(1/2) - 1)^2*(13950053777408*a^2*b*c^5*d^8 - 3487513444352*a*b^3*c^4*d^8 + 1730871820288*a*b^5
*c^2*d^10 + 14224931684352*a^3*b*c^4*d^10 + 47244640256*a^2*b^5*c*d^12 + 360777252864*a^4*b*c^3*d^12 - 1047972
0202240*a^2*b^3*c^3*d^10 - 279172874240*a^3*b^3*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 + (((1 - d*x)^(1/2) - 1)*(1
5118284881920*a^2*c^6*d^7 + 13606456393728*a^3*c^5*d^9 - 1511828488192*a^4*c^4*d^11 - 3779571220480*a*b^2*c^5*
d^7 + 1632087572480*a*b^4*c^3*d^9 - 9929964388352*a^2*b^2*c^4*d^9 - 944892805120*a^2*b^4*c^2*d^11 + 2095944040
448*a^3*b^2*c^3*d^11 + 128849018880*a*b^6*c*d^11))/((d*x + 1)^(1/2) - 1) - 223338299392*a*b^3*c^4*d^8 + 893353
197568*a^2*b*c^5*d^8 + 124554051584*a*b^5*c^2*d^10 + 1236950581248*a^3*b*c^4*d^10 + 30064771072*a^2*b^5*c*d^12
+ 257698037760*a^4*b*c^3*d^12 - 807453851648*a^2*b^3*c^3*d^10 - 184683593728*a^3*b^3*c^2*d^12) + 68719476736*
a*c^6*d^6 - (((1 - d*x)^(1/2) - 1)*(231928233984*a*b^3*c^3*d^9 - 2233382993920*a^2*b*c^4*d^9 - 197568495616*a^
3*b*c^3*d^11 + 124554051584*a^2*b^3*c^2*d^11 + 1340029796352*a*b*c^5*d^7 - 21474836480*a*b^5*c*d^11))/((d*x +
1)^(1/2) - 1) + 687194767360*a^2*c^5*d^8 + 1859720839168*a^3*c^4*d^10 + (((1 - d*x)^(1/2) - 1)^2*(1073741824*a
*b^6*d^12 - 2267742732288*a*c^6*d^6 + 10960756539392*a^2*c^5*d^8 + 6000069312512*a^3*c^4*d^10 - 2546915606528*
a*b^2*c^4*d^8 + 505732399104*a*b^4*c^2*d^10 - 6442450944*a^2*b^4*c*d^12 - 3152505995264*a^2*b^2*c^3*d^10 + 966
3676416*a^3*b^2*c^2*d^12))/((d*x + 1)^(1/2) - 1)^2 - 330712481792*a*b^2*c^4*d^8 + 149250113536*a*b^4*c^2*d^10
- 6442450944*a^2*b^4*c*d^12 - 919123001344*a^2*b^2*c^3*d^10 + 9663676416*a^3*b^2*c^2*d^12) + (((1 - d*x)^(1/2)
- 1)*(1889785610240*a*c^5*d^7 - 188978561024*a^2*c^4*d^9 + 146028888064*a*b^2*c^3*d^9))/((d*x + 1)^(1/2) - 1)
- 2147483648*a*b^3*c^2*d^10 + 34359738368*a^2*b*c^3*d^10 + 146028888064*a*b*c^4*d^8) + 283467841536*a*c^4*d^8
+ (2*((1 - d*x)^(1/2) - 1)^2*(519691042816*a*c^4*d^8 + 1073741824*a*b^2*c^2*d^10))/((d*x + 1)^(1/2) - 1)^2 +
2147483648*a*b^2*c^2*d^10 + (34359738368*a*b*c^3*d^9*((1 - d*x)^(1/2) - 1))/((d*x + 1)^(1/2) - 1)))*(-(8*a*c^3
- 2*b^2*c^2 + b^4*d^2 - b*d^2*(-(4*a*c - b^2)^3)^(1/2) + 8*a^2*c^2*d^2 - 6*a*b^2*c*d^2)/(2*(16*a^2*c^4 + b^4*
c^2 - b^6*d^2 - 8*a*b^2*c^3 + a^2*b^4*d^4 + 32*a^3*c^3*d^2 + 16*a^4*c^2*d^4 - 8*a^3*b^2*c*d^4 - 32*a^2*b^2*c^2
*d^2 + 10*a*b^4*c*d^2)))^(1/2)*2i

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {- d x + 1} \sqrt {d x + 1} \left (a + b x + c x^{2}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(c*x**2+b*x+a)/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)

[Out]

Integral(1/(sqrt(-d*x + 1)*sqrt(d*x + 1)*(a + b*x + c*x**2)), x)

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