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

Optimal. Leaf size=192 \[ \frac {7 c^{5/2} d^{5/2} e \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{\left (c d^2-a e^2\right )^{9/2}}-\frac {7 c^2 d^2 e}{\sqrt {d+e x} \left (c d^2-a e^2\right )^4}-\frac {7 c d e}{3 (d+e x)^{3/2} \left (c d^2-a e^2\right )^3}-\frac {1}{(d+e x)^{5/2} \left (c d^2-a e^2\right ) (a e+c d x)}-\frac {7 e}{5 (d+e x)^{5/2} \left (c d^2-a e^2\right )^2} \]

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Rubi [A]  time = 0.13, antiderivative size = 192, normalized size of antiderivative = 1.00, number of steps used = 7, 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 {7 c^2 d^2 e}{\sqrt {d+e x} \left (c d^2-a e^2\right )^4}+\frac {7 c^{5/2} d^{5/2} e \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{\left (c d^2-a e^2\right )^{9/2}}-\frac {7 c d e}{3 (d+e x)^{3/2} \left (c d^2-a e^2\right )^3}-\frac {1}{(d+e x)^{5/2} \left (c d^2-a e^2\right ) (a e+c d x)}-\frac {7 e}{5 (d+e x)^{5/2} \left (c d^2-a e^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-7*e)/(5*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*(d + e*x)^(5/2)) - (7*c*d*e)/(
3*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) - (7*c^2*d^2*e)/((c*d^2 - a*e^2)^4*Sqrt[d + e*x]) + (7*c^(5/2)*d^(5/2)*e*
ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(9/2)

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

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Mathematica [C]  time = 0.02, size = 59, normalized size = 0.31 \begin {gather*} -\frac {2 e \, _2F_1\left (-\frac {5}{2},2;-\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 )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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IntegrateAlgebraic [A]  time = 0.54, size = 270, normalized size = 1.41 \begin {gather*} \frac {6 a^3 e^7-18 a^2 c d^2 e^5-14 a^2 c d e^5 (d+e x)+18 a c^2 d^4 e^3+28 a c^2 d^3 e^3 (d+e x)+70 a c^2 d^2 e^3 (d+e x)^2-6 c^3 d^6 e-14 c^3 d^5 e (d+e x)-70 c^3 d^4 e (d+e x)^2+105 c^3 d^3 e (d+e x)^3}{15 (d+e x)^{5/2} \left (c d^2-a e^2\right )^4 \left (-a e^2+c d^2-c d (d+e x)\right )}+\frac {7 c^{5/2} d^{5/2} e \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 )}{\left (a e^2-c d^2\right )^{9/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-6*c^3*d^6*e + 18*a*c^2*d^4*e^3 - 18*a^2*c*d^2*e^5 + 6*a^3*e^7 - 14*c^3*d^5*e*(d + e*x) + 28*a*c^2*d^3*e^3*(d
+ e*x) - 14*a^2*c*d*e^5*(d + e*x) - 70*c^3*d^4*e*(d + e*x)^2 + 70*a*c^2*d^2*e^3*(d + e*x)^2 + 105*c^3*d^3*e*(
d + e*x)^3)/(15*(c*d^2 - a*e^2)^4*(d + e*x)^(5/2)*(c*d^2 - a*e^2 - c*d*(d + e*x))) + (7*c^(5/2)*d^(5/2)*e*ArcT
an[(Sqrt[c]*Sqrt[d]*Sqrt[-(c*d^2) + a*e^2]*Sqrt[d + e*x])/(c*d^2 - a*e^2)])/(-(c*d^2) + a*e^2)^(9/2)

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fricas [B]  time = 0.45, size = 1331, normalized size = 6.93

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

[1/30*(105*(c^3*d^3*e^4*x^4 + a*c^2*d^5*e^2 + (3*c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + 3*(c^3*d^5*e^2 + a*c^2*d^3
*e^4)*x^2 + (c^3*d^6*e + 3*a*c^2*d^4*e^3)*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*(105*c^3*d^3*e^3*x^3 + 15*c^3*d^6 + 11
6*a*c^2*d^4*e^2 - 32*a^2*c*d^2*e^4 + 6*a^3*e^6 + 35*(7*c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + 7*(23*c^3*d^5*e +
24*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a*c^4*d^11*e - 4*a^2*c^3*d^9*e^3 + 6*a^3*c^2*d^7*e^5 - 4*
a^4*c*d^5*e^7 + a^5*d^3*e^9 + (c^5*d^9*e^3 - 4*a*c^4*d^7*e^5 + 6*a^2*c^3*d^5*e^7 - 4*a^3*c^2*d^3*e^9 + a^4*c*d
*e^11)*x^4 + (3*c^5*d^10*e^2 - 11*a*c^4*d^8*e^4 + 14*a^2*c^3*d^6*e^6 - 6*a^3*c^2*d^4*e^8 - a^4*c*d^2*e^10 + a^
5*e^12)*x^3 + 3*(c^5*d^11*e - 3*a*c^4*d^9*e^3 + 2*a^2*c^3*d^7*e^5 + 2*a^3*c^2*d^5*e^7 - 3*a^4*c*d^3*e^9 + a^5*
d*e^11)*x^2 + (c^5*d^12 - a*c^4*d^10*e^2 - 6*a^2*c^3*d^8*e^4 + 14*a^3*c^2*d^6*e^6 - 11*a^4*c*d^4*e^8 + 3*a^5*d
^2*e^10)*x), 1/15*(105*(c^3*d^3*e^4*x^4 + a*c^2*d^5*e^2 + (3*c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + 3*(c^3*d^5*e^2
+ a*c^2*d^3*e^4)*x^2 + (c^3*d^6*e + 3*a*c^2*d^4*e^3)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sq
rt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (105*c^3*d^3*e^3*x^3 + 15*c^3*d^6 + 116*a*c^2*d^4*
e^2 - 32*a^2*c*d^2*e^4 + 6*a^3*e^6 + 35*(7*c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + 7*(23*c^3*d^5*e + 24*a*c^2*d^3
*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a*c^4*d^11*e - 4*a^2*c^3*d^9*e^3 + 6*a^3*c^2*d^7*e^5 - 4*a^4*c*d^5*e^
7 + a^5*d^3*e^9 + (c^5*d^9*e^3 - 4*a*c^4*d^7*e^5 + 6*a^2*c^3*d^5*e^7 - 4*a^3*c^2*d^3*e^9 + a^4*c*d*e^11)*x^4 +
(3*c^5*d^10*e^2 - 11*a*c^4*d^8*e^4 + 14*a^2*c^3*d^6*e^6 - 6*a^3*c^2*d^4*e^8 - a^4*c*d^2*e^10 + a^5*e^12)*x^3
+ 3*(c^5*d^11*e - 3*a*c^4*d^9*e^3 + 2*a^2*c^3*d^7*e^5 + 2*a^3*c^2*d^5*e^7 - 3*a^4*c*d^3*e^9 + a^5*d*e^11)*x^2
+ (c^5*d^12 - a*c^4*d^10*e^2 - 6*a^2*c^3*d^8*e^4 + 14*a^3*c^2*d^6*e^6 - 11*a^4*c*d^4*e^8 + 3*a^5*d^2*e^10)*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)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((12*a^7*c*d*exp(1)*exp(2)^7-6*a^7*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)*exp
(2)^7-148*a^6*c^2*d^3*exp(1)^3*exp(2)^5+64*a^6*c^2*d^3*exp(1)*exp(2)^6-12*a^6*c^2*d^2*exp(1)*exp(2)^6+74*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)*ex
p(1)^3*exp(2)^5-32*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)*exp(1)*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)*exp(1)*exp(2)^6+6*a^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)*exp(2)^6+608*a^5*c^3*d^5*exp(1)^5*exp(2)^3-476*a^5*c^3*d^5*exp(1)^3*exp(2)^4+120*a^5*c^3*d^5*
exp(1)*exp(2)^5+124*a^5*c^3*d^4*exp(1)^3*exp(2)^4-52*a^5*c^3*d^4*exp(1)*exp(2)^5-304*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)*exp(1)^5*exp(2)^3+23
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)*exp(1)^3*exp(2)^4-60*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)*exp(1)*exp(2)^5-100*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)*exp(1)^3*exp(2)^4+28*a^5*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)*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)*exp
(1)*exp(2)^5-62*a^5*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)^3*exp(2)^4+26*a^5*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)*exp(2)^5-12*a^5*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)*exp(2)^5-12*a^5*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)*exp(2)^5-832*a^4*c^4*d^7*exp(1)^7*exp(2)+672*a^4*c^4*d^7*exp(1)^5*exp(2)^2-328*a^4*c^4*d^7*exp(
1)^3*exp(2)^3+68*a^4*c^4*d^7*exp(1)*exp(2)^4-384*a^4*c^4*d^6*exp(1)^5*exp(2)^2+272*a^4*c^4*d^6*exp(1)^3*exp(2)
^3-68*a^4*c^4*d^6*exp(1)*exp(2)^4+416*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)*exp(1)^7*exp(2)-336*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)*exp(1)^5*exp(2)^2+164*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)*exp(1)^3*exp(2)
^3-34*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)*exp(1)*exp(2)^4+208*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)*exp(1)^5*exp(2)^2-16*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)*exp(1)^3*exp(2)^3-12*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)*exp(1)*exp(2)^4+50*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
)*exp(1)^3*exp(2)^3-20*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*ex
p(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^4+192*a^4*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*ex
p(2))*exp(1)^5*exp(2)^2-136*a^4*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)^3*exp(2
)^3+34*a^4*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)*exp(2)^4+76*a^4*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)^3*exp(2)^3-16*a^4*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)*exp(2)^4+100*a^4*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)^3*exp(2)^3-40*a^4*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)
*exp(2)^4+6*a^4*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)*exp(2)^4+12*a^4*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)*exp(2)^4+832*a^3*c^5*d^9*exp(1)^7-672*a^3*c
^5*d^9*exp(1)^5*exp(2)+328*a^3*c^5*d^9*exp(1)^3*exp(2)^2-68*a^3*c^5*d^9*exp(1)*exp(2)^3+320*a^3*c^5*d^8*exp(1)
^7-192*a^3*c^5*d^8*exp(1)^5*exp(2)+168*a^3*c^5*d^8*exp(1)^3*exp(2)^2-56*a^3*c^5*d^8*exp(1)*exp(2)^3-416*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)*e
xp(1)^7+336*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)*exp(1)^5*exp(2)-164*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)*exp(1)^3*exp(2)^2+34*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)*exp(1)*exp(2)^3-416*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)*exp(1)^5*exp(2)+2
32*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)*exp(1)^3*exp(2)^2-56*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)*exp(1)*exp(2)^3-104*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)*exp(1)^5*exp(2)+58*a^3*c^4*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)*exp(1)^3*exp(2)^2-14*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)*e
xp(1)*exp(2)^3-160*a^3*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)^7+96*a^3*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)^5*exp(2)-84*a^3*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)^3*exp(2)^2+28*a^3*c^3*d^6*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)*exp(2)^3-80*a^3*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)^5*e
xp(2)-68*a^3*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*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)^3*exp(2)^2+28*a^3*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)*exp(2)^3-208*a^3*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)^5*exp(2)+116*a^3*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)^3*exp(2)^2-28*a^3*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)*exp(2)^3-38*a^3*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)^3*exp(2)^2+14*a^
3*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)*exp(2)^3-76*a^3*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)^3*exp(2)^2+28*a^3*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)*exp(2)^3-608*a^2*c^6*d^11*exp(1)^5+476*a^2*c^6*d^11*exp(1)^3*exp(2)-120*a^2
*c^6*d^11*exp(1)*exp(2)^2-384*a^2*c^6*d^10*exp(1)^5+272*a^2*c^6*d^10*exp(1)^3*exp(2)-68*a^2*c^6*d^10*exp(1)*ex
p(2)^2+304*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)*exp(1)^5-238*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)*exp(1)^3*exp(2)+60*a^2*c^5*d^10*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)*exp(1)*exp(2)^2+208*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)*exp(1)^5-16*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)*exp(1)^
3*exp(2)-12*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)*exp(1)*exp(2)^2+104*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)*exp(1)^5-58*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)*exp(1)^3*exp(2)+14*a^2*c^5*d^8*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)*exp(1)*exp(2)^2+192*a^2*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)*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)^5-136*a^2*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)^3*exp(2)+34*a^2*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)*exp(2)^2+80*a^2*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)^5+68*a^
2*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)^3*exp(2)-28*a^2*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)*exp(2)^2+208*a^2*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)^5-116*a^2*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))*ex
p(1)^3*exp(2)+28*a^2*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)*exp(2)^2+40*a^2
*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)^5-4*a^2*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)^3*exp(2)+80*a^2*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)^5-8*a^2*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)^3*exp(2
)+148*a*c^7*d^13*exp(1)^3-64*a*c^7*d^13*exp(1)*exp(2)+124*a*c^7*d^12*exp(1)^3-52*a*c^7*d^12*exp(1)*exp(2)-74*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)*exp(1)^3+32*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)*exp(1)*exp(2)-100*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)*exp(1)^3+28*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)*exp(1)*exp(2)-50*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)*exp(1)^3+20*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)*exp(1)*exp(2)-62
*a*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))*sqr
t(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)^3+26*a*c^5*d^10*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)*sqrt(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)*exp(2)-76*a*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)^3+16*a*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)*exp(2)-100*a*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)^3+40*a*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)*exp(2)-38*a*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)^3+14*a*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)*exp(2)-76*a*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)^3+28*a*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)*exp(2)-12*c^8*d^15*exp(1)-12*c^8*d^14*exp(1)+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)*exp(1)+12*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)+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)*exp(1)+6*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*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)+12*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)+12*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)+6*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)+12*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))/(16*a^9*d^3*exp(1)^6*exp(2)^6-48*a^9*d^3*exp(1)^4*
exp(2)^7+48*a^9*d^3*exp(1)^2*exp(2)^8-16*a^9*d^3*exp(2)^9-192*a^8*c*d^5*exp(1)^8*exp(2)^4+672*a^8*c*d^5*exp(1)
^6*exp(2)^5-864*a^8*c*d^5*exp(1)^4*exp(2)^6+480*a^8*c*d^5*exp(1)^2*exp(2)^7-96*a^8*c*d^5*exp(2)^8-32*a^8*c*d^4
*exp(1)^6*exp(2)^5+96*a^8*c*d^4*exp(1)^4*exp(2)^6-96*a^8*c*d^4*exp(1)^2*exp(2)^7+32*a^8*c*d^4*exp(2)^8+768*a^7
*c^2*d^7*exp(1)^10*exp(2)^2-3072*a^7*c^2*d^7*exp(1)^8*exp(2)^3+4848*a^7*c^2*d^7*exp(1)^6*exp(2)^4-3792*a^7*c^2
*d^7*exp(1)^4*exp(2)^5+1488*a^7*c^2*d^7*exp(1)^2*exp(2)^6-240*a^7*c^2*d^7*exp(2)^7+256*a^7*c^2*d^6*exp(1)^8*ex
p(2)^3-864*a^7*c^2*d^6*exp(1)^6*exp(2)^4+1056*a^7*c^2*d^6*exp(1)^4*exp(2)^5-544*a^7*c^2*d^6*exp(1)^2*exp(2)^6+
96*a^7*c^2*d^6*exp(2)^7+16*a^7*c^2*d^5*exp(1)^6*exp(2)^4-48*a^7*c^2*d^5*exp(1)^4*exp(2)^5+48*a^7*c^2*d^5*exp(1
)^2*exp(2)^6-16*a^7*c^2*d^5*exp(2)^7-1024*a^6*c^3*d^9*exp(1)^12+4608*a^6*c^3*d^9*exp(1)^10*exp(2)-8832*a^6*c^3
*d^9*exp(1)^8*exp(2)^2+9408*a^6*c^3*d^9*exp(1)^6*exp(2)^3-5952*a^6*c^3*d^9*exp(1)^4*exp(2)^4+2112*a^6*c^3*d^9*
exp(1)^2*exp(2)^5-320*a^6*c^3*d^9*exp(2)^6-512*a^6*c^3*d^8*exp(1)^10*exp(2)+1792*a^6*c^3*d^8*exp(1)^8*exp(2)^2
-2368*a^6*c^3*d^8*exp(1)^6*exp(2)^3+1472*a^6*c^3*d^8*exp(1)^4*exp(2)^4-448*a^6*c^3*d^8*exp(1)^2*exp(2)^5+64*a^
6*c^3*d^8*exp(2)^6-128*a^6*c^3*d^7*exp(1)^8*exp(2)^2+448*a^6*c^3*d^7*exp(1)^6*exp(2)^3-576*a^6*c^3*d^7*exp(1)^
4*exp(2)^4+320*a^6*c^3*d^7*exp(1)^2*exp(2)^5-64*a^6*c^3*d^7*exp(2)^6+768*a^5*c^4*d^11*exp(1)^10-3072*a^5*c^4*d
^11*exp(1)^8*exp(2)+4848*a^5*c^4*d^11*exp(1)^6*exp(2)^2-3792*a^5*c^4*d^11*exp(1)^4*exp(2)^3+1488*a^5*c^4*d^11*
exp(1)^2*exp(2)^4-240*a^5*c^4*d^11*exp(2)^5+512*a^5*c^4*d^10*exp(1)^10-1792*a^5*c^4*d^10*exp(1)^8*exp(2)+2368*
a^5*c^4*d^10*exp(1)^6*exp(2)^2-1472*a^5*c^4*d^10*exp(1)^4*exp(2)^3+448*a^5*c^4*d^10*exp(1)^2*exp(2)^4-64*a^5*c
^4*d^10*exp(2)^5+256*a^5*c^4*d^9*exp(1)^10-1024*a^5*c^4*d^9*exp(1)^8*exp(2)+1632*a^5*c^4*d^9*exp(1)^6*exp(2)^2
-1312*a^5*c^4*d^9*exp(1)^4*exp(2)^3+544*a^5*c^4*d^9*exp(1)^2*exp(2)^4-96*a^5*c^4*d^9*exp(2)^5-192*a^4*c^5*d^13
*exp(1)^8+672*a^4*c^5*d^13*exp(1)^6*exp(2)-864*a^4*c^5*d^13*exp(1)^4*exp(2)^2+480*a^4*c^5*d^13*exp(1)^2*exp(2)
^3-96*a^4*c^5*d^13*exp(2)^4-256*a^4*c^5*d^12*exp(1)^8+864*a^4*c^5*d^12*exp(1)^6*exp(2)-1056*a^4*c^5*d^12*exp(1
)^4*exp(2)^2+544*a^4*c^5*d^12*exp(1)^2*exp(2)^3-96*a^4*c^5*d^12*exp(2)^4-128*a^4*c^5*d^11*exp(1)^8+448*a^4*c^5
*d^11*exp(1)^6*exp(2)-576*a^4*c^5*d^11*exp(1)^4*exp(2)^2+320*a^4*c^5*d^11*exp(1)^2*exp(2)^3-64*a^4*c^5*d^11*ex
p(2)^4+16*a^3*c^6*d^15*exp(1)^6-48*a^3*c^6*d^15*exp(1)^4*exp(2)+48*a^3*c^6*d^15*exp(1)^2*exp(2)^2-16*a^3*c^6*d
^15*exp(2)^3+32*a^3*c^6*d^14*exp(1)^6-96*a^3*c^6*d^14*exp(1)^4*exp(2)+96*a^3*c^6*d^14*exp(1)^2*exp(2)^2-32*a^3
*c^6*d^14*exp(2)^3+16*a^3*c^6*d^13*exp(1)^6-48*a^3*c^6*d^13*exp(1)^4*exp(2)+48*a^3*c^6*d^13*exp(1)^2*exp(2)^2-
16*a^3*c^6*d^13*exp(2)^3)/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(2*c^3*d^8*exp(1)^4*a^2-4*c^3*d^8*exp(1)^2
*a^2*exp(2)+2*c^3*d^8*a^2*exp(2)^2-8*c^2*d^6*exp(1)^6*a^3+18*c^2*d^6*exp(1)^4*a^3*exp(2)-12*c^2*d^6*exp(1)^2*a
^3*exp(2)^2+2*c^2*d^6*a^3*exp(2)^3+8*c*d^4*exp(1)^6*a^4*exp(2)-18*c*d^4*exp(1)^4*a^4*exp(2)^2+12*c*d^4*exp(1)^
2*a^4*exp(2)^3-2*c*d^4*a^4*exp(2)^4-2*d^2*exp(1)^4*a^5*exp(2)^3+4*d^2*exp(1)^2*a^5*exp(2)^4-2*d^2*a^5*exp(2)^5
+sqrt((-2*c^3*d^8*exp(1)^4*a^2+4*c^3*d^8*exp(1)^2*a^2*exp(2)-2*c^3*d^8*a^2*exp(2)^2+8*c^2*d^6*exp(1)^6*a^3-18*
c^2*d^6*exp(1)^4*a^3*exp(2)+12*c^2*d^6*exp(1)^2*a^3*exp(2)^2-2*c^2*d^6*a^3*exp(2)^3-8*c*d^4*exp(1)^6*a^4*exp(2
)+18*c*d^4*exp(1)^4*a^4*exp(2)^2-12*c*d^4*exp(1)^2*a^4*exp(2)^3+2*c*d^4*a^4*exp(2)^4+2*d^2*exp(1)^4*a^5*exp(2)
^3-4*d^2*exp(1)^2*a^5*exp(2)^4+2*d^2*a^5*exp(2)^5)*(-2*c^3*d^8*exp(1)^4*a^2+4*c^3*d^8*exp(1)^2*a^2*exp(2)-2*c^
3*d^8*a^2*exp(2)^2+8*c^2*d^6*exp(1)^6*a^3-18*c^2*d^6*exp(1)^4*a^3*exp(2)+12*c^2*d^6*exp(1)^2*a^3*exp(2)^2-2*c^
2*d^6*a^3*exp(2)^3-8*c*d^4*exp(1)^6*a^4*exp(2)+18*c*d^4*exp(1)^4*a^4*exp(2)^2-12*c*d^4*exp(1)^2*a^4*exp(2)^3+2
*c*d^4*a^4*exp(2)^4+2*d^2*exp(1)^4*a^5*exp(2)^3-4*d^2*exp(1)^2*a^5*exp(2)^4+2*d^2*a^5*exp(2)^5)-4*(2*c^3*d^7*e
xp(1)^4*a^2-4*c^3*d^7*exp(1)^2*a^2*exp(2)+2*c^3*d^7*a^2*exp(2)^2-8*c^2*d^5*exp(1)^6*a^3+20*c^2*d^5*exp(1)^4*a^
3*exp(2)-16*c^2*d^5*exp(1)^2*a^3*exp(2)^2+4*c^2*d^5*a^3*exp(2)^3+2*c*d^3*exp(1)^4*a^4*exp(2)^2-4*c*d^3*exp(1)^
2*a^4*exp(2)^3+2*c*d^3*a^4*exp(2)^4)*(2*c^2*d^7*exp(1)^6*a^3-6*c^2*d^7*exp(1)^4*a^3*exp(2)+6*c^2*d^7*exp(1)^2*
a^3*exp(2)^2-2*c^2*d^7*a^3*exp(2)^3-8*c*d^5*exp(1)^8*a^4+28*c*d^5*exp(1)^6*a^4*exp(2)-36*c*d^5*exp(1)^4*a^4*ex
p(2)^2+20*c*d^5*exp(1)^2*a^4*exp(2)^3-4*c*d^5*a^4*exp(2)^4+2*d^3*exp(1)^6*a^5*exp(2)^2-6*d^3*exp(1)^4*a^5*exp(
2)^3+6*d^3*exp(1)^2*a^5*exp(2)^4-2*d^3*a^5*exp(2)^5)))/2/(2*c^3*d^7*exp(1)^4*a^2-4*c^3*d^7*exp(1)^2*a^2*exp(2)
+2*c^3*d^7*a^2*exp(2)^2-8*c^2*d^5*exp(1)^6*a^3+20*c^2*d^5*exp(1)^4*a^3*exp(2)-16*c^2*d^5*exp(1)^2*a^3*exp(2)^2
+4*c^2*d^5*a^3*exp(2)^3+2*c*d^3*exp(1)^4*a^4*exp(2)^2-4*c*d^3*exp(1)^2*a^4*exp(2)^3+2*c*d^3*a^4*exp(2)^4)))-(1
2*a^7*c*d*exp(1)*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)*exp(1)*exp(2)^7-148*a^6*c^2*d^3*exp(1)^3*exp(2)^5+64*a^6*c^2*d^3*exp(1)*exp(2)^6-12*a
^6*c^2*d^2*exp(1)*exp(2)^6-74*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)*exp(1)^3*exp(2)^5+32*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)*exp(1)*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)*exp(1)*exp(2)^6+6*a^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)*exp(2)^6+608*a^5*c^3*d^5*exp(1)^5*exp(2)^3-476*a^5*c^3*d^5
*exp(1)^3*exp(2)^4+120*a^5*c^3*d^5*exp(1)*exp(2)^5+124*a^5*c^3*d^4*exp(1)^3*exp(2)^4-52*a^5*c^3*d^4*exp(1)*exp
(2)^5+304*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*e
xp(2))*sqrt(2)*exp(1)^5*exp(2)^3-238*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)*exp(1)^3*exp(2)^4+60*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)*exp(1)*exp(2)^5+100*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)*exp(1)^3*exp(2)^4
-28*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)*exp(1)*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)*exp(1)*exp(2)^5-62*a^5*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*e
xp(2))*exp(1)^3*exp(2)^4+26*a^5*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)*exp(2)^5-
12*a^5*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)*exp(2)^5-12*a^5*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)*exp(2)^5-832*a^4*c^4*d^7*exp(1)^7*exp(2)+672*a^4*c^4*d^7*exp
(1)^5*exp(2)^2-328*a^4*c^4*d^7*exp(1)^3*exp(2)^3+68*a^4*c^4*d^7*exp(1)*exp(2)^4-384*a^4*c^4*d^6*exp(1)^5*exp(2
)^2+272*a^4*c^4*d^6*exp(1)^3*exp(2)^3-68*a^4*c^4*d^6*exp(1)*exp(2)^4-416*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)*exp(1)^7*exp(2)+336*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)*exp(1)^
5*exp(2)^2-164*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)*exp(1)^3*exp(2)^3+34*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)*exp(1)*exp(2)^4-208*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)*exp(1)^5*exp(2)^2+16*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)*exp(1)^3*exp(
2)^3+12*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)*exp(1)*exp(2)^4-50*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)*exp(1)^3*exp(2)^3+20*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)*exp(1)*exp(2)^4+192*a^4*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)^5*exp(2)^2-136*a^4*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)^3*exp(2)^3+34*a^4*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*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)*exp(2)^4+76*a^4*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)^3*exp(2)^3-16*a^
4*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)*exp(2)^4+100*a^4*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)^3*exp(2)^3-40*a^4*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)*exp(2)^4+6*a^4*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)*exp(2)^4+12*a^4*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)*exp(2)^4
+832*a^3*c^5*d^9*exp(1)^7-672*a^3*c^5*d^9*exp(1)^5*exp(2)+328*a^3*c^5*d^9*exp(1)^3*exp(2)^2-68*a^3*c^5*d^9*exp
(1)*exp(2)^3+320*a^3*c^5*d^8*exp(1)^7-192*a^3*c^5*d^8*exp(1)^5*exp(2)+168*a^3*c^5*d^8*exp(1)^3*exp(2)^2-56*a^3
*c^5*d^8*exp(1)*exp(2)^3+416*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)*exp(1)^7-336*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)*exp(1)^5*exp(2)+164*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)*exp(1)^3*exp(2)^2-34*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)*exp(1)*
exp(2)^3+416*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)*exp(1)^5*exp(2)-232*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)*exp(1)^3*exp(2)^2+56*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)*exp(1)*exp(2)^3+104*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)*exp(1)^5*exp(2)-
58*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)*exp(1)^3*exp(2)^2+14*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)*exp(1)*exp(2)^3-160*a^3*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)^7+96*a^3*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*e
xp(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)^5*exp(2)-84
*a^3*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))*sq
rt(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)^3*exp(2)^2+28*a^3*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)*exp(2)^3-80*a^3*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*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^5*exp(2)-68*a^3*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)^3*exp(2)^2+28*a^3*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*ex
p(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)*exp(2)^3-208
*a^3*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)^5*exp(2)+116*a^3*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)^3*exp(2)^2-28*a^3*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)*exp(2)^3-38*a^3*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)^3*exp(2)^2+14*a^3*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)*ex
p(2)^3-76*a^3*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)^3*exp(2)^2+28*a^3*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)*exp(2)^3-608*a^2*c^6*d^11*exp(1)^5+476*a
^2*c^6*d^11*exp(1)^3*exp(2)-120*a^2*c^6*d^11*exp(1)*exp(2)^2-384*a^2*c^6*d^10*exp(1)^5+272*a^2*c^6*d^10*exp(1)
^3*exp(2)-68*a^2*c^6*d^10*exp(1)*exp(2)^2-304*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)*exp(1)^5+238*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)*exp(1)^3*exp(2)-60*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)*exp(1)*exp(2)^
2-208*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)*exp(1)^5+16*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*ex
p(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)+12*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)*exp(1)*exp(2)^2-104*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)*exp(1)^5+58*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)*exp(1)^3*exp(2)-
14*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)*exp(1)*exp(2)^2+192*a^2*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)^5-136*a
^2*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)^3*exp(2)+34*a^2*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)*exp(2)^2+80*a^2*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)^5+68*a^2*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)^3*
exp(2)-28*a^2*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)*sqrt(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)*exp(2)^2+208*a^2*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)^5-116*a^2*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)^3*exp(2)+28*a^2*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)*exp(2)^2+40*a^2*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)^5-4
*a^2*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))*sq
rt(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)^3*exp(2)+80*a^2*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)^5-8*a^2*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)^3*exp(2)+148*a*c^7*d^13*exp(1)^3-64*a*c^7*d^13*exp(1)*exp(2)+124*a*c^7*d^12*exp(1)
^3-52*a*c^7*d^12*exp(1)*exp(2)+74*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)*exp(1)^3-32*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)*exp(1)*exp(2)+100*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)*exp(1)^3-28*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)*exp(1)*exp(2)+50*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)*exp(1)^3-20*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)*exp(1)*exp(2)-62*a*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)^
3+26*a*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)*exp(2)-76*a*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)^3+16*a*c^5*d^9*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)*exp(2)-100*a*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)^3+4
0*a*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)*exp(2)-38*a*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)^3+14*a*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)*exp(2)-76*a*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)^3+28*
a*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)*exp(2)-12*c^8*d^15*exp(1)-12*c^8*d
^14*exp(1)-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*e
xp(2))*sqrt(2)*exp(1)-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*exp(2))*sqrt(2)*exp(1)-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)*exp(1)+6*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)+12*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*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)+12*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)+6*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)+12*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))/(16*a^9*d^3*exp
(1)^6*exp(2)^6-48*a^9*d^3*exp(1)^4*exp(2)^7+48*a^9*d^3*exp(1)^2*exp(2)^8-16*a^9*d^3*exp(2)^9-192*a^8*c*d^5*exp
(1)^8*exp(2)^4+672*a^8*c*d^5*exp(1)^6*exp(2)^5-864*a^8*c*d^5*exp(1)^4*exp(2)^6+480*a^8*c*d^5*exp(1)^2*exp(2)^7
-96*a^8*c*d^5*exp(2)^8-32*a^8*c*d^4*exp(1)^6*exp(2)^5+96*a^8*c*d^4*exp(1)^4*exp(2)^6-96*a^8*c*d^4*exp(1)^2*exp
(2)^7+32*a^8*c*d^4*exp(2)^8+768*a^7*c^2*d^7*exp(1)^10*exp(2)^2-3072*a^7*c^2*d^7*exp(1)^8*exp(2)^3+4848*a^7*c^2
*d^7*exp(1)^6*exp(2)^4-3792*a^7*c^2*d^7*exp(1)^4*exp(2)^5+1488*a^7*c^2*d^7*exp(1)^2*exp(2)^6-240*a^7*c^2*d^7*e
xp(2)^7+256*a^7*c^2*d^6*exp(1)^8*exp(2)^3-864*a^7*c^2*d^6*exp(1)^6*exp(2)^4+1056*a^7*c^2*d^6*exp(1)^4*exp(2)^5
-544*a^7*c^2*d^6*exp(1)^2*exp(2)^6+96*a^7*c^2*d^6*exp(2)^7+16*a^7*c^2*d^5*exp(1)^6*exp(2)^4-48*a^7*c^2*d^5*exp
(1)^4*exp(2)^5+48*a^7*c^2*d^5*exp(1)^2*exp(2)^6-16*a^7*c^2*d^5*exp(2)^7-1024*a^6*c^3*d^9*exp(1)^12+4608*a^6*c^
3*d^9*exp(1)^10*exp(2)-8832*a^6*c^3*d^9*exp(1)^8*exp(2)^2+9408*a^6*c^3*d^9*exp(1)^6*exp(2)^3-5952*a^6*c^3*d^9*
exp(1)^4*exp(2)^4+2112*a^6*c^3*d^9*exp(1)^2*exp(2)^5-320*a^6*c^3*d^9*exp(2)^6-512*a^6*c^3*d^8*exp(1)^10*exp(2)
+1792*a^6*c^3*d^8*exp(1)^8*exp(2)^2-2368*a^6*c^3*d^8*exp(1)^6*exp(2)^3+1472*a^6*c^3*d^8*exp(1)^4*exp(2)^4-448*
a^6*c^3*d^8*exp(1)^2*exp(2)^5+64*a^6*c^3*d^8*exp(2)^6-128*a^6*c^3*d^7*exp(1)^8*exp(2)^2+448*a^6*c^3*d^7*exp(1)
^6*exp(2)^3-576*a^6*c^3*d^7*exp(1)^4*exp(2)^4+320*a^6*c^3*d^7*exp(1)^2*exp(2)^5-64*a^6*c^3*d^7*exp(2)^6+768*a^
5*c^4*d^11*exp(1)^10-3072*a^5*c^4*d^11*exp(1)^8*exp(2)+4848*a^5*c^4*d^11*exp(1)^6*exp(2)^2-3792*a^5*c^4*d^11*e
xp(1)^4*exp(2)^3+1488*a^5*c^4*d^11*exp(1)^2*exp(2)^4-240*a^5*c^4*d^11*exp(2)^5+512*a^5*c^4*d^10*exp(1)^10-1792
*a^5*c^4*d^10*exp(1)^8*exp(2)+2368*a^5*c^4*d^10*exp(1)^6*exp(2)^2-1472*a^5*c^4*d^10*exp(1)^4*exp(2)^3+448*a^5*
c^4*d^10*exp(1)^2*exp(2)^4-64*a^5*c^4*d^10*exp(2)^5+256*a^5*c^4*d^9*exp(1)^10-1024*a^5*c^4*d^9*exp(1)^8*exp(2)
+1632*a^5*c^4*d^9*exp(1)^6*exp(2)^2-1312*a^5*c^4*d^9*exp(1)^4*exp(2)^3+544*a^5*c^4*d^9*exp(1)^2*exp(2)^4-96*a^
5*c^4*d^9*exp(2)^5-192*a^4*c^5*d^13*exp(1)^8+672*a^4*c^5*d^13*exp(1)^6*exp(2)-864*a^4*c^5*d^13*exp(1)^4*exp(2)
^2+480*a^4*c^5*d^13*exp(1)^2*exp(2)^3-96*a^4*c^5*d^13*exp(2)^4-256*a^4*c^5*d^12*exp(1)^8+864*a^4*c^5*d^12*exp(
1)^6*exp(2)-1056*a^4*c^5*d^12*exp(1)^4*exp(2)^2+544*a^4*c^5*d^12*exp(1)^2*exp(2)^3-96*a^4*c^5*d^12*exp(2)^4-12
8*a^4*c^5*d^11*exp(1)^8+448*a^4*c^5*d^11*exp(1)^6*exp(2)-576*a^4*c^5*d^11*exp(1)^4*exp(2)^2+320*a^4*c^5*d^11*e
xp(1)^2*exp(2)^3-64*a^4*c^5*d^11*exp(2)^4+16*a^3*c^6*d^15*exp(1)^6-48*a^3*c^6*d^15*exp(1)^4*exp(2)+48*a^3*c^6*
d^15*exp(1)^2*exp(2)^2-16*a^3*c^6*d^15*exp(2)^3+32*a^3*c^6*d^14*exp(1)^6-96*a^3*c^6*d^14*exp(1)^4*exp(2)+96*a^
3*c^6*d^14*exp(1)^2*exp(2)^2-32*a^3*c^6*d^14*exp(2)^3+16*a^3*c^6*d^13*exp(1)^6-48*a^3*c^6*d^13*exp(1)^4*exp(2)
+48*a^3*c^6*d^13*exp(1)^2*exp(2)^2-16*a^3*c^6*d^13*exp(2)^3)/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(2*c^3*
d^8*exp(1)^4*a^2-4*c^3*d^8*exp(1)^2*a^2*exp(2)+2*c^3*d^8*a^2*exp(2)^2-8*c^2*d^6*exp(1)^6*a^3+18*c^2*d^6*exp(1)
^4*a^3*exp(2)-12*c^2*d^6*exp(1)^2*a^3*exp(2)^2+2*c^2*d^6*a^3*exp(2)^3+8*c*d^4*exp(1)^6*a^4*exp(2)-18*c*d^4*exp
(1)^4*a^4*exp(2)^2+12*c*d^4*exp(1)^2*a^4*exp(2)^3-2*c*d^4*a^4*exp(2)^4-2*d^2*exp(1)^4*a^5*exp(2)^3+4*d^2*exp(1
)^2*a^5*exp(2)^4-2*d^2*a^5*exp(2)^5-sqrt((-2*c^3*d^8*exp(1)^4*a^2+4*c^3*d^8*exp(1)^2*a^2*exp(2)-2*c^3*d^8*a^2*
exp(2)^2+8*c^2*d^6*exp(1)^6*a^3-18*c^2*d^6*exp(1)^4*a^3*exp(2)+12*c^2*d^6*exp(1)^2*a^3*exp(2)^2-2*c^2*d^6*a^3*
exp(2)^3-8*c*d^4*exp(1)^6*a^4*exp(2)+18*c*d^4*exp(1)^4*a^4*exp(2)^2-12*c*d^4*exp(1)^2*a^4*exp(2)^3+2*c*d^4*a^4
*exp(2)^4+2*d^2*exp(1)^4*a^5*exp(2)^3-4*d^2*exp(1)^2*a^5*exp(2)^4+2*d^2*a^5*exp(2)^5)*(-2*c^3*d^8*exp(1)^4*a^2
+4*c^3*d^8*exp(1)^2*a^2*exp(2)-2*c^3*d^8*a^2*exp(2)^2+8*c^2*d^6*exp(1)^6*a^3-18*c^2*d^6*exp(1)^4*a^3*exp(2)+12
*c^2*d^6*exp(1)^2*a^3*exp(2)^2-2*c^2*d^6*a^3*exp(2)^3-8*c*d^4*exp(1)^6*a^4*exp(2)+18*c*d^4*exp(1)^4*a^4*exp(2)
^2-12*c*d^4*exp(1)^2*a^4*exp(2)^3+2*c*d^4*a^4*exp(2)^4+2*d^2*exp(1)^4*a^5*exp(2)^3-4*d^2*exp(1)^2*a^5*exp(2)^4
+2*d^2*a^5*exp(2)^5)-4*(2*c^3*d^7*exp(1)^4*a^2-4*c^3*d^7*exp(1)^2*a^2*exp(2)+2*c^3*d^7*a^2*exp(2)^2-8*c^2*d^5*
exp(1)^6*a^3+20*c^2*d^5*exp(1)^4*a^3*exp(2)-16*c^2*d^5*exp(1)^2*a^3*exp(2)^2+4*c^2*d^5*a^3*exp(2)^3+2*c*d^3*ex
p(1)^4*a^4*exp(2)^2-4*c*d^3*exp(1)^2*a^4*exp(2)^3+2*c*d^3*a^4*exp(2)^4)*(2*c^2*d^7*exp(1)^6*a^3-6*c^2*d^7*exp(
1)^4*a^3*exp(2)+6*c^2*d^7*exp(1)^2*a^3*exp(2)^2-2*c^2*d^7*a^3*exp(2)^3-8*c*d^5*exp(1)^8*a^4+28*c*d^5*exp(1)^6*
a^4*exp(2)-36*c*d^5*exp(1)^4*a^4*exp(2)^2+20*c*d^5*exp(1)^2*a^4*exp(2)^3-4*c*d^5*a^4*exp(2)^4+2*d^3*exp(1)^6*a
^5*exp(2)^2-6*d^3*exp(1)^4*a^5*exp(2)^3+6*d^3*exp(1)^2*a^5*exp(2)^4-2*d^3*a^5*exp(2)^5)))/2/(2*c^3*d^7*exp(1)^
4*a^2-4*c^3*d^7*exp(1)^2*a^2*exp(2)+2*c^3*d^7*a^2*exp(2)^2-8*c^2*d^5*exp(1)^6*a^3+20*c^2*d^5*exp(1)^4*a^3*exp(
2)-16*c^2*d^5*exp(1)^2*a^3*exp(2)^2+4*c^2*d^5*a^3*exp(2)^3+2*c*d^3*exp(1)^4*a^4*exp(2)^2-4*c*d^3*exp(1)^2*a^4*
exp(2)^3+2*c*d^3*a^4*exp(2)^4)))+(-3*(d+x*exp(1))^2*c^3*d^5*exp(1)+10*(d+x*exp(1))^2*c^2*d^3*exp(1)^3*a-4*(d+x
*exp(1))^2*c^2*d^3*exp(1)*a*exp(2)-3*(d+x*exp(1))^2*c*d*exp(1)*a^2*exp(2)^2+3*(d+x*exp(1))*c^3*d^6*exp(1)-11*(
d+x*exp(1))*c^2*d^4*exp(1)^3*a+2*(d+x*exp(1))*c^2*d^4*exp(1)*a*exp(2)+11*(d+x*exp(1))*c*d^2*exp(1)^3*a^2*exp(2
)-2*(d+x*exp(1))*c*d^2*exp(1)*a^2*exp(2)^2-3*(d+x*exp(1))*exp(1)*a^3*exp(2)^3-2*c^2*d^5*exp(1)^3*a+2*c^2*d^5*e
xp(1)*a*exp(2)+8*c*d^3*exp(1)^5*a^2-12*c*d^3*exp(1)^3*a^2*exp(2)+4*c*d^3*exp(1)*a^2*exp(2)^2-2*d*exp(1)^3*a^3*
exp(2)^2+2*d*exp(1)*a^3*exp(2)^3)/(2*c^2*d^6*exp(1)^4*a^2-4*c^2*d^6*exp(1)^2*a^2*exp(2)+2*c^2*d^6*a^2*exp(2)^2
-8*c*d^4*exp(1)^6*a^3+20*c*d^4*exp(1)^4*a^3*exp(2)-16*c*d^4*exp(1)^2*a^3*exp(2)^2+4*c*d^4*a^3*exp(2)^3+2*d^2*e
xp(1)^4*a^4*exp(2)^2-4*d^2*exp(1)^2*a^4*exp(2)^3+2*d^2*a^4*exp(2)^4)/(sqrt(d+x*exp(1))*(d+x*exp(1))^2*c*d-sqrt
(d+x*exp(1))*(d+x*exp(1))*c*d^2+sqrt(d+x*exp(1))*(d+x*exp(1))*a*exp(2)+sqrt(d+x*exp(1))*d*exp(1)^2*a-sqrt(d+x*
exp(1))*d*a*exp(2)))

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maple [A]  time = 0.07, size = 193, normalized size = 1.01 \begin {gather*} -\frac {7 c^{3} d^{3} e \arctan \left (\frac {\sqrt {e x +d}\, c d}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}\right )}{\left (a \,e^{2}-c \,d^{2}\right )^{4} \sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}-\frac {\sqrt {e x +d}\, c^{3} d^{3} e}{\left (a \,e^{2}-c \,d^{2}\right )^{4} \left (c d e x +a \,e^{2}\right )}-\frac {6 c^{2} d^{2} e}{\left (a \,e^{2}-c \,d^{2}\right )^{4} \sqrt {e x +d}}+\frac {4 c d e}{3 \left (a \,e^{2}-c \,d^{2}\right )^{3} \left (e x +d \right )^{\frac {3}{2}}}-\frac {2 e}{5 \left (a \,e^{2}-c \,d^{2}\right )^{2} \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)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)

[Out]

-e*c^3*d^3/(a*e^2-c*d^2)^4*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)-7*e*c^3*d^3/(a*e^2-c*d^2)^4/((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/(a*e^2-c*d^2)^2/(e*x+d)^(5/2)-6*e/(a*e^2-c*d^2)^4*c
^2*d^2/(e*x+d)^(1/2)+4/3*e/(a*e^2-c*d^2)^3*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)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,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 = 0.83, size = 244, normalized size = 1.27 \begin {gather*} -\frac {\frac {2\,e}{5\,\left (a\,e^2-c\,d^2\right )}-\frac {14\,c\,d\,e\,\left (d+e\,x\right )}{15\,{\left (a\,e^2-c\,d^2\right )}^2}+\frac {14\,c^2\,d^2\,e\,{\left (d+e\,x\right )}^2}{3\,{\left (a\,e^2-c\,d^2\right )}^3}+\frac {7\,c^3\,d^3\,e\,{\left (d+e\,x\right )}^3}{{\left (a\,e^2-c\,d^2\right )}^4}}{\left (a\,e^2-c\,d^2\right )\,{\left (d+e\,x\right )}^{5/2}+c\,d\,{\left (d+e\,x\right )}^{7/2}}-\frac {7\,c^{5/2}\,d^{5/2}\,e\,\mathrm {atan}\left (\frac {\sqrt {c}\,\sqrt {d}\,\sqrt {d+e\,x}\,\left (a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right )}{{\left (a\,e^2-c\,d^2\right )}^{9/2}}\right )}{{\left (a\,e^2-c\,d^2\right )}^{9/2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- ((2*e)/(5*(a*e^2 - c*d^2)) - (14*c*d*e*(d + e*x))/(15*(a*e^2 - c*d^2)^2) + (14*c^2*d^2*e*(d + e*x)^2)/(3*(a*
e^2 - c*d^2)^3) + (7*c^3*d^3*e*(d + e*x)^3)/(a*e^2 - c*d^2)^4)/((a*e^2 - c*d^2)*(d + e*x)^(5/2) + c*d*(d + e*x
)^(7/2)) - (7*c^(5/2)*d^(5/2)*e*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4
*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^(9/2)))/(a*e^2 - c*d^2)^(9/2)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (d + e x\right )^{\frac {7}{2}} \left (a e + c d x\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/((d + e*x)**(7/2)*(a*e + c*d*x)**2), x)

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