3.18.10 \(\int \frac {1}{\sqrt {d+e x} (a d e+(c d^2+a e^2) x+c d e x^2)^3} \, dx\)

Optimal. Leaf size=244 \[ -\frac {63 c^{5/2} d^{5/2} e^2 \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{4 \left (c d^2-a e^2\right )^{11/2}}+\frac {63 c^2 d^2 e^2}{4 \sqrt {d+e x} \left (c d^2-a e^2\right )^5}+\frac {21 c d e^2}{4 (d+e x)^{3/2} \left (c d^2-a e^2\right )^4}+\frac {9 e}{4 (d+e x)^{5/2} \left (c d^2-a e^2\right )^2 (a e+c d x)}-\frac {1}{2 (d+e x)^{5/2} \left (c d^2-a e^2\right ) (a e+c d x)^2}+\frac {63 e^2}{20 (d+e x)^{5/2} \left (c d^2-a e^2\right )^3} \]

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Rubi [A]  time = 0.22, antiderivative size = 244, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {626, 51, 63, 208} \begin {gather*} \frac {63 c^2 d^2 e^2}{4 \sqrt {d+e x} \left (c d^2-a e^2\right )^5}-\frac {63 c^{5/2} d^{5/2} e^2 \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{4 \left (c d^2-a e^2\right )^{11/2}}+\frac {21 c d e^2}{4 (d+e x)^{3/2} \left (c d^2-a e^2\right )^4}+\frac {9 e}{4 (d+e x)^{5/2} \left (c d^2-a e^2\right )^2 (a e+c d x)}-\frac {1}{2 (d+e x)^{5/2} \left (c d^2-a e^2\right ) (a e+c d x)^2}+\frac {63 e^2}{20 (d+e x)^{5/2} \left (c d^2-a e^2\right )^3} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(63*e^2)/(20*(c*d^2 - a*e^2)^3*(d + e*x)^(5/2)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*(d + e*x)^(5/2)) + (9*e
)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*(d + e*x)^(5/2)) + (21*c*d*e^2)/(4*(c*d^2 - a*e^2)^4*(d + e*x)^(3/2)) + (
63*c^2*d^2*e^2)/(4*(c*d^2 - a*e^2)^5*Sqrt[d + e*x]) - (63*c^(5/2)*d^(5/2)*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d
+ e*x])/Sqrt[c*d^2 - a*e^2]])/(4*(c*d^2 - a*e^2)^(11/2))

Rule 51

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*(m + n + 2))/((b*c - a*d)*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^n,
x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && LtQ[m, -1] &&  !(LtQ[n, -1] && (EqQ[a, 0] || (NeQ[
c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && IntLinearQ[a, b, c, d, m, n, x]

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 208

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

Rule 626

Int[((d_) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[(d + e*x)^(m + p)*(a
/d + (c*x)/e)^p, x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && EqQ[c*d^2 - b*d*e + a*e^2, 0] &&
IntegerQ[p]

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {d+e x} \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^3} \, dx &=\int \frac {1}{(a e+c d x)^3 (d+e x)^{7/2}} \, dx\\ &=-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}-\frac {(9 e) \int \frac {1}{(a e+c d x)^2 (d+e x)^{7/2}} \, dx}{4 \left (c d^2-a e^2\right )}\\ &=-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {\left (63 e^2\right ) \int \frac {1}{(a e+c d x) (d+e x)^{7/2}} \, dx}{8 \left (c d^2-a e^2\right )^2}\\ &=\frac {63 e^2}{20 \left (c d^2-a e^2\right )^3 (d+e x)^{5/2}}-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {\left (63 c d e^2\right ) \int \frac {1}{(a e+c d x) (d+e x)^{5/2}} \, dx}{8 \left (c d^2-a e^2\right )^3}\\ &=\frac {63 e^2}{20 \left (c d^2-a e^2\right )^3 (d+e x)^{5/2}}-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {21 c d e^2}{4 \left (c d^2-a e^2\right )^4 (d+e x)^{3/2}}+\frac {\left (63 c^2 d^2 e^2\right ) \int \frac {1}{(a e+c d x) (d+e x)^{3/2}} \, dx}{8 \left (c d^2-a e^2\right )^4}\\ &=\frac {63 e^2}{20 \left (c d^2-a e^2\right )^3 (d+e x)^{5/2}}-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {21 c d e^2}{4 \left (c d^2-a e^2\right )^4 (d+e x)^{3/2}}+\frac {63 c^2 d^2 e^2}{4 \left (c d^2-a e^2\right )^5 \sqrt {d+e x}}+\frac {\left (63 c^3 d^3 e^2\right ) \int \frac {1}{(a e+c d x) \sqrt {d+e x}} \, dx}{8 \left (c d^2-a e^2\right )^5}\\ &=\frac {63 e^2}{20 \left (c d^2-a e^2\right )^3 (d+e x)^{5/2}}-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {21 c d e^2}{4 \left (c d^2-a e^2\right )^4 (d+e x)^{3/2}}+\frac {63 c^2 d^2 e^2}{4 \left (c d^2-a e^2\right )^5 \sqrt {d+e x}}+\frac {\left (63 c^3 d^3 e\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {c d^2}{e}+a e+\frac {c d x^2}{e}} \, dx,x,\sqrt {d+e x}\right )}{4 \left (c d^2-a e^2\right )^5}\\ &=\frac {63 e^2}{20 \left (c d^2-a e^2\right )^3 (d+e x)^{5/2}}-\frac {1}{2 \left (c d^2-a e^2\right ) (a e+c d x)^2 (d+e x)^{5/2}}+\frac {9 e}{4 \left (c d^2-a e^2\right )^2 (a e+c d x) (d+e x)^{5/2}}+\frac {21 c d e^2}{4 \left (c d^2-a e^2\right )^4 (d+e x)^{3/2}}+\frac {63 c^2 d^2 e^2}{4 \left (c d^2-a e^2\right )^5 \sqrt {d+e x}}-\frac {63 c^{5/2} d^{5/2} e^2 \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{4 \left (c d^2-a e^2\right )^{11/2}}\\ \end {align*}

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Mathematica [C]  time = 0.02, size = 61, normalized size = 0.25 \begin {gather*} -\frac {2 e^2 \, _2F_1\left (-\frac {5}{2},3;-\frac {3}{2};-\frac {c d (d+e x)}{a e^2-c d^2}\right )}{5 (d+e x)^{5/2} \left (a e^2-c d^2\right )^3} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-2*e^2*Hypergeometric2F1[-5/2, 3, -3/2, -((c*d*(d + e*x))/(-(c*d^2) + a*e^2))])/(5*(-(c*d^2) + a*e^2)^3*(d +
e*x)^(5/2))

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IntegrateAlgebraic [A]  time = 0.96, size = 361, normalized size = 1.48 \begin {gather*} \frac {e^2 \left (8 a^4 e^8-32 a^3 c d^2 e^6-24 a^3 c d e^6 (d+e x)+48 a^2 c^2 d^4 e^4+72 a^2 c^2 d^3 e^4 (d+e x)+168 a^2 c^2 d^2 e^4 (d+e x)^2-32 a c^3 d^6 e^2-72 a c^3 d^5 e^2 (d+e x)-336 a c^3 d^4 e^2 (d+e x)^2+525 a c^3 d^3 e^2 (d+e x)^3+8 c^4 d^8+24 c^4 d^7 (d+e x)+168 c^4 d^6 (d+e x)^2-525 c^4 d^5 (d+e x)^3+315 c^4 d^4 (d+e x)^4\right )}{20 (d+e x)^{5/2} \left (c d^2-a e^2\right )^5 \left (-a e^2+c d^2-c d (d+e x)\right )^2}+\frac {63 c^{5/2} d^{5/2} e^2 \tan ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x} \sqrt {a e^2-c d^2}}{c d^2-a e^2}\right )}{4 \left (a e^2-c d^2\right )^{11/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[1/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3),x]

[Out]

(e^2*(8*c^4*d^8 - 32*a*c^3*d^6*e^2 + 48*a^2*c^2*d^4*e^4 - 32*a^3*c*d^2*e^6 + 8*a^4*e^8 + 24*c^4*d^7*(d + e*x)
- 72*a*c^3*d^5*e^2*(d + e*x) + 72*a^2*c^2*d^3*e^4*(d + e*x) - 24*a^3*c*d*e^6*(d + e*x) + 168*c^4*d^6*(d + e*x)
^2 - 336*a*c^3*d^4*e^2*(d + e*x)^2 + 168*a^2*c^2*d^2*e^4*(d + e*x)^2 - 525*c^4*d^5*(d + e*x)^3 + 525*a*c^3*d^3
*e^2*(d + e*x)^3 + 315*c^4*d^4*(d + e*x)^4))/(20*(c*d^2 - a*e^2)^5*(d + e*x)^(5/2)*(c*d^2 - a*e^2 - c*d*(d + e
*x))^2) + (63*c^(5/2)*d^(5/2)*e^2*ArcTan[(Sqrt[c]*Sqrt[d]*Sqrt[-(c*d^2) + a*e^2]*Sqrt[d + e*x])/(c*d^2 - a*e^2
)])/(4*(-(c*d^2) + a*e^2)^(11/2))

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fricas [B]  time = 0.46, size = 2007, normalized size = 8.23

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

[1/40*(315*(c^4*d^4*e^5*x^5 + a^2*c^2*d^5*e^4 + (3*c^4*d^5*e^4 + 2*a*c^3*d^3*e^6)*x^4 + (3*c^4*d^6*e^3 + 6*a*c
^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + (c^4*d^7*e^2 + 6*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6)*x^2 + (2*a*c^3*d^6*e^3
+ 3*a^2*c^2*d^4*e^5)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x
+ d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(315*c^4*d^4*e^4*x^4 - 10*c^4*d^8 + 85*a*c^3*d^6*e^2 + 288
*a^2*c^2*d^4*e^4 - 56*a^3*c*d^2*e^6 + 8*a^4*e^8 + 105*(7*c^4*d^5*e^3 + 5*a*c^3*d^3*e^5)*x^3 + 21*(23*c^4*d^6*e
^2 + 59*a*c^3*d^4*e^4 + 8*a^2*c^2*d^2*e^6)*x^2 + 3*(15*c^4*d^7*e + 277*a*c^3*d^5*e^3 + 136*a^2*c^2*d^3*e^5 - 8
*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(a^2*c^5*d^13*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e
^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*
e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 -
10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d
^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 -
a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 - 17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a
^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10
*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x), -1/20*(315*(c^4*d^4*e
^5*x^5 + a^2*c^2*d^5*e^4 + (3*c^4*d^5*e^4 + 2*a*c^3*d^3*e^6)*x^4 + (3*c^4*d^6*e^3 + 6*a*c^3*d^4*e^5 + a^2*c^2*
d^2*e^7)*x^3 + (c^4*d^7*e^2 + 6*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6)*x^2 + (2*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5)
*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d
^2)) - (315*c^4*d^4*e^4*x^4 - 10*c^4*d^8 + 85*a*c^3*d^6*e^2 + 288*a^2*c^2*d^4*e^4 - 56*a^3*c*d^2*e^6 + 8*a^4*e
^8 + 105*(7*c^4*d^5*e^3 + 5*a*c^3*d^3*e^5)*x^3 + 21*(23*c^4*d^6*e^2 + 59*a*c^3*d^4*e^4 + 8*a^2*c^2*d^2*e^6)*x^
2 + 3*(15*c^4*d^7*e + 277*a*c^3*d^5*e^3 + 136*a^2*c^2*d^3*e^5 - 8*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(a^2*c^5*d^13
*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d
^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*
x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 - 10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a
^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e
^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 - a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 -
17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*
e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^
9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x)]

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-12*a^8*c*d*exp(1)^2*exp(2)^8+6*a^8*
sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^
2*exp(2)^8+204*a^7*c^2*d^3*exp(1)^4*exp(2)^6-108*a^7*c^2*d^3*exp(1)^2*exp(2)^7+12*a^7*c^2*d^2*exp(1)^2*exp(2)^
7-102*a^7*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))
*sqrt(2)*exp(1)^4*exp(2)^6+54*a^7*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d
^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^7-12*a^7*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^
2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^7-6*a^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^7-1392*a^6*c^3*d^5*exp(1)^6*exp(2)^4+1560*a^6*c^3*d^5*exp(1)^4*exp(2)
^5-504*a^6*c^3*d^5*exp(1)^2*exp(2)^6-180*a^6*c^3*d^4*exp(1)^4*exp(2)^5+96*a^6*c^3*d^4*exp(1)^2*exp(2)^6+696*a^
6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*exp(1)^6*exp(2)^4-780*a^6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*
exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^5+252*a^6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1
)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+156*a^6*c^2*d^3*sqrt(-c^2*d^3+c*d*s
qrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^5-72*a^6*c
^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*
exp(1)^2*exp(2)^6+6*a^6*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2
))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+90*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)*exp(1)^4*exp(2)^5-48*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*
a^6*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*a^6*c*d*(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+4416*a^5*c^4*d^7*exp(1)^8*exp(2)^2-7680*a^5*c^4*d^
7*exp(1)^6*exp(2)^3+5172*a^5*c^4*d^7*exp(1)^4*exp(2)^4-1236*a^5*c^4*d^7*exp(1)^2*exp(2)^5+1056*a^5*c^4*d^6*exp
(1)^6*exp(2)^3-1212*a^5*c^4*d^6*exp(1)^4*exp(2)^4+408*a^5*c^4*d^6*exp(1)^2*exp(2)^5-2208*a^5*c^3*d^6*sqrt(-c^2
*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)^
2+3840*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(
2))*sqrt(2)*exp(1)^6*exp(2)^3-2586*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+618*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-768*a^5*c^3*d^5*sqrt(-c^2
*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^
3+756*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2
))*sqrt(2)*exp(1)^4*exp(2)^4-240*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*
a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-78*a^5*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+42*a^5*c^3*d^4*sqrt(-c^2*d^3
+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-52
8*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*s
qrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^3+606*a^5*c^2*d^4*sqrt(-
c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4-204*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2
*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a
^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-132*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1
)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^
2*exp(2))*exp(1)^4*exp(2)^4+60*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*ex
p(2)^5-156*a^5*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4+84*a^5*c^2
*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-6*a^5*c^2*d^2*sqrt(-c^2*d^3+
c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-12*a^5*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-5376*a^4*c^5*d^9*exp(1)^10+12672*a^4*c^5*d^9*exp(1)^8*exp(2)-14112*a
^4*c^5*d^9*exp(1)^6*exp(2)^2+7632*a^4*c^5*d^9*exp(1)^4*exp(2)^3-1656*a^4*c^5*d^9*exp(1)^2*exp(2)^4-2112*a^4*c^
5*d^8*exp(1)^8*exp(2)+3168*a^4*c^5*d^8*exp(1)^6*exp(2)^2-1800*a^4*c^5*d^8*exp(1)^4*exp(2)^3+324*a^4*c^5*d^8*ex
p(1)^2*exp(2)^4+2688*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*exp(1)^10-6336*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)+7056*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-3816*a^4*c^4*d^8*sqr
t(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*e
xp(2)^3+828*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+1344*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(
2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)-1728*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2+984*a^4*c^4*d^7*sqrt(
-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp
(2)^3-180*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*e
xp(2))*sqrt(2)*exp(1)^2*exp(2)^4+384*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-456*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+162*a^4*c^4*d^6*sqrt(-c
^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2
)^4+1056*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*ex
p(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^8*exp(2)-1584*a^4*c^3*d^6*
sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^
2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2+900*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sq
rt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(
1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-162*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2
*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*
a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+528*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(
1)^6*exp(2)^2-528*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))
+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+180*a^
4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+768*a^4*c^3*d^5*(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2-912*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+324*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a
*c*d^2*exp(2))*exp(1)^2*exp(2)^4+66*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)
^4*exp(2)^3-36*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*
c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+132*a^4*c
^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-72*a^4*c^3*d^4*(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+4416*a^3*c^6*d^11*exp(1)^8-7680*a^3*c^6*d^11
*exp(1)^6*exp(2)+5172*a^3*c^6*d^11*exp(1)^4*exp(2)^2-1236*a^3*c^6*d^11*exp(1)^2*exp(2)^3+2112*a^3*c^6*d^10*exp
(1)^8-3168*a^3*c^6*d^10*exp(1)^6*exp(2)+1800*a^3*c^6*d^10*exp(1)^4*exp(2)^2-324*a^3*c^6*d^10*exp(1)^2*exp(2)^3
-2208*a^3*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(
2))*sqrt(2)*exp(1)^8+3840*a^3*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^
2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)-2586*a^3*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp
(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+618*a^3*c^5*d^10*sqrt(-c^2*d^3+c*
d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-1344*
a^3*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqr
t(2)*exp(1)^8+1728*a^3*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)-984*a^3*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+180*a^3*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-672*a^3*c^5*d^8*
sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^
8+1248*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(
2))*sqrt(2)*exp(1)^6*exp(2)-948*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a
*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+252*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-1056*a^3*c^4*d^8*sqrt(-c^2*d
^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^8+1584*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2
*a*c*d^2*exp(2))*exp(1)^6*exp(2)-900*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1
)^4*exp(2)^2+162*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+
a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-1056*a^
3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+1320*a^3*c^4*d^7*sqrt(-c^2*d
^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-504*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-1344*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))*exp(1)^8+2496*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-
1896*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+504*a^3*c^4*d^7*
(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-264*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+330*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2
*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-126*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp
(1)^2*exp(2)^3-528*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+660*
a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-252*a^3*c^4*d^6*(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-1392*a^2*c^7*d^13*exp(1)^6+1560*a^2*c^
7*d^13*exp(1)^4*exp(2)-504*a^2*c^7*d^13*exp(1)^2*exp(2)^2-1056*a^2*c^7*d^12*exp(1)^6+1212*a^2*c^7*d^12*exp(1)^
4*exp(2)-408*a^2*c^7*d^12*exp(1)^2*exp(2)^2+696*a^2*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-780*a^2*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4
-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+252*a^2*c^6*d^12*sqrt
(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*ex
p(2)^2+768*a^2*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*exp(1)^6-756*a^2*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+240*a^2*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+384*a^2*c^6*d^10*sqrt(-c^2*d^3
+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-456*a^2*c^6
*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*e
xp(1)^4*exp(2)+162*a^2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2
))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+528*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*ex
p(2))*exp(1)^6-606*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2
))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+204*a^
2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt
(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+528*a^2*c^5*d^9*sqrt(-c^2
*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-528*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+180*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(
1)^2*exp(2)^2+768*a^2*c^5*d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-912*a^2*c^5*
d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+324*a^2*c^5*d^9*(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+264*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-330*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1
)^4*exp(2)+126*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*
c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+528*a^2*c
^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-660*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+252*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+204*a*c^8*d^15*exp(1)^4-108*a*c^8*d^15*exp(1)^2*exp(2)+180*a*c^8*d^14*e
xp(1)^4-96*a*c^8*d^14*exp(1)^2*exp(2)-102*a*c^7*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+54*a*c^7*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-156*a*c^7*d^13*sqrt(-c^2*d^3+c*d
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+72*a*c^7*d^13*s
qrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2
*exp(2)-78*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*e
xp(2))*sqrt(2)*exp(1)^4+42*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-90*a*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*e
xp(2))*exp(1)^4+48*a*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))
+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-132*a*c^
6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*
sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+60*a*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c
^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-156*a*c^6*d^11*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*
d^2*exp(2))*exp(1)^4+84*a*c^6*d^11*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-
66*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*s
qrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+36*a*c^6*d^10*sqrt(-c^2*d^3+c*d
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-132*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))*exp(1)^4+72*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*
exp(2)-12*c^9*d^17*exp(1)^2-12*c^9*d^16*exp(1)^2+6*c^8*d^16*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+12*c^8*d^15*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+6*c^8*d^14*sqrt(-c^2*d^3+c*d*sqrt(
c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+6*c^7*d^14*sqrt(-c^2*
d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+12*c^7*d^13*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*ex
p(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c
*d^2*exp(2))*exp(1)^2+12*c^7*d^13*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*c^7*d^
12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt
(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+12*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^
2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2)/(64*a^11*d^3*exp(1)^6*exp(2)^8-192*a^11*d^3*exp(1)^4*exp(2)^9+192*a^11*
d^3*exp(1)^2*exp(2)^10-64*a^11*d^3*exp(2)^11-1024*a^10*c*d^5*exp(1)^8*exp(2)^6+3584*a^10*c*d^5*exp(1)^6*exp(2)
^7-4608*a^10*c*d^5*exp(1)^4*exp(2)^8+2560*a^10*c*d^5*exp(1)^2*exp(2)^9-512*a^10*c*d^5*exp(2)^10-128*a^10*c*d^4
*exp(1)^6*exp(2)^7+384*a^10*c*d^4*exp(1)^4*exp(2)^8-384*a^10*c*d^4*exp(1)^2*exp(2)^9+128*a^10*c*d^4*exp(2)^10+
6144*a^9*c^2*d^7*exp(1)^10*exp(2)^4-24576*a^9*c^2*d^7*exp(1)^8*exp(2)^5+38656*a^9*c^2*d^7*exp(1)^6*exp(2)^6-29
952*a^9*c^2*d^7*exp(1)^4*exp(2)^7+11520*a^9*c^2*d^7*exp(1)^2*exp(2)^8-1792*a^9*c^2*d^7*exp(2)^9+1536*a^9*c^2*d
^6*exp(1)^8*exp(2)^5-5248*a^9*c^2*d^6*exp(1)^6*exp(2)^6+6528*a^9*c^2*d^6*exp(1)^4*exp(2)^7-3456*a^9*c^2*d^6*ex
p(1)^2*exp(2)^8+640*a^9*c^2*d^6*exp(2)^9+64*a^9*c^2*d^5*exp(1)^6*exp(2)^6-192*a^9*c^2*d^5*exp(1)^4*exp(2)^7+19
2*a^9*c^2*d^5*exp(1)^2*exp(2)^8-64*a^9*c^2*d^5*exp(2)^9-16384*a^8*c^3*d^9*exp(1)^12*exp(2)^2+73728*a^8*c^3*d^9
*exp(1)^10*exp(2)^3-138240*a^8*c^3*d^9*exp(1)^8*exp(2)^4+139776*a^8*c^3*d^9*exp(1)^6*exp(2)^5-81408*a^8*c^3*d^
9*exp(1)^4*exp(2)^6+26112*a^8*c^3*d^9*exp(1)^2*exp(2)^7-3584*a^8*c^3*d^9*exp(2)^8-6144*a^8*c^3*d^8*exp(1)^10*e
xp(2)^3+23040*a^8*c^3*d^8*exp(1)^8*exp(2)^4-33408*a^8*c^3*d^8*exp(1)^6*exp(2)^5+23424*a^8*c^3*d^8*exp(1)^4*exp
(2)^6-8064*a^8*c^3*d^8*exp(1)^2*exp(2)^7+1152*a^8*c^3*d^8*exp(2)^8-768*a^8*c^3*d^7*exp(1)^8*exp(2)^4+2688*a^8*
c^3*d^7*exp(1)^6*exp(2)^5-3456*a^8*c^3*d^7*exp(1)^4*exp(2)^6+1920*a^8*c^3*d^7*exp(1)^2*exp(2)^7-384*a^8*c^3*d^
7*exp(2)^8+16384*a^7*c^4*d^11*exp(1)^14-81920*a^7*c^4*d^11*exp(1)^12*exp(2)+184320*a^7*c^4*d^11*exp(1)^10*exp(
2)^2-245760*a^7*c^4*d^11*exp(1)^8*exp(2)^3+209280*a^7*c^4*d^11*exp(1)^6*exp(2)^4-111744*a^7*c^4*d^11*exp(1)^4*
exp(2)^5+33920*a^7*c^4*d^11*exp(1)^2*exp(2)^6-4480*a^7*c^4*d^11*exp(2)^7+8192*a^7*c^4*d^10*exp(1)^12*exp(2)-30
720*a^7*c^4*d^10*exp(1)^10*exp(2)^2+46080*a^7*c^4*d^10*exp(1)^8*exp(2)^3-36480*a^7*c^4*d^10*exp(1)^6*exp(2)^4+
17280*a^7*c^4*d^10*exp(1)^4*exp(2)^5-4992*a^7*c^4*d^10*exp(1)^2*exp(2)^6+640*a^7*c^4*d^10*exp(2)^7+3072*a^7*c^
4*d^9*exp(1)^10*exp(2)^2-12288*a^7*c^4*d^9*exp(1)^8*exp(2)^3+19392*a^7*c^4*d^9*exp(1)^6*exp(2)^4-15168*a^7*c^4
*d^9*exp(1)^4*exp(2)^5+5952*a^7*c^4*d^9*exp(1)^2*exp(2)^6-960*a^7*c^4*d^9*exp(2)^7-16384*a^6*c^5*d^13*exp(1)^1
2+73728*a^6*c^5*d^13*exp(1)^10*exp(2)-138240*a^6*c^5*d^13*exp(1)^8*exp(2)^2+139776*a^6*c^5*d^13*exp(1)^6*exp(2
)^3-81408*a^6*c^5*d^13*exp(1)^4*exp(2)^4+26112*a^6*c^5*d^13*exp(1)^2*exp(2)^5-3584*a^6*c^5*d^13*exp(2)^6-8192*
a^6*c^5*d^12*exp(1)^12+30720*a^6*c^5*d^12*exp(1)^10*exp(2)-46080*a^6*c^5*d^12*exp(1)^8*exp(2)^2+36480*a^6*c^5*
d^12*exp(1)^6*exp(2)^3-17280*a^6*c^5*d^12*exp(1)^4*exp(2)^4+4992*a^6*c^5*d^12*exp(1)^2*exp(2)^5-640*a^6*c^5*d^
12*exp(2)^6-4096*a^6*c^5*d^11*exp(1)^12+18432*a^6*c^5*d^11*exp(1)^10*exp(2)-35328*a^6*c^5*d^11*exp(1)^8*exp(2)
^2+37632*a^6*c^5*d^11*exp(1)^6*exp(2)^3-23808*a^6*c^5*d^11*exp(1)^4*exp(2)^4+8448*a^6*c^5*d^11*exp(1)^2*exp(2)
^5-1280*a^6*c^5*d^11*exp(2)^6+6144*a^5*c^6*d^15*exp(1)^10-24576*a^5*c^6*d^15*exp(1)^8*exp(2)+38656*a^5*c^6*d^1
5*exp(1)^6*exp(2)^2-29952*a^5*c^6*d^15*exp(1)^4*exp(2)^3+11520*a^5*c^6*d^15*exp(1)^2*exp(2)^4-1792*a^5*c^6*d^1
5*exp(2)^5+6144*a^5*c^6*d^14*exp(1)^10-23040*a^5*c^6*d^14*exp(1)^8*exp(2)+33408*a^5*c^6*d^14*exp(1)^6*exp(2)^2
-23424*a^5*c^6*d^14*exp(1)^4*exp(2)^3+8064*a^5*c^6*d^14*exp(1)^2*exp(2)^4-1152*a^5*c^6*d^14*exp(2)^5+3072*a^5*
c^6*d^13*exp(1)^10-12288*a^5*c^6*d^13*exp(1)^8*exp(2)+19392*a^5*c^6*d^13*exp(1)^6*exp(2)^2-15168*a^5*c^6*d^13*
exp(1)^4*exp(2)^3+5952*a^5*c^6*d^13*exp(1)^2*exp(2)^4-960*a^5*c^6*d^13*exp(2)^5-1024*a^4*c^7*d^17*exp(1)^8+358
4*a^4*c^7*d^17*exp(1)^6*exp(2)-4608*a^4*c^7*d^17*exp(1)^4*exp(2)^2+2560*a^4*c^7*d^17*exp(1)^2*exp(2)^3-512*a^4
*c^7*d^17*exp(2)^4-1536*a^4*c^7*d^16*exp(1)^8+5248*a^4*c^7*d^16*exp(1)^6*exp(2)-6528*a^4*c^7*d^16*exp(1)^4*exp
(2)^2+3456*a^4*c^7*d^16*exp(1)^2*exp(2)^3-640*a^4*c^7*d^16*exp(2)^4-768*a^4*c^7*d^15*exp(1)^8+2688*a^4*c^7*d^1
5*exp(1)^6*exp(2)-3456*a^4*c^7*d^15*exp(1)^4*exp(2)^2+1920*a^4*c^7*d^15*exp(1)^2*exp(2)^3-384*a^4*c^7*d^15*exp
(2)^4+64*a^3*c^8*d^19*exp(1)^6-192*a^3*c^8*d^19*exp(1)^4*exp(2)+192*a^3*c^8*d^19*exp(1)^2*exp(2)^2-64*a^3*c^8*
d^19*exp(2)^3+128*a^3*c^8*d^18*exp(1)^6-384*a^3*c^8*d^18*exp(1)^4*exp(2)+384*a^3*c^8*d^18*exp(1)^2*exp(2)^2-12
8*a^3*c^8*d^18*exp(2)^3+64*a^3*c^8*d^17*exp(1)^6-192*a^3*c^8*d^17*exp(1)^4*exp(2)+192*a^3*c^8*d^17*exp(1)^2*ex
p(2)^2-64*a^3*c^8*d^17*exp(2)^3)/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(-8*a^7*d^2*exp(1)^4*exp(2)^5+16*a^
7*d^2*exp(1)^2*exp(2)^6-8*a^7*d^2*exp(2)^7+64*a^6*d^4*exp(1)^6*exp(2)^3*c-152*a^6*d^4*exp(1)^4*exp(2)^4*c+112*
a^6*d^4*exp(1)^2*exp(2)^5*c-24*a^6*d^4*exp(2)^6*c-128*a^5*d^6*exp(1)^8*exp(2)*c^2+320*a^5*d^6*exp(1)^6*exp(2)^
2*c^2-272*a^5*d^6*exp(1)^4*exp(2)^3*c^2+96*a^5*d^6*exp(1)^2*exp(2)^4*c^2-16*a^5*d^6*exp(2)^5*c^2+128*a^4*d^8*e
xp(1)^8*c^3-320*a^4*d^8*exp(1)^6*exp(2)*c^3+272*a^4*d^8*exp(1)^4*exp(2)^2*c^3-96*a^4*d^8*exp(1)^2*exp(2)^3*c^3
+16*a^4*d^8*exp(2)^4*c^3-64*a^3*d^10*exp(1)^6*c^4+152*a^3*d^10*exp(1)^4*exp(2)*c^4-112*a^3*d^10*exp(1)^2*exp(2
)^2*c^4+24*a^3*d^10*exp(2)^3*c^4+8*a^2*d^12*exp(1)^4*c^5-16*a^2*d^12*exp(1)^2*exp(2)*c^5+8*a^2*d^12*exp(2)^2*c
^5+sqrt((8*a^7*d^2*exp(1)^4*exp(2)^5-16*a^7*d^2*exp(1)^2*exp(2)^6+8*a^7*d^2*exp(2)^7-64*a^6*d^4*exp(1)^6*exp(2
)^3*c+152*a^6*d^4*exp(1)^4*exp(2)^4*c-112*a^6*d^4*exp(1)^2*exp(2)^5*c+24*a^6*d^4*exp(2)^6*c+128*a^5*d^6*exp(1)
^8*exp(2)*c^2-320*a^5*d^6*exp(1)^6*exp(2)^2*c^2+272*a^5*d^6*exp(1)^4*exp(2)^3*c^2-96*a^5*d^6*exp(1)^2*exp(2)^4
*c^2+16*a^5*d^6*exp(2)^5*c^2-128*a^4*d^8*exp(1)^8*c^3+320*a^4*d^8*exp(1)^6*exp(2)*c^3-272*a^4*d^8*exp(1)^4*exp
(2)^2*c^3+96*a^4*d^8*exp(1)^2*exp(2)^3*c^3-16*a^4*d^8*exp(2)^4*c^3+64*a^3*d^10*exp(1)^6*c^4-152*a^3*d^10*exp(1
)^4*exp(2)*c^4+112*a^3*d^10*exp(1)^2*exp(2)^2*c^4-24*a^3*d^10*exp(2)^3*c^4-8*a^2*d^12*exp(1)^4*c^5+16*a^2*d^12
*exp(1)^2*exp(2)*c^5-8*a^2*d^12*exp(2)^2*c^5)*(8*a^7*d^2*exp(1)^4*exp(2)^5-16*a^7*d^2*exp(1)^2*exp(2)^6+8*a^7*
d^2*exp(2)^7-64*a^6*d^4*exp(1)^6*exp(2)^3*c+152*a^6*d^4*exp(1)^4*exp(2)^4*c-112*a^6*d^4*exp(1)^2*exp(2)^5*c+24
*a^6*d^4*exp(2)^6*c+128*a^5*d^6*exp(1)^8*exp(2)*c^2-320*a^5*d^6*exp(1)^6*exp(2)^2*c^2+272*a^5*d^6*exp(1)^4*exp
(2)^3*c^2-96*a^5*d^6*exp(1)^2*exp(2)^4*c^2+16*a^5*d^6*exp(2)^5*c^2-128*a^4*d^8*exp(1)^8*c^3+320*a^4*d^8*exp(1)
^6*exp(2)*c^3-272*a^4*d^8*exp(1)^4*exp(2)^2*c^3+96*a^4*d^8*exp(1)^2*exp(2)^3*c^3-16*a^4*d^8*exp(2)^4*c^3+64*a^
3*d^10*exp(1)^6*c^4-152*a^3*d^10*exp(1)^4*exp(2)*c^4+112*a^3*d^10*exp(1)^2*exp(2)^2*c^4-24*a^3*d^10*exp(2)^3*c
^4-8*a^2*d^12*exp(1)^4*c^5+16*a^2*d^12*exp(1)^2*exp(2)*c^5-8*a^2*d^12*exp(2)^2*c^5)-4*(8*a^6*d^3*exp(1)^4*exp(
2)^4*c-16*a^6*d^3*exp(1)^2*exp(2)^5*c+8*a^6*d^3*exp(2)^6*c-64*a^5*d^5*exp(1)^6*exp(2)^2*c^2+160*a^5*d^5*exp(1)
^4*exp(2)^3*c^2-128*a^5*d^5*exp(1)^2*exp(2)^4*c^2+32*a^5*d^5*exp(2)^5*c^2+128*a^4*d^7*exp(1)^8*c^3-384*a^4*d^7
*exp(1)^6*exp(2)*c^3+432*a^4*d^7*exp(1)^4*exp(2)^2*c^3-224*a^4*d^7*exp(1)^2*exp(2)^3*c^3+48*a^4*d^7*exp(2)^4*c
^3-64*a^3*d^9*exp(1)^6*c^4+160*a^3*d^9*exp(1)^4*exp(2)*c^4-128*a^3*d^9*exp(1)^2*exp(2)^2*c^4+32*a^3*d^9*exp(2)
^3*c^4+8*a^2*d^11*exp(1)^4*c^5-16*a^2*d^11*exp(1)^2*exp(2)*c^5+8*a^2*d^11*exp(2)^2*c^5)*(8*a^7*d^3*exp(1)^6*ex
p(2)^4-24*a^7*d^3*exp(1)^4*exp(2)^5+24*a^7*d^3*exp(1)^2*exp(2)^6-8*a^7*d^3*exp(2)^7-64*a^6*d^5*exp(1)^8*exp(2)
^2*c+224*a^6*d^5*exp(1)^6*exp(2)^3*c-288*a^6*d^5*exp(1)^4*exp(2)^4*c+160*a^6*d^5*exp(1)^2*exp(2)^5*c-32*a^6*d^
5*exp(2)^6*c+128*a^5*d^7*exp(1)^10*c^2-512*a^5*d^7*exp(1)^8*exp(2)*c^2+816*a^5*d^7*exp(1)^6*exp(2)^2*c^2-656*a
^5*d^7*exp(1)^4*exp(2)^3*c^2+272*a^5*d^7*exp(1)^2*exp(2)^4*c^2-48*a^5*d^7*exp(2)^5*c^2-64*a^4*d^9*exp(1)^8*c^3
+224*a^4*d^9*exp(1)^6*exp(2)*c^3-288*a^4*d^9*exp(1)^4*exp(2)^2*c^3+160*a^4*d^9*exp(1)^2*exp(2)^3*c^3-32*a^4*d^
9*exp(2)^4*c^3+8*a^3*d^11*exp(1)^6*c^4-24*a^3*d^11*exp(1)^4*exp(2)*c^4+24*a^3*d^11*exp(1)^2*exp(2)^2*c^4-8*a^3
*d^11*exp(2)^3*c^4)))/2/(8*a^6*d^3*exp(1)^4*exp(2)^4*c-16*a^6*d^3*exp(1)^2*exp(2)^5*c+8*a^6*d^3*exp(2)^6*c-64*
a^5*d^5*exp(1)^6*exp(2)^2*c^2+160*a^5*d^5*exp(1)^4*exp(2)^3*c^2-128*a^5*d^5*exp(1)^2*exp(2)^4*c^2+32*a^5*d^5*e
xp(2)^5*c^2+128*a^4*d^7*exp(1)^8*c^3-384*a^4*d^7*exp(1)^6*exp(2)*c^3+432*a^4*d^7*exp(1)^4*exp(2)^2*c^3-224*a^4
*d^7*exp(1)^2*exp(2)^3*c^3+48*a^4*d^7*exp(2)^4*c^3-64*a^3*d^9*exp(1)^6*c^4+160*a^3*d^9*exp(1)^4*exp(2)*c^4-128
*a^3*d^9*exp(1)^2*exp(2)^2*c^4+32*a^3*d^9*exp(2)^3*c^4+8*a^2*d^11*exp(1)^4*c^5-16*a^2*d^11*exp(1)^2*exp(2)*c^5
+8*a^2*d^11*exp(2)^2*c^5)))-(-12*a^8*c*d*exp(1)^2*exp(2)^8-6*a^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(
1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^8+204*a^7*c^2*d^3*exp(1)^4*exp(2)^6-
108*a^7*c^2*d^3*exp(1)^2*exp(2)^7+12*a^7*c^2*d^2*exp(1)^2*exp(2)^7+102*a^7*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^
4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^6-54*a^7*c*d^2*sqrt(
-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp
(2)^7+12*a^7*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2)
)*sqrt(2)*exp(1)^2*exp(2)^7-6*a^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp
(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^7-13
92*a^6*c^3*d^5*exp(1)^6*exp(2)^4+1560*a^6*c^3*d^5*exp(1)^4*exp(2)^5-504*a^6*c^3*d^5*exp(1)^2*exp(2)^6-180*a^6*
c^3*d^4*exp(1)^4*exp(2)^5+96*a^6*c^3*d^4*exp(1)^2*exp(2)^6-696*a^6*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^4+780*a^6*c^2*d^4*sqrt(-c^
2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)
^5-252*a^6*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(
2))*sqrt(2)*exp(1)^2*exp(2)^6-156*a^6*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2
*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^5+72*a^6*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6-6*a^6*c^2*d^2*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+90
*a^6*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt
(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^5-48*a^6*c*d^2*sqrt(-c^2*d^
3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*a^6*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*a^6*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp
(1)^2*exp(2)^6+4416*a^5*c^4*d^7*exp(1)^8*exp(2)^2-7680*a^5*c^4*d^7*exp(1)^6*exp(2)^3+5172*a^5*c^4*d^7*exp(1)^4
*exp(2)^4-1236*a^5*c^4*d^7*exp(1)^2*exp(2)^5+1056*a^5*c^4*d^6*exp(1)^6*exp(2)^3-1212*a^5*c^4*d^6*exp(1)^4*exp(
2)^4+408*a^5*c^4*d^6*exp(1)^2*exp(2)^5+2208*a^5*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)^2-3840*a^5*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2
*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^3+2586*a^5*c^3*d^
6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1
)^4*exp(2)^4-618*a^5*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+
a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+768*a^5*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^3-756*a^5*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+240*a^5*c^3*d^5*
sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^
2*exp(2)^5+78*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c
*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4-42*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(
2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-528*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^3+606*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a
^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp
(2))*exp(1)^4*exp(2)^4-204*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^
2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)
^5-132*a^5*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(
2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4+60*a^5*c^2*d^3*sq
rt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-156*a^5*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp
(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4+84*a^5*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-6*a^5*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp
(1)^2*exp(2)^5-12*a^5*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-537
6*a^4*c^5*d^9*exp(1)^10+12672*a^4*c^5*d^9*exp(1)^8*exp(2)-14112*a^4*c^5*d^9*exp(1)^6*exp(2)^2+7632*a^4*c^5*d^9
*exp(1)^4*exp(2)^3-1656*a^4*c^5*d^9*exp(1)^2*exp(2)^4-2112*a^4*c^5*d^8*exp(1)^8*exp(2)+3168*a^4*c^5*d^8*exp(1)
^6*exp(2)^2-1800*a^4*c^5*d^8*exp(1)^4*exp(2)^3+324*a^4*c^5*d^8*exp(1)^2*exp(2)^4-2688*a^4*c^4*d^8*sqrt(-c^2*d^
3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^10+6336*a^4*
c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)
*exp(1)^8*exp(2)-7056*a^4*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp
(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2+3816*a^4*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^
2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-828*a^4*c^4*d^8*sqrt(-c^2*d^3-c*d*sqr
t(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-1344*a^4*c
^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*
exp(1)^8*exp(2)+1728*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-984*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+180*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(
c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-384*a^4*c^4*
d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp
(1)^6*exp(2)^2+456*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-162*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^
2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+1056*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c
^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^8*exp(2)-1584*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(
1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d
^2*exp(2))*exp(1)^6*exp(2)^2+900*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*
a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*
exp(2)^3-162*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*
d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+528*a^4*c^3
*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sq
rt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2-528*a^4*c^3*d^5*sqrt(-c^2*d^3-c
*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2
*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+180*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+768*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))*exp(1)^6*exp(2)^2-912*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(
2)^3+324*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+66*a^4*c^3*d
^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt
(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-36*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*
sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*ex
p(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+132*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-72*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2
))*exp(1)^2*exp(2)^4+4416*a^3*c^6*d^11*exp(1)^8-7680*a^3*c^6*d^11*exp(1)^6*exp(2)+5172*a^3*c^6*d^11*exp(1)^4*e
xp(2)^2-1236*a^3*c^6*d^11*exp(1)^2*exp(2)^3+2112*a^3*c^6*d^10*exp(1)^8-3168*a^3*c^6*d^10*exp(1)^6*exp(2)+1800*
a^3*c^6*d^10*exp(1)^4*exp(2)^2-324*a^3*c^6*d^10*exp(1)^2*exp(2)^3+2208*a^3*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2
*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8-3840*a^3*c^5*d^10*sqrt(-
c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(
2)+2586*a^3*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*ex
p(2))*sqrt(2)*exp(1)^4*exp(2)^2-618*a^3*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+1344*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8-1728*a^3*c^5*d^9*sqrt(-c^2*d^3-
c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)+984*a
^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt
(2)*exp(1)^4*exp(2)^2-180*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+672*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(
1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8-1248*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2
*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)+948*a^3*c^5*d^8*s
qrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4
*exp(2)^2-252*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c
*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-1056*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*
exp(1)^8+1584*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c
*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-900*a^3*c^4*
d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqr
t(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+162*a^3*c^4*d^8*sqrt(-c^2*d^3-c*
d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-1056*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+1320*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*
exp(1)^4*exp(2)^2-504*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp
(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-13
44*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^8+2496*a^3*c^4*d^7*(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-1896*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+504*a^3*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))*exp(1)^2*exp(2)^3-264*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)
^6*exp(2)+330*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c
*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-126*a^3*c^
4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*s
qrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-528*a^3*c^4*d^6*(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+660*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*e
xp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-252*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))*exp(1)^2*exp(2)^3-1392*a^2*c^7*d^13*exp(1)^6+1560*a^2*c^7*d^13*exp(1)^4*exp(2)-504*a^2*c^7*d^13*exp(1
)^2*exp(2)^2-1056*a^2*c^7*d^12*exp(1)^6+1212*a^2*c^7*d^12*exp(1)^4*exp(2)-408*a^2*c^7*d^12*exp(1)^2*exp(2)^2-6
96*a^2*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))
*sqrt(2)*exp(1)^6+780*a^2*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*ex
p(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-252*a^2*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-768*a^2*c^6*d^11*sqrt(-c^2*d^3-c*d*sqr
t(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+756*a^2*c^6*d^11*sq
rt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*
exp(2)-240*a^2*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-384*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(
2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+456*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-162*a^2*c^6*d^10*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+52
8*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*
sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-606*a^2*c^5*d^10*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+204*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+528*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)*exp(1)^6-528*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*
c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+180*a^2*c^5
*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sq
rt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+768*a^2*c^5*d^9*(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-912*a^2*c^5*d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+324*a^2*c^5*d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*e
xp(1)^2*exp(2)^2+264*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-330*a^2*c^5*
d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqr
t(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+126*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*
sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*ex
p(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+528*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^6-660*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1
)^4*exp(2)+252*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+204*a*
c^8*d^15*exp(1)^4-108*a*c^8*d^15*exp(1)^2*exp(2)+180*a*c^8*d^14*exp(1)^4-96*a*c^8*d^14*exp(1)^2*exp(2)+102*a*c
^7*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)
*exp(1)^4-54*a*c^7*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*exp(1)^2*exp(2)+156*a*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-72*a*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1
)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+78*a*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(
c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-42*a*c^7*d^12*sqrt(-c
^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2
)-90*a*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))
*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a*c^6*d^12*sqrt(-c^2*d^3-c
*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2
*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-132*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))*exp(1)^4+60*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*
d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(
2)-156*a*c^6*d^11*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+84*a*c^6*d^11*(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-66*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+36*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)
^2*exp(2)-132*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+72*a*c^6*d^10*(c^
2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-12*c^9*d^17*exp(1)^2-12*c^9*d^16*exp(1
)^2-6*c^8*d^16*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*
sqrt(2)*exp(1)^2-12*c^8*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+
a*c*d*exp(2))*sqrt(2)*exp(1)^2-6*c^8*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c
*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+6*c^7*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*e
xp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))
*exp(1)^2+12*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*e
xp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+12*c^7*d^13*(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))*exp(1)^2+12*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2)/(64*a^
11*d^3*exp(1)^6*exp(2)^8-192*a^11*d^3*exp(1)^4*exp(2)^9+192*a^11*d^3*exp(1)^2*exp(2)^10-64*a^11*d^3*exp(2)^11-
1024*a^10*c*d^5*exp(1)^8*exp(2)^6+3584*a^10*c*d^5*exp(1)^6*exp(2)^7-4608*a^10*c*d^5*exp(1)^4*exp(2)^8+2560*a^1
0*c*d^5*exp(1)^2*exp(2)^9-512*a^10*c*d^5*exp(2)^10-128*a^10*c*d^4*exp(1)^6*exp(2)^7+384*a^10*c*d^4*exp(1)^4*ex
p(2)^8-384*a^10*c*d^4*exp(1)^2*exp(2)^9+128*a^10*c*d^4*exp(2)^10+6144*a^9*c^2*d^7*exp(1)^10*exp(2)^4-24576*a^9
*c^2*d^7*exp(1)^8*exp(2)^5+38656*a^9*c^2*d^7*exp(1)^6*exp(2)^6-29952*a^9*c^2*d^7*exp(1)^4*exp(2)^7+11520*a^9*c
^2*d^7*exp(1)^2*exp(2)^8-1792*a^9*c^2*d^7*exp(2)^9+1536*a^9*c^2*d^6*exp(1)^8*exp(2)^5-5248*a^9*c^2*d^6*exp(1)^
6*exp(2)^6+6528*a^9*c^2*d^6*exp(1)^4*exp(2)^7-3456*a^9*c^2*d^6*exp(1)^2*exp(2)^8+640*a^9*c^2*d^6*exp(2)^9+64*a
^9*c^2*d^5*exp(1)^6*exp(2)^6-192*a^9*c^2*d^5*exp(1)^4*exp(2)^7+192*a^9*c^2*d^5*exp(1)^2*exp(2)^8-64*a^9*c^2*d^
5*exp(2)^9-16384*a^8*c^3*d^9*exp(1)^12*exp(2)^2+73728*a^8*c^3*d^9*exp(1)^10*exp(2)^3-138240*a^8*c^3*d^9*exp(1)
^8*exp(2)^4+139776*a^8*c^3*d^9*exp(1)^6*exp(2)^5-81408*a^8*c^3*d^9*exp(1)^4*exp(2)^6+26112*a^8*c^3*d^9*exp(1)^
2*exp(2)^7-3584*a^8*c^3*d^9*exp(2)^8-6144*a^8*c^3*d^8*exp(1)^10*exp(2)^3+23040*a^8*c^3*d^8*exp(1)^8*exp(2)^4-3
3408*a^8*c^3*d^8*exp(1)^6*exp(2)^5+23424*a^8*c^3*d^8*exp(1)^4*exp(2)^6-8064*a^8*c^3*d^8*exp(1)^2*exp(2)^7+1152
*a^8*c^3*d^8*exp(2)^8-768*a^8*c^3*d^7*exp(1)^8*exp(2)^4+2688*a^8*c^3*d^7*exp(1)^6*exp(2)^5-3456*a^8*c^3*d^7*ex
p(1)^4*exp(2)^6+1920*a^8*c^3*d^7*exp(1)^2*exp(2)^7-384*a^8*c^3*d^7*exp(2)^8+16384*a^7*c^4*d^11*exp(1)^14-81920
*a^7*c^4*d^11*exp(1)^12*exp(2)+184320*a^7*c^4*d^11*exp(1)^10*exp(2)^2-245760*a^7*c^4*d^11*exp(1)^8*exp(2)^3+20
9280*a^7*c^4*d^11*exp(1)^6*exp(2)^4-111744*a^7*c^4*d^11*exp(1)^4*exp(2)^5+33920*a^7*c^4*d^11*exp(1)^2*exp(2)^6
-4480*a^7*c^4*d^11*exp(2)^7+8192*a^7*c^4*d^10*exp(1)^12*exp(2)-30720*a^7*c^4*d^10*exp(1)^10*exp(2)^2+46080*a^7
*c^4*d^10*exp(1)^8*exp(2)^3-36480*a^7*c^4*d^10*exp(1)^6*exp(2)^4+17280*a^7*c^4*d^10*exp(1)^4*exp(2)^5-4992*a^7
*c^4*d^10*exp(1)^2*exp(2)^6+640*a^7*c^4*d^10*exp(2)^7+3072*a^7*c^4*d^9*exp(1)^10*exp(2)^2-12288*a^7*c^4*d^9*ex
p(1)^8*exp(2)^3+19392*a^7*c^4*d^9*exp(1)^6*exp(2)^4-15168*a^7*c^4*d^9*exp(1)^4*exp(2)^5+5952*a^7*c^4*d^9*exp(1
)^2*exp(2)^6-960*a^7*c^4*d^9*exp(2)^7-16384*a^6*c^5*d^13*exp(1)^12+73728*a^6*c^5*d^13*exp(1)^10*exp(2)-138240*
a^6*c^5*d^13*exp(1)^8*exp(2)^2+139776*a^6*c^5*d^13*exp(1)^6*exp(2)^3-81408*a^6*c^5*d^13*exp(1)^4*exp(2)^4+2611
2*a^6*c^5*d^13*exp(1)^2*exp(2)^5-3584*a^6*c^5*d^13*exp(2)^6-8192*a^6*c^5*d^12*exp(1)^12+30720*a^6*c^5*d^12*exp
(1)^10*exp(2)-46080*a^6*c^5*d^12*exp(1)^8*exp(2)^2+36480*a^6*c^5*d^12*exp(1)^6*exp(2)^3-17280*a^6*c^5*d^12*exp
(1)^4*exp(2)^4+4992*a^6*c^5*d^12*exp(1)^2*exp(2)^5-640*a^6*c^5*d^12*exp(2)^6-4096*a^6*c^5*d^11*exp(1)^12+18432
*a^6*c^5*d^11*exp(1)^10*exp(2)-35328*a^6*c^5*d^11*exp(1)^8*exp(2)^2+37632*a^6*c^5*d^11*exp(1)^6*exp(2)^3-23808
*a^6*c^5*d^11*exp(1)^4*exp(2)^4+8448*a^6*c^5*d^11*exp(1)^2*exp(2)^5-1280*a^6*c^5*d^11*exp(2)^6+6144*a^5*c^6*d^
15*exp(1)^10-24576*a^5*c^6*d^15*exp(1)^8*exp(2)+38656*a^5*c^6*d^15*exp(1)^6*exp(2)^2-29952*a^5*c^6*d^15*exp(1)
^4*exp(2)^3+11520*a^5*c^6*d^15*exp(1)^2*exp(2)^4-1792*a^5*c^6*d^15*exp(2)^5+6144*a^5*c^6*d^14*exp(1)^10-23040*
a^5*c^6*d^14*exp(1)^8*exp(2)+33408*a^5*c^6*d^14*exp(1)^6*exp(2)^2-23424*a^5*c^6*d^14*exp(1)^4*exp(2)^3+8064*a^
5*c^6*d^14*exp(1)^2*exp(2)^4-1152*a^5*c^6*d^14*exp(2)^5+3072*a^5*c^6*d^13*exp(1)^10-12288*a^5*c^6*d^13*exp(1)^
8*exp(2)+19392*a^5*c^6*d^13*exp(1)^6*exp(2)^2-15168*a^5*c^6*d^13*exp(1)^4*exp(2)^3+5952*a^5*c^6*d^13*exp(1)^2*
exp(2)^4-960*a^5*c^6*d^13*exp(2)^5-1024*a^4*c^7*d^17*exp(1)^8+3584*a^4*c^7*d^17*exp(1)^6*exp(2)-4608*a^4*c^7*d
^17*exp(1)^4*exp(2)^2+2560*a^4*c^7*d^17*exp(1)^2*exp(2)^3-512*a^4*c^7*d^17*exp(2)^4-1536*a^4*c^7*d^16*exp(1)^8
+5248*a^4*c^7*d^16*exp(1)^6*exp(2)-6528*a^4*c^7*d^16*exp(1)^4*exp(2)^2+3456*a^4*c^7*d^16*exp(1)^2*exp(2)^3-640
*a^4*c^7*d^16*exp(2)^4-768*a^4*c^7*d^15*exp(1)^8+2688*a^4*c^7*d^15*exp(1)^6*exp(2)-3456*a^4*c^7*d^15*exp(1)^4*
exp(2)^2+1920*a^4*c^7*d^15*exp(1)^2*exp(2)^3-384*a^4*c^7*d^15*exp(2)^4+64*a^3*c^8*d^19*exp(1)^6-192*a^3*c^8*d^
19*exp(1)^4*exp(2)+192*a^3*c^8*d^19*exp(1)^2*exp(2)^2-64*a^3*c^8*d^19*exp(2)^3+128*a^3*c^8*d^18*exp(1)^6-384*a
^3*c^8*d^18*exp(1)^4*exp(2)+384*a^3*c^8*d^18*exp(1)^2*exp(2)^2-128*a^3*c^8*d^18*exp(2)^3+64*a^3*c^8*d^17*exp(1
)^6-192*a^3*c^8*d^17*exp(1)^4*exp(2)+192*a^3*c^8*d^17*exp(1)^2*exp(2)^2-64*a^3*c^8*d^17*exp(2)^3)/abs(c)/abs(d
)*atan(sqrt(d+x*exp(1))/sqrt(-(-8*a^7*d^2*exp(1)^4*exp(2)^5+16*a^7*d^2*exp(1)^2*exp(2)^6-8*a^7*d^2*exp(2)^7+64
*a^6*d^4*exp(1)^6*exp(2)^3*c-152*a^6*d^4*exp(1)^4*exp(2)^4*c+112*a^6*d^4*exp(1)^2*exp(2)^5*c-24*a^6*d^4*exp(2)
^6*c-128*a^5*d^6*exp(1)^8*exp(2)*c^2+320*a^5*d^6*exp(1)^6*exp(2)^2*c^2-272*a^5*d^6*exp(1)^4*exp(2)^3*c^2+96*a^
5*d^6*exp(1)^2*exp(2)^4*c^2-16*a^5*d^6*exp(2)^5*c^2+128*a^4*d^8*exp(1)^8*c^3-320*a^4*d^8*exp(1)^6*exp(2)*c^3+2
72*a^4*d^8*exp(1)^4*exp(2)^2*c^3-96*a^4*d^8*exp(1)^2*exp(2)^3*c^3+16*a^4*d^8*exp(2)^4*c^3-64*a^3*d^10*exp(1)^6
*c^4+152*a^3*d^10*exp(1)^4*exp(2)*c^4-112*a^3*d^10*exp(1)^2*exp(2)^2*c^4+24*a^3*d^10*exp(2)^3*c^4+8*a^2*d^12*e
xp(1)^4*c^5-16*a^2*d^12*exp(1)^2*exp(2)*c^5+8*a^2*d^12*exp(2)^2*c^5-sqrt((8*a^7*d^2*exp(1)^4*exp(2)^5-16*a^7*d
^2*exp(1)^2*exp(2)^6+8*a^7*d^2*exp(2)^7-64*a^6*d^4*exp(1)^6*exp(2)^3*c+152*a^6*d^4*exp(1)^4*exp(2)^4*c-112*a^6
*d^4*exp(1)^2*exp(2)^5*c+24*a^6*d^4*exp(2)^6*c+128*a^5*d^6*exp(1)^8*exp(2)*c^2-320*a^5*d^6*exp(1)^6*exp(2)^2*c
^2+272*a^5*d^6*exp(1)^4*exp(2)^3*c^2-96*a^5*d^6*exp(1)^2*exp(2)^4*c^2+16*a^5*d^6*exp(2)^5*c^2-128*a^4*d^8*exp(
1)^8*c^3+320*a^4*d^8*exp(1)^6*exp(2)*c^3-272*a^4*d^8*exp(1)^4*exp(2)^2*c^3+96*a^4*d^8*exp(1)^2*exp(2)^3*c^3-16
*a^4*d^8*exp(2)^4*c^3+64*a^3*d^10*exp(1)^6*c^4-152*a^3*d^10*exp(1)^4*exp(2)*c^4+112*a^3*d^10*exp(1)^2*exp(2)^2
*c^4-24*a^3*d^10*exp(2)^3*c^4-8*a^2*d^12*exp(1)^4*c^5+16*a^2*d^12*exp(1)^2*exp(2)*c^5-8*a^2*d^12*exp(2)^2*c^5)
*(8*a^7*d^2*exp(1)^4*exp(2)^5-16*a^7*d^2*exp(1)^2*exp(2)^6+8*a^7*d^2*exp(2)^7-64*a^6*d^4*exp(1)^6*exp(2)^3*c+1
52*a^6*d^4*exp(1)^4*exp(2)^4*c-112*a^6*d^4*exp(1)^2*exp(2)^5*c+24*a^6*d^4*exp(2)^6*c+128*a^5*d^6*exp(1)^8*exp(
2)*c^2-320*a^5*d^6*exp(1)^6*exp(2)^2*c^2+272*a^5*d^6*exp(1)^4*exp(2)^3*c^2-96*a^5*d^6*exp(1)^2*exp(2)^4*c^2+16
*a^5*d^6*exp(2)^5*c^2-128*a^4*d^8*exp(1)^8*c^3+320*a^4*d^8*exp(1)^6*exp(2)*c^3-272*a^4*d^8*exp(1)^4*exp(2)^2*c
^3+96*a^4*d^8*exp(1)^2*exp(2)^3*c^3-16*a^4*d^8*exp(2)^4*c^3+64*a^3*d^10*exp(1)^6*c^4-152*a^3*d^10*exp(1)^4*exp
(2)*c^4+112*a^3*d^10*exp(1)^2*exp(2)^2*c^4-24*a^3*d^10*exp(2)^3*c^4-8*a^2*d^12*exp(1)^4*c^5+16*a^2*d^12*exp(1)
^2*exp(2)*c^5-8*a^2*d^12*exp(2)^2*c^5)-4*(8*a^6*d^3*exp(1)^4*exp(2)^4*c-16*a^6*d^3*exp(1)^2*exp(2)^5*c+8*a^6*d
^3*exp(2)^6*c-64*a^5*d^5*exp(1)^6*exp(2)^2*c^2+160*a^5*d^5*exp(1)^4*exp(2)^3*c^2-128*a^5*d^5*exp(1)^2*exp(2)^4
*c^2+32*a^5*d^5*exp(2)^5*c^2+128*a^4*d^7*exp(1)^8*c^3-384*a^4*d^7*exp(1)^6*exp(2)*c^3+432*a^4*d^7*exp(1)^4*exp
(2)^2*c^3-224*a^4*d^7*exp(1)^2*exp(2)^3*c^3+48*a^4*d^7*exp(2)^4*c^3-64*a^3*d^9*exp(1)^6*c^4+160*a^3*d^9*exp(1)
^4*exp(2)*c^4-128*a^3*d^9*exp(1)^2*exp(2)^2*c^4+32*a^3*d^9*exp(2)^3*c^4+8*a^2*d^11*exp(1)^4*c^5-16*a^2*d^11*ex
p(1)^2*exp(2)*c^5+8*a^2*d^11*exp(2)^2*c^5)*(8*a^7*d^3*exp(1)^6*exp(2)^4-24*a^7*d^3*exp(1)^4*exp(2)^5+24*a^7*d^
3*exp(1)^2*exp(2)^6-8*a^7*d^3*exp(2)^7-64*a^6*d^5*exp(1)^8*exp(2)^2*c+224*a^6*d^5*exp(1)^6*exp(2)^3*c-288*a^6*
d^5*exp(1)^4*exp(2)^4*c+160*a^6*d^5*exp(1)^2*exp(2)^5*c-32*a^6*d^5*exp(2)^6*c+128*a^5*d^7*exp(1)^10*c^2-512*a^
5*d^7*exp(1)^8*exp(2)*c^2+816*a^5*d^7*exp(1)^6*exp(2)^2*c^2-656*a^5*d^7*exp(1)^4*exp(2)^3*c^2+272*a^5*d^7*exp(
1)^2*exp(2)^4*c^2-48*a^5*d^7*exp(2)^5*c^2-64*a^4*d^9*exp(1)^8*c^3+224*a^4*d^9*exp(1)^6*exp(2)*c^3-288*a^4*d^9*
exp(1)^4*exp(2)^2*c^3+160*a^4*d^9*exp(1)^2*exp(2)^3*c^3-32*a^4*d^9*exp(2)^4*c^3+8*a^3*d^11*exp(1)^6*c^4-24*a^3
*d^11*exp(1)^4*exp(2)*c^4+24*a^3*d^11*exp(1)^2*exp(2)^2*c^4-8*a^3*d^11*exp(2)^3*c^4)))/2/(8*a^6*d^3*exp(1)^4*e
xp(2)^4*c-16*a^6*d^3*exp(1)^2*exp(2)^5*c+8*a^6*d^3*exp(2)^6*c-64*a^5*d^5*exp(1)^6*exp(2)^2*c^2+160*a^5*d^5*exp
(1)^4*exp(2)^3*c^2-128*a^5*d^5*exp(1)^2*exp(2)^4*c^2+32*a^5*d^5*exp(2)^5*c^2+128*a^4*d^7*exp(1)^8*c^3-384*a^4*
d^7*exp(1)^6*exp(2)*c^3+432*a^4*d^7*exp(1)^4*exp(2)^2*c^3-224*a^4*d^7*exp(1)^2*exp(2)^3*c^3+48*a^4*d^7*exp(2)^
4*c^3-64*a^3*d^9*exp(1)^6*c^4+160*a^3*d^9*exp(1)^4*exp(2)*c^4-128*a^3*d^9*exp(1)^2*exp(2)^2*c^4+32*a^3*d^9*exp
(2)^3*c^4+8*a^2*d^11*exp(1)^4*c^5-16*a^2*d^11*exp(1)^2*exp(2)*c^5+8*a^2*d^11*exp(2)^2*c^5)))+(-3*sqrt(d+x*exp(
1))*(d+x*exp(1))^3*a^3*d^2*exp(1)^2*exp(2)^3*c^2+24*sqrt(d+x*exp(1))*(d+x*exp(1))^3*a^2*d^4*exp(1)^4*exp(2)*c^
3-15*sqrt(d+x*exp(1))*(d+x*exp(1))^3*a^2*d^4*exp(1)^2*exp(2)^2*c^3-24*sqrt(d+x*exp(1))*(d+x*exp(1))^3*a*d^6*ex
p(1)^4*c^4+15*sqrt(d+x*exp(1))*(d+x*exp(1))^3*a*d^6*exp(1)^2*exp(2)*c^4+3*sqrt(d+x*exp(1))*(d+x*exp(1))^3*d^8*
exp(1)^2*c^5-6*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a^4*d*exp(1)^2*exp(2)^4*c+49*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a^
3*d^3*exp(1)^4*exp(2)^2*c^2-25*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a^3*d^3*exp(1)^2*exp(2)^3*c^2-28*sqrt(d+x*exp(1
))*(d+x*exp(1))^2*a^2*d^5*exp(1)^6*c^3-42*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a^2*d^5*exp(1)^4*exp(2)*c^3+34*sqrt(
d+x*exp(1))*(d+x*exp(1))^2*a^2*d^5*exp(1)^2*exp(2)^2*c^3+49*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a*d^7*exp(1)^4*c^4
-25*sqrt(d+x*exp(1))*(d+x*exp(1))^2*a*d^7*exp(1)^2*exp(2)*c^4-6*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^9*exp(1)^2*c
^5-3*sqrt(d+x*exp(1))*(d+x*exp(1))*a^5*exp(1)^2*exp(2)^5+20*sqrt(d+x*exp(1))*(d+x*exp(1))*a^4*d^2*exp(1)^4*exp
(2)^3*c-5*sqrt(d+x*exp(1))*(d+x*exp(1))*a^4*d^2*exp(1)^2*exp(2)^4*c+4*sqrt(d+x*exp(1))*(d+x*exp(1))*a^3*d^4*ex
p(1)^6*exp(2)*c^2-68*sqrt(d+x*exp(1))*(d+x*exp(1))*a^3*d^4*exp(1)^4*exp(2)^2*c^2+34*sqrt(d+x*exp(1))*(d+x*exp(
1))*a^3*d^4*exp(1)^2*exp(2)^3*c^2-4*sqrt(d+x*exp(1))*(d+x*exp(1))*a^2*d^6*exp(1)^6*c^3+68*sqrt(d+x*exp(1))*(d+
x*exp(1))*a^2*d^6*exp(1)^4*exp(2)*c^3-34*sqrt(d+x*exp(1))*(d+x*exp(1))*a^2*d^6*exp(1)^2*exp(2)^2*c^3-20*sqrt(d
+x*exp(1))*(d+x*exp(1))*a*d^8*exp(1)^4*c^4+5*sqrt(d+x*exp(1))*(d+x*exp(1))*a*d^8*exp(1)^2*exp(2)*c^4+3*sqrt(d+
x*exp(1))*(d+x*exp(1))*d^10*exp(1)^2*c^5-5*sqrt(d+x*exp(1))*a^5*d*exp(1)^4*exp(2)^4+5*sqrt(d+x*exp(1))*a^5*d*e
xp(1)^2*exp(2)^5+37*sqrt(d+x*exp(1))*a^4*d^3*exp(1)^6*exp(2)^2*c-54*sqrt(d+x*exp(1))*a^4*d^3*exp(1)^4*exp(2)^3
*c+17*sqrt(d+x*exp(1))*a^4*d^3*exp(1)^2*exp(2)^4*c-44*sqrt(d+x*exp(1))*a^3*d^5*exp(1)^8*c^2+58*sqrt(d+x*exp(1)
)*a^3*d^5*exp(1)^6*exp(2)*c^2-14*sqrt(d+x*exp(1))*a^3*d^5*exp(1)^4*exp(2)^2*c^2+37*sqrt(d+x*exp(1))*a^2*d^7*ex
p(1)^6*c^3-54*sqrt(d+x*exp(1))*a^2*d^7*exp(1)^4*exp(2)*c^3+17*sqrt(d+x*exp(1))*a^2*d^7*exp(1)^2*exp(2)^2*c^3-5
*sqrt(d+x*exp(1))*a*d^9*exp(1)^4*c^4+5*sqrt(d+x*exp(1))*a*d^9*exp(1)^2*exp(2)*c^4)/(-8*a^6*d^2*exp(1)^4*exp(2)
^4+16*a^6*d^2*exp(1)^2*exp(2)^5-8*a^6*d^2*exp(2)^6+64*a^5*d^4*exp(1)^6*exp(2)^2*c-160*a^5*d^4*exp(1)^4*exp(2)^
3*c+128*a^5*d^4*exp(1)^2*exp(2)^4*c-32*a^5*d^4*exp(2)^5*c-128*a^4*d^6*exp(1)^8*c^2+384*a^4*d^6*exp(1)^6*exp(2)
*c^2-432*a^4*d^6*exp(1)^4*exp(2)^2*c^2+224*a^4*d^6*exp(1)^2*exp(2)^3*c^2-48*a^4*d^6*exp(2)^4*c^2+64*a^3*d^8*ex
p(1)^6*c^3-160*a^3*d^8*exp(1)^4*exp(2)*c^3+128*a^3*d^8*exp(1)^2*exp(2)^2*c^3-32*a^3*d^8*exp(2)^3*c^3-8*a^2*d^1
0*exp(1)^4*c^4+16*a^2*d^10*exp(1)^2*exp(2)*c^4-8*a^2*d^10*exp(2)^2*c^4)/((d+x*exp(1))^2*d*c+(d+x*exp(1))*a*exp
(2)-(d+x*exp(1))*d^2*c+a*d*exp(1)^2-a*d*exp(2))^2)

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maple [A]  time = 0.06, size = 294, normalized size = 1.20 \begin {gather*} -\frac {17 \sqrt {e x +d}\, a \,c^{3} d^{3} e^{4}}{4 \left (a \,e^{2}-c \,d^{2}\right )^{5} \left (c d e x +a \,e^{2}\right )^{2}}+\frac {17 \sqrt {e x +d}\, c^{4} d^{5} e^{2}}{4 \left (a \,e^{2}-c \,d^{2}\right )^{5} \left (c d e x +a \,e^{2}\right )^{2}}-\frac {15 \left (e x +d \right )^{\frac {3}{2}} c^{4} d^{4} e^{2}}{4 \left (a \,e^{2}-c \,d^{2}\right )^{5} \left (c d e x +a \,e^{2}\right )^{2}}-\frac {63 c^{3} d^{3} e^{2} \arctan \left (\frac {\sqrt {e x +d}\, c d}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}\right )}{4 \left (a \,e^{2}-c \,d^{2}\right )^{5} \sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}-\frac {12 c^{2} d^{2} e^{2}}{\left (a \,e^{2}-c \,d^{2}\right )^{5} \sqrt {e x +d}}+\frac {2 c d \,e^{2}}{\left (a \,e^{2}-c \,d^{2}\right )^{4} \left (e x +d \right )^{\frac {3}{2}}}-\frac {2 e^{2}}{5 \left (a \,e^{2}-c \,d^{2}\right )^{3} \left (e x +d \right )^{\frac {5}{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15/4*e^2/(a*e^2-c*d^2)^5*c^4*d^4/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)-17/4*e^4/(a*e^2-c*d^2)^5*c^3*d^3/(c*d*e*x+a*
e^2)^2*(e*x+d)^(1/2)*a+17/4*e^2/(a*e^2-c*d^2)^5*c^4*d^5/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)-63/4*e^2/(a*e^2-c*d^2)
^5*c^3*d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/5*e^2/(a*e^2-c*d^2)
^3/(e*x+d)^(5/2)-12*e^2/(a*e^2-c*d^2)^5*c^2*d^2/(e*x+d)^(1/2)+2*e^2/(a*e^2-c*d^2)^4*c*d/(e*x+d)^(3/2)

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(a*e^2-c*d^2>0)', see `assume?`
for more details)Is a*e^2-c*d^2 positive or negative?

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mupad [B]  time = 0.95, size = 344, normalized size = 1.41 \begin {gather*} -\frac {\frac {2\,e^2}{5\,\left (a\,e^2-c\,d^2\right )}-\frac {6\,c\,d\,e^2\,\left (d+e\,x\right )}{5\,{\left (a\,e^2-c\,d^2\right )}^2}+\frac {42\,c^2\,d^2\,e^2\,{\left (d+e\,x\right )}^2}{5\,{\left (a\,e^2-c\,d^2\right )}^3}+\frac {105\,c^3\,d^3\,e^2\,{\left (d+e\,x\right )}^3}{4\,{\left (a\,e^2-c\,d^2\right )}^4}+\frac {63\,c^4\,d^4\,e^2\,{\left (d+e\,x\right )}^4}{4\,{\left (a\,e^2-c\,d^2\right )}^5}}{{\left (d+e\,x\right )}^{5/2}\,\left (a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right )-\left (2\,c^2\,d^3-2\,a\,c\,d\,e^2\right )\,{\left (d+e\,x\right )}^{7/2}+c^2\,d^2\,{\left (d+e\,x\right )}^{9/2}}-\frac {63\,c^{5/2}\,d^{5/2}\,e^2\,\mathrm {atan}\left (\frac {\sqrt {c}\,\sqrt {d}\,\sqrt {d+e\,x}\,\left (a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right )}{{\left (a\,e^2-c\,d^2\right )}^{11/2}}\right )}{4\,{\left (a\,e^2-c\,d^2\right )}^{11/2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- ((2*e^2)/(5*(a*e^2 - c*d^2)) - (6*c*d*e^2*(d + e*x))/(5*(a*e^2 - c*d^2)^2) + (42*c^2*d^2*e^2*(d + e*x)^2)/(5
*(a*e^2 - c*d^2)^3) + (105*c^3*d^3*e^2*(d + e*x)^3)/(4*(a*e^2 - c*d^2)^4) + (63*c^4*d^4*e^2*(d + e*x)^4)/(4*(a
*e^2 - c*d^2)^5))/((d + e*x)^(5/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2) - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(
7/2) + c^2*d^2*(d + e*x)^(9/2)) - (63*c^(5/2)*d^(5/2)*e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^5*e^10 - c^
5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6))/(a*e^2 - c*d^2)^(11/2))
)/(4*(a*e^2 - c*d^2)^(11/2))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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