∫ (d+ex)5∕2 ___________________________________

3.2002 \(\int \frac {(d+e x)^{5/2}}{a d e+(c d^2+a e^2) x+c d e x^2} \, dx\)

Optimal. Leaf size=114 \[ -\frac {2 \left (c d^2-a e^2\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{5/2} d^{5/2}}+\frac {2 \sqrt {d+e x} \left (c d^2-a e^2\right )}{c^2 d^2}+\frac {2 (d+e x)^{3/2}}{3 c d} \]

[Out]

2/3*(e*x+d)^(3/2)/c/d-2*(-a*e^2+c*d^2)^(3/2)*arctanh(c^(1/2)*d^(1/2)*(e*x+d)^(1/2)/(-a*e^2+c*d^2)^(1/2))/c^(5/

2)/d^(5/2)+2*(-a*e^2+c*d^2)*(e*x+d)^(1/2)/c^2/d^2

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Rubi [A] time = 0.07, antiderivative size = 114, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {626, 50, 63, 208} \[ \frac {2 \sqrt {d+e x} \left (c d^2-a e^2\right )}{c^2 d^2}-\frac {2 \left (c d^2-a e^2\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{5/2} d^{5/2}}+\frac {2 (d+e x)^{3/2}}{3 c d} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

(2*(c*d^2 - a*e^2)*Sqrt[d + e*x])/(c^2*d^2) + (2*(d + e*x)^(3/2))/(3*c*d) - (2*(c*d^2 - a*e^2)^(3/2)*ArcTanh[(

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

Rule 50

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*

(m + n + 1)), x] + Dist[(n*(b*c - a*d))/(b*(m + n + 1)), Int[(a + b*x)^m*(c + d*x)^(n - 1), x], x] /; FreeQ[{a

, b, c, d}, x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && NeQ[m + n + 1, 0] && !(IGtQ[m, 0] && ( !IntegerQ[n] || (G

tQ[m, 0] && LtQ[m - n, 0]))) && !ILtQ[m + n + 2, 0] && 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 {(d+e x)^{5/2}}{a d e+\left (c d^2+a e^2\right ) x+c d e x^2} \, dx &=\int \frac {(d+e x)^{3/2}}{a e+c d x} \, dx\\ &=\frac {2 (d+e x)^{3/2}}{3 c d}+\frac {\left (c d^2-a e^2\right ) \int \frac {\sqrt {d+e x}}{a e+c d x} \, dx}{c d}\\ &=\frac {2 \left (c d^2-a e^2\right ) \sqrt {d+e x}}{c^2 d^2}+\frac {2 (d+e x)^{3/2}}{3 c d}+\frac {\left (c d^2-a e^2\right )^2 \int \frac {1}{(a e+c d x) \sqrt {d+e x}} \, dx}{c^2 d^2}\\ &=\frac {2 \left (c d^2-a e^2\right ) \sqrt {d+e x}}{c^2 d^2}+\frac {2 (d+e x)^{3/2}}{3 c d}+\frac {\left (2 \left (c d^2-a e^2\right )^2\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 )}{c^2 d^2 e}\\ &=\frac {2 \left (c d^2-a e^2\right ) \sqrt {d+e x}}{c^2 d^2}+\frac {2 (d+e x)^{3/2}}{3 c d}-\frac {2 \left (c d^2-a e^2\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{5/2} d^{5/2}}\\ \end {align*}

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Mathematica [A] time = 0.08, size = 102, normalized size = 0.89 \[ \frac {2 \sqrt {d+e x} \left (c d (4 d+e x)-3 a e^2\right )}{3 c^2 d^2}-\frac {2 \left (c d^2-a e^2\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{5/2} d^{5/2}} \]

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

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

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

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fricas [A] time = 0.88, size = 254, normalized size = 2.23 \[ \left [\frac {3 \, {\left (c d^{2} - a e^{2}\right )} \sqrt {\frac {c d^{2} - a e^{2}}{c d}} \log \left (\frac {c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt {e x + d} c d \sqrt {\frac {c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right ) + 2 \, {\left (c d e x + 4 \, c d^{2} - 3 \, a e^{2}\right )} \sqrt {e x + d}}{3 \, c^{2} d^{2}}, -\frac {2 \, {\left (3 \, {\left (c d^{2} - a e^{2}\right )} \sqrt {-\frac {c d^{2} - a e^{2}}{c d}} \arctan \left (-\frac {\sqrt {e x + d} c d \sqrt {-\frac {c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right ) - {\left (c d e x + 4 \, c d^{2} - 3 \, a e^{2}\right )} \sqrt {e x + d}\right )}}{3 \, c^{2} d^{2}}\right ] \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm="fricas")

[Out]

[1/3*(3*(c*d^2 - a*e^2)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt(

(c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(c*d*e*x + 4*c*d^2 - 3*a*e^2)*sqrt(e*x + d))/(c^2*d^2), -2/3*(3*(c*

d^2 - a*e^2)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^

2)) - (c*d*e*x + 4*c*d^2 - 3*a*e^2)*sqrt(e*x + d))/(c^2*d^2)]

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: ((-4*a^6*c^2*d^2*exp(2)^6+2*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(2)^6+36*a^5*c^3*d^4*exp(1)^2*exp(2)^4-12*a^5*c^3*d^4*exp(2

)^5-18*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)^2*exp(2)^4+6*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(2)^5-4*a^5*c*d*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(2)^5-96*a^4*c^4*d^6*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*exp(1)^2*exp(2)^3-12*a^4*c^4*d^6*exp(2)

^4+48*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)^4*exp(2)^2-24*a^4*c^2*d^4*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)*sqrt(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+6*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(2)^4+20*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*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*exp(2)^3+2*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(2)^4+4*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(2)^4+64*a^3*c^5*d^8*exp(1)^6+24*a^3*c^5*d^8*e

xp(1)^2*exp(2)^2-8*a^3*c^5*d^8*exp(2)^3-32*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*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)^6-12*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)^2*exp(2)^2+4*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(2)^3-16*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)^4*exp(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*ex

p(2))*exp(1)^2*exp(2)^2+4*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(2)^3-10*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)^2*exp(2)^2+2*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(2)^3-20*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)^2*exp(2)^2+4*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(

2)^3-96*a^2*c^6*d^10*exp(1)^4+48*a^2*c^6*d^10*exp(1)^2*exp(2)-12*a^2*c^6*d^10*exp(2)^2+48*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)^4-24*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)^2*exp(2)+6*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(2)

^2+16*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)^4+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)^2*exp(2)-4*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(2)^2+8*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)^4+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))*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)^2*exp(2)+16*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)^4+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)^2*exp(2)+36*a*c^7*d^12*exp(1)^2-12*a*c^7*d^12*exp(2)-18*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)^2+6*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(2)-20*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)^2-10*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)^2+2*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(2)-20*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)^2+4*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(2)-4*c^8*d^14+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)*sqrt(c^2*d^4-4*a*c*d

^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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*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))+

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)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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)))*c^2*d^2+(8*a^6*c^3*d^4*exp(1)^2*exp(2)^5-8*a^6*c^3*d^4*exp(2)^6+4*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*ex

p(2)^5-4*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*ex

p(2))*sqrt(2)*exp(2)^6-64*a^5*c^4*d^6*exp(1)^4*exp(2)^3+88*a^5*c^4*d^6*exp(1)^2*exp(2)^4-24*a^5*c^4*d^6*exp(2)

^5-32*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)^3+44*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)^4-12*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(2)^5-8*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)^4+8*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(2)

^5+128*a^4*c^5*d^8*exp(1)^6*exp(2)-192*a^4*c^5*d^8*exp(1)^4*exp(2)^2+80*a^4*c^5*d^8*exp(1)^2*exp(2)^3-16*a^4*c

^5*d^8*exp(2)^4+64*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)-96*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*e

xp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+40*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)^3-8*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(2)^4+32

*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))*sq

rt(2)*exp(1)^4*exp(2)^2-32*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)^3+4*a^4*c^4*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)^3-4*a^4*c^4*d^5*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(2)^4-8*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)^3+8*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(2)^4-128*a^3*c^6*d^10*exp(1)^6+192*a^3*c^6*d^10*exp(1)^4*exp(2)-80*a^3*

c^6*d^10*exp(1)^2*exp(2)^2+16*a^3*c^6*d^10*exp(2)^3-64*a^3*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)*exp(1)^6+96*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)-40*a^3*c^5*d^9*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)^2*

exp(2)^2+8*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(2)^3-64*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)+80*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)^2-16*a^3*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(2)^3-16*a^3*c^5*d^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)^4*e

xp(2)+20*a^3*c^5*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*ex

p(2))*sqrt(2)*exp(1)^2*exp(2)^2-4*a^3*c^5*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(2)^3+32*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)-40*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)^2+8*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(2)^3+64*a^2*c^7*d^12*ex

p(1)^4-88*a^2*c^7*d^12*exp(1)^2*exp(2)+24*a^2*c^7*d^12*exp(2)^2+32*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)^4-44*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)+12*

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))*sq

rt(2)*exp(2)^2+32*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)^4-32*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)+16*a^2*c^6*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)^4-20*a^2*c^6*d^9*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)^2*exp(2)+4*a^2*c^6*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(

2)^2-32*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+40*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)-8*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(2)^2-8*a*c^8*d^14*exp(1)^2+8*a*c^8*d^14*exp(2)-4*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+4*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(2)-

8*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))*sq

rt(2)*exp(1)^2+8*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(2)-4*a*c^7*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+4*a*c^7*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(2)+8*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)^2-8*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(2))*abs

(c)*abs(d)+4*a^6*c^4*d^4*exp(2)^6-2*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)*sqrt(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(2)

^6-28*a^5*c^5*d^6*exp(1)^2*exp(2)^4+4*a^5*c^5*d^6*exp(2)^5+14*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)*sqrt(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)^4-2*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)*sqrt(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(2)^5+4*a^5*c^3*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*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(2)^5+48*a^4*c^6*d^8*exp(1)^4*

exp(2)^2+16*a^4*c^6*d^8*exp(1)^2*exp(2)^3-4*a^4*c^6*d^8*exp(2)^4-24*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)*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))*exp(1)^4*exp(2)^2-8*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)*sqrt(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+2*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*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(2)^4-12*a^4*c^

4*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)*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)^3-8*a^4*c^4*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(2)^4-2*a^4*c^4*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(2)^4-4*a^4*c^4*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(2)^4-96*a^3*c^7

*d^10*exp(1)^4*exp(2)+24*a^3*c^7*d^10*exp(1)^2*exp(2)^2-8*a^3*c^7*d^10*exp(2)^3+48*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)*sqrt(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)-12*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)*sqrt(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+4*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)*sqrt(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(

2)^3+36*a^3*c^5*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)^2+4*a^3*c^5*d^7*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(2)^3+6*a^3*c^5*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)^2+2*a^3*c^5*d^6*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(2)^3+12*a^3*c^5*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)^2+4*a^3*c^

5*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(2)^3+48*a^2*c^8*d^12*exp(1)^4+16*a^2*c^8*

d^12*exp(1)^2*exp(2)-4*a^2*c^8*d^12*exp(2)^2-24*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)*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)^4-8*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)*sqrt(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*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)

*sqrt(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(2)^2-36*a^2*c^6*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)-4*a^2*c^6*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(2)^2-12*a^2*c^6*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)-24*a

^2*c^6*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)-28*a*c^9*d^14*exp(1)^2+4

*a*c^9*d^14*exp(2)+14*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)*sqrt(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)^2-2*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)*sqrt(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(2)+12*a*c^7*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+8*a*c^7*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(2)+6

*a*c^7*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)^2+2*a*c^7*d^10*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(2)+12*a*c^7*d^10*(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)^2+4*a*c^7*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(2)+4*c^10*d^16-2*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)*

sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^8*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)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^

2+2*a*c*d^2*exp(2))-2*c^8*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))-4*c^8*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)))/(8*a^5*c^4*d^5*exp(1)^2*exp(2)^4-8*a^5*c^4*d^5*exp(2)^5-64*a^4

*c^5*d^7*exp(1)^4*exp(2)^2+96*a^4*c^5*d^7*exp(1)^2*exp(2)^3-32*a^4*c^5*d^7*exp(2)^4-16*a^4*c^5*d^6*exp(1)^2*ex

p(2)^3+16*a^4*c^5*d^6*exp(2)^4+128*a^3*c^6*d^9*exp(1)^6-256*a^3*c^6*d^9*exp(1)^4*exp(2)+176*a^3*c^6*d^9*exp(1)

^2*exp(2)^2-48*a^3*c^6*d^9*exp(2)^3+64*a^3*c^6*d^8*exp(1)^4*exp(2)-80*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a^3*c^6

*d^8*exp(2)^3+8*a^3*c^6*d^7*exp(1)^2*exp(2)^2-8*a^3*c^6*d^7*exp(2)^3-64*a^2*c^7*d^11*exp(1)^4+96*a^2*c^7*d^11*

exp(1)^2*exp(2)-32*a^2*c^7*d^11*exp(2)^2-64*a^2*c^7*d^10*exp(1)^4+80*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2*c^7*d

^10*exp(2)^2-32*a^2*c^7*d^9*exp(1)^4+48*a^2*c^7*d^9*exp(1)^2*exp(2)-16*a^2*c^7*d^9*exp(2)^2+8*a*c^8*d^13*exp(1

)^2-8*a*c^8*d^13*exp(2)+16*a*c^8*d^12*exp(1)^2-16*a*c^8*d^12*exp(2)+8*a*c^8*d^11*exp(1)^2-8*a*c^8*d^11*exp(2))

/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^5*c^4-d^3*c^3*a*exp(2)+sqrt((-d^5*c^4+d^3*c^3*a*exp(2))*(-d^5*c^4+d^3*

c^3*a*exp(2))-4*d^4*c^4*(d^4*exp(1)^2*c^3*a-d^4*c^3*a*exp(2))))/2/d^4/c^4))-((-4*a^6*c^2*d^2*exp(2)^6+2*a^6*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(2)^6+36*a^5*c^3*d^4*exp(1)^2*exp(2)^4-12*a^5*c^3*d^4

*exp(2)^5-18*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)^2*exp(2)^4+6*a^5*c*d^2*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)*sqrt(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(2)^5-4*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(2)^5-96*a^4*c^4*d^6*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*exp(1)^2*exp(2)^3-12*a^4*c^4*d^6*

exp(2)^4+48*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)^4*exp(2)^2-24*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)^2*exp(2)^3+6*a^4*c^2*d^4*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(2)^4+20*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*e

xp(2))*exp(1)^2*exp(2)^3+2*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(2)^4+4*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(2)^4+64*a^3*c^5*d^8*exp(1)^6+24*a^3*c^5

*d^8*exp(1)^2*exp(2)^2-8*a^3*c^5*d^8*exp(2)^3-32*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*e

xp(2))*exp(1)^6-12*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)^2*exp(2)^2+4*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(2)^3-16*a^3*c^3*d^5*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)*sqrt(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)-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)^2*exp(2)^2+4*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(2)^3-1

0*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))*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)^2*exp(2)^2+2*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(2)^3-20*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)^2*exp(2)^2+4*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(2)^3-96*a^2*c^6*d^10*exp(1)^4+48*a^2*c^6*d^10*exp(1)^2*exp(2)-12*a^2*c^6*d^10*exp(2)^2+48*a^2*c^4*d^8*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)^4-24*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)^2*exp(2)+6*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*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(2)^2+16*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)^4+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)^2*exp(2)-4*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*e

xp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+8*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

)^4+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)^2*exp(2)+16*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)^4+8*a^2*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)^2*exp(2)+36*a*c^7*d^12*exp(1)^2-12*a*c^7*d^12*exp(2)-18*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)^2+6*a*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)*sqrt(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(2)-20*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)^2-10*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)^2+2*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*ex

p(2)^2+2*a*c*d^2*exp(2))*exp(2)-20*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)

^2+4*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(2)-4*c^8*d^14+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)*sqrt(c^2*d^4-4

*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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*ex

p(2))+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)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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)))*c^2*d^2+(8*a^6*c^3*d^4*exp(1)^2*exp(2)^5-8*a^6*c^3*d^4*exp(2)^6-4*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)^5+4*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(2)^6-64*a^5*c^4*d^6*exp(1)^4*exp(2)^3+88*a^5*c^4*d^6*exp(1)^2*exp(2)^4-24*a^5*c^4*d^6*

exp(2)^5+32*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)^3-44*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)^4+12*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(2)^5+8*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)^4-8*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(2)^5+128*a^4*c^5*d^8*exp(1)^6*exp(2)-192*a^4*c^5*d^8*exp(1)^4*exp(2)^2+80*a^4*c^5*d^8*exp(1)^2*exp(2)^3-16

*a^4*c^5*d^8*exp(2)^4-64*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)+96*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)^2-40*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)^3+8*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(2

)^4-32*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)^2+32*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)^3-4*a^4*c^4*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)^3+4*a^4*c^4*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(2)^4-8*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)^3+8*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(2)^4-128*a^3*c^6*d^10*exp(1)^6+192*a^3*c^6*d^10*exp(1)^4*exp(2)-8

0*a^3*c^6*d^10*exp(1)^2*exp(2)^2+16*a^3*c^6*d^10*exp(2)^3+64*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)^6-96*a^3*c^5*d^9*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)^4*exp(2)+40*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)^2-8*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(2)^3+64*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)-80*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)^2+16*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(2)^3+16*a^3*c^5*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)-20*a^3*c^5*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)^2+4*a^3*c^5*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(2)^3+32*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)-40*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))*ex

p(1)^2*exp(2)^2+8*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(2)^3+64*a^2*c^7*d

^12*exp(1)^4-88*a^2*c^7*d^12*exp(1)^2*exp(2)+24*a^2*c^7*d^12*exp(2)^2-32*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+44*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)-12*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(2)^2-32*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+32*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*e

xp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-16*a^2*c^6*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+20*a^2*c^6*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)-4*a^2

*c^6*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(2)^2-32*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+40*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)-8*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(2)^2-8*a*c^8*d^14*exp(1)^2+8*a*c^8*d^14*exp(2)+4*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)^2-4*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)*e

xp(2)+8*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)^2-8*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(2)+4*a*c^7*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)^2-4*a*c^7*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(2)+8*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)^2-8*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(2

))*abs(c)*abs(d)+4*a^6*c^4*d^4*exp(2)^6-2*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*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(2)^6-28*a^5*c^5*d^6*exp(1)^2*exp(2)^4+4*a^5*c^5*d^6*exp(2)^5+14*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)*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))*exp(1)^2*exp(2)^4-2*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)*sqrt(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(2)^5+4*a^5*c^3*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(2)^5+48*a^4*c^6*d^8*exp

(1)^4*exp(2)^2+16*a^4*c^6*d^8*exp(1)^2*exp(2)^3-4*a^4*c^6*d^8*exp(2)^4-24*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)*sqrt(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)^2-8*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)*sqrt(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+2*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)*sqrt(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(2)^4-12*

a^4*c^4*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))*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)^2*exp(2)^3-8*a^4*c^4*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(2)^4-2*a^4*c^4*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(2)^4-4*a^4*c^4*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(2)^4-96*a

^3*c^7*d^10*exp(1)^4*exp(2)+24*a^3*c^7*d^10*exp(1)^2*exp(2)^2-8*a^3*c^7*d^10*exp(2)^3+48*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)*sqrt(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)-12*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)*sqrt(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+4*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)*sqrt(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(2)^3+36*a^3*c^5*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)^2+4*a^3*c^5*

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)*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(2)^3+6*a^3*c^5*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)^2+2*a^3*c^5*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*e

xp(2))*exp(2)^3+12*a^3*c^5*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)^2+4*

a^3*c^5*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(2)^3+48*a^2*c^8*d^12*exp(1)^4+16*a^

2*c^8*d^12*exp(1)^2*exp(2)-4*a^2*c^8*d^12*exp(2)^2-24*a^2*c^6*d^10*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)^4-8*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)*sqrt(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

*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))*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(2)^2-36*a^2*c^6*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)-4*a^2*c^6*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(2)^2-12*a^2*c^6*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

)-24*a^2*c^6*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)-28*a*c^9*d^14*exp(

1)^2+4*a*c^9*d^14*exp(2)+14*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)*sqrt(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)^2-2*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)*

sqrt(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(2)+12*a*c^7*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+8*a*c^7*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))*ex

p(2)+6*a*c^7*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+2*a*c^7*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(2)+12*a*c^7*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+4*a*c^7*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(2)+4*c^10*d^1

6-2*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))*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))-4*c^8*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)*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))-2*c^8*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))-4*c^8*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)))/(8*a^5*c^4*d^5*exp(1)^2*exp(2)^4-8*a^5*c^4*d^5*exp(2)^5-

64*a^4*c^5*d^7*exp(1)^4*exp(2)^2+96*a^4*c^5*d^7*exp(1)^2*exp(2)^3-32*a^4*c^5*d^7*exp(2)^4-16*a^4*c^5*d^6*exp(1

)^2*exp(2)^3+16*a^4*c^5*d^6*exp(2)^4+128*a^3*c^6*d^9*exp(1)^6-256*a^3*c^6*d^9*exp(1)^4*exp(2)+176*a^3*c^6*d^9*

exp(1)^2*exp(2)^2-48*a^3*c^6*d^9*exp(2)^3+64*a^3*c^6*d^8*exp(1)^4*exp(2)-80*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a

^3*c^6*d^8*exp(2)^3+8*a^3*c^6*d^7*exp(1)^2*exp(2)^2-8*a^3*c^6*d^7*exp(2)^3-64*a^2*c^7*d^11*exp(1)^4+96*a^2*c^7

*d^11*exp(1)^2*exp(2)-32*a^2*c^7*d^11*exp(2)^2-64*a^2*c^7*d^10*exp(1)^4+80*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2

*c^7*d^10*exp(2)^2-32*a^2*c^7*d^9*exp(1)^4+48*a^2*c^7*d^9*exp(1)^2*exp(2)-16*a^2*c^7*d^9*exp(2)^2+8*a*c^8*d^13

*exp(1)^2-8*a*c^8*d^13*exp(2)+16*a*c^8*d^12*exp(1)^2-16*a*c^8*d^12*exp(2)+8*a*c^8*d^11*exp(1)^2-8*a*c^8*d^11*e

xp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^5*c^4-d^3*c^3*a*exp(2)-sqrt((-d^5*c^4+d^3*c^3*a*exp(2))*(-d^5*c^

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

xp(1))*d^2*c^2+2*sqrt(d+x*exp(1))*d^3*c^2-2*sqrt(d+x*exp(1))*d*c*a*exp(2))/d^3/c^3

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maple [B] time = 0.05, size = 211, normalized size = 1.85 \[ \frac {2 a^{2} e^{4} \arctan \left (\frac {\sqrt {e x +d}\, c d}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}\right )}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}\, c^{2} d^{2}}-\frac {4 a \,e^{2} \arctan \left (\frac {\sqrt {e x +d}\, c d}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}\right )}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}\, c}+\frac {2 d^{2} \arctan \left (\frac {\sqrt {e x +d}\, c d}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}\right )}{\sqrt {\left (a \,e^{2}-c \,d^{2}\right ) c d}}-\frac {2 \sqrt {e x +d}\, a \,e^{2}}{c^{2} d^{2}}+\frac {2 \sqrt {e x +d}}{c}+\frac {2 \left (e x +d \right )^{\frac {3}{2}}}{3 c d} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)

[Out]

2/3*(e*x+d)^(3/2)/c/d-2/c^2/d^2*a*e^2*(e*x+d)^(1/2)+2/c*(e*x+d)^(1/2)+2/c^2/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arct

an((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^4-4/c/((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)*a*e^2+2*d^2/((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)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^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 = 0.09, size = 121, normalized size = 1.06 \[ \frac {2\,{\left (d+e\,x\right )}^{3/2}}{3\,c\,d}+\frac {2\,\mathrm {atan}\left (\frac {\sqrt {c}\,\sqrt {d}\,{\left (a\,e^2-c\,d^2\right )}^{3/2}\,\sqrt {d+e\,x}}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}\right )\,{\left (a\,e^2-c\,d^2\right )}^{3/2}}{c^{5/2}\,d^{5/2}}-\frac {2\,\left (a\,e^2-c\,d^2\right )\,\sqrt {d+e\,x}}{c^2\,d^2} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)

[Out]

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

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

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sympy [A] time = 65.93, size = 107, normalized size = 0.94 \[ \frac {2 \left (d + e x\right )^{\frac {3}{2}}}{3 c d} + \frac {\sqrt {d + e x} \left (- 2 a e^{2} + 2 c d^{2}\right )}{c^{2} d^{2}} + \frac {2 \left (a e^{2} - c d^{2}\right )^{2} \operatorname {atan}{\left (\frac {\sqrt {d + e x}}{\sqrt {\frac {a e^{2} - c d^{2}}{c d}}} \right )}}{c^{3} d^{3} \sqrt {\frac {a e^{2} - c d^{2}}{c d}}} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)

[Out]

2*(d + e*x)**(3/2)/(3*c*d) + sqrt(d + e*x)*(-2*a*e**2 + 2*c*d**2)/(c**2*d**2) + 2*(a*e**2 - c*d**2)**2*atan(sq

rt(d + e*x)/sqrt((a*e**2 - c*d**2)/(c*d)))/(c**3*d**3*sqrt((a*e**2 - c*d**2)/(c*d)))

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