3.17.85 \(\int \frac {(d+e x)^{7/2}}{a d e+(c d^2+a e^2) x+c d e x^2} \, dx\)

Optimal. Leaf size=147 \[ -\frac {2 \left (c d^2-a e^2\right )^{5/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{7/2} d^{7/2}}+\frac {2 \sqrt {d+e x} \left (c d^2-a e^2\right )^2}{c^3 d^3}+\frac {2 (d+e x)^{3/2} \left (c d^2-a e^2\right )}{3 c^2 d^2}+\frac {2 (d+e x)^{5/2}}{5 c d} \]

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Rubi [A]  time = 0.09, antiderivative size = 147, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {626, 50, 63, 208} \begin {gather*} \frac {2 \sqrt {d+e x} \left (c d^2-a e^2\right )^2}{c^3 d^3}+\frac {2 (d+e x)^{3/2} \left (c d^2-a e^2\right )}{3 c^2 d^2}-\frac {2 \left (c d^2-a e^2\right )^{5/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{7/2} d^{7/2}}+\frac {2 (d+e x)^{5/2}}{5 c d} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]

[Out]

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

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

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Mathematica [A]  time = 0.11, size = 135, normalized size = 0.92 \begin {gather*} \frac {2 \sqrt {d+e x} \left (15 a^2 e^4-5 a c d e^2 (7 d+e x)+c^2 d^2 \left (23 d^2+11 d e x+3 e^2 x^2\right )\right )}{15 c^3 d^3}-\frac {2 \left (c d^2-a e^2\right )^{5/2} \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x}}{\sqrt {c d^2-a e^2}}\right )}{c^{7/2} d^{7/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]

[Out]

(2*Sqrt[d + e*x]*(15*a^2*e^4 - 5*a*c*d*e^2*(7*d + e*x) + c^2*d^2*(23*d^2 + 11*d*e*x + 3*e^2*x^2)))/(15*c^3*d^3
) - (2*(c*d^2 - a*e^2)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(7/2)*d^(7/2))

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IntegrateAlgebraic [A]  time = 0.17, size = 167, normalized size = 1.14 \begin {gather*} \frac {2 \sqrt {d+e x} \left (15 a^2 e^4-30 a c d^2 e^2-5 a c d e^2 (d+e x)+15 c^2 d^4+5 c^2 d^3 (d+e x)+3 c^2 d^2 (d+e x)^2\right )}{15 c^3 d^3}+\frac {2 \left (a e^2-c d^2\right )^{5/2} \tan ^{-1}\left (\frac {\sqrt {c} \sqrt {d} \sqrt {d+e x} \sqrt {a e^2-c d^2}}{c d^2-a e^2}\right )}{c^{7/2} d^{7/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]

[Out]

(2*Sqrt[d + e*x]*(15*c^2*d^4 - 30*a*c*d^2*e^2 + 15*a^2*e^4 + 5*c^2*d^3*(d + e*x) - 5*a*c*d*e^2*(d + e*x) + 3*c
^2*d^2*(d + e*x)^2))/(15*c^3*d^3) + (2*(-(c*d^2) + a*e^2)^(5/2)*ArcTan[(Sqrt[c]*Sqrt[d]*Sqrt[-(c*d^2) + a*e^2]
*Sqrt[d + e*x])/(c*d^2 - a*e^2)])/(c^(7/2)*d^(7/2))

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fricas [A]  time = 0.44, size = 366, normalized size = 2.49 \begin {gather*} \left [\frac {15 \, {\left (c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\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 (3 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + {\left (11 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right )} x\right )} \sqrt {e x + d}}{15 \, c^{3} d^{3}}, -\frac {2 \, {\left (15 \, {\left (c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\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 (3 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + {\left (11 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right )} x\right )} \sqrt {e x + d}\right )}}{15 \, c^{3} d^{3}}\right ] \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm="fricas")

[Out]

[1/15*(15*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*s
qrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(3*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 35*a*c*d^2*
e^2 + 15*a^2*e^4 + (11*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^3*d^3), -2/15*(15*(c^2*d^4 - 2*a*c*d^2*e^
2 + a^2*e^4)*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)) - (3*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 35*a*c*d^2*e^2 + 15*a^2*e^4 + (11*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x
+ d))/(c^3*d^3)]

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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((e*x+d)^(7/2)/(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^7*c^2*d^2*exp(2)^7-2*a^7*sqrt(-c^2
*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^7-40*a^6*c^3*d^4*exp(1)^2*exp(2)^5+12*a^6*c^3*d^4*exp(2)
^6+20*a^6*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))
*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-6*a^6*c*d^2*sqrt(-c^
2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+4*a^6*c*d*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(2)^6+128*a^5*c^4*d^6*exp(1)^4*exp(2)^3-56*a^5*c^4*d^6*exp(1)^2*exp(2)^4+12*a^5*c^4*d^6*exp(2)
^5-64*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2
))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+28*a^5*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)^4-6*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^
2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-24*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*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)^4-2*a^5*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c^2*d^
2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-128*a^4*c^5*d^8*exp(1)^6*exp(2)-16*a^4*c
^5*d^8*exp(1)^2*exp(2)^3+4*a^4*c^5*d^8*exp(2)^4+64*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)
^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))*exp(1)^6*exp(2)+8*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^
2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)
^3-2*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2)
)*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+32*a^4*c^3*d^5*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+32*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*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*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)^4+12*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^
4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(
c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+24*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)^3-4*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+16*a^3*c^6*d^10*exp(1)^2*exp(2)^2-4*a^3*c^6*d^10*exp(2)^3-64*a^
3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-8*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqr
t(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*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^4*d^8*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(2)^3-64*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*
exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-1
6*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))*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)^2-16*a^3*c^4*d^6*sqrt(-c
^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-4*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-
4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-32*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*e
xp(2))*exp(1)^4*exp(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(1)^2*exp(2
)^2-128*a^2*c^7*d^12*exp(1)^4+56*a^2*c^7*d^12*exp(1)^2*exp(2)-12*a^2*c^7*d^12*exp(2)^2+64*a^2*c^5*d^10*sqrt(-c
^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-28*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp
(2)^2+32*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*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)^4+32*a^2*c^5*d^9*sqrt(-c^2
*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(
2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^
4+4*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))
*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+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+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(1)^2*exp(2)+40*a*c^8*d^14*exp(1)^2-12*a*c^8*d^14*exp(2)-20*a*c^6*d^12*sqrt(-c^2*d^
3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp
(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*
d^2*exp(2))*exp(2)-24*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-12*a*c^6*d^1
0*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*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^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*e
xp(2)^2+2*a*c*d^2*exp(2))*exp(2)-24*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+4*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)-4*c^9*d^16+2*c^7*d^14*sqrt
(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^
4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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)*sqrt(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^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))+4*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(
1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(-8*a^7*c^3*d^4*exp(1)^2*exp(2)^6+8*a^7*c^3*d^4*exp(2)^7-4*a^7*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)*e
xp(1)^2*exp(2)^6+4*a^7*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)^7+72*a^6*c^4*d^6*exp(1)^4*exp(2)^4-96*a^6*c^4*d^6*exp(1)^2*exp(2)^5+24*a^6*c^4*
d^6*exp(2)^6+36*a^6*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a
*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4-48*a^6*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*ex
p(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+12*a^6*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)^6+8*a^6*c^3*d^4*sqrt(-c^2*d^3-
c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-8*a
^6*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)^6-192*a^5*c^5*d^8*exp(1)^6*exp(2)^2+288*a^5*c^5*d^8*exp(1)^4*exp(2)^3-120*a^5*c^5*d^8*exp(1)^2*exp(
2)^4+24*a^5*c^5*d^8*exp(2)^5-96*a^5*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a
*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2+144*a^5*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-60*a^5*c^4*d^7*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+12
*a^5*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))*sq
rt(2)*exp(2)^5-40*a^5*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))
+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+40*a^5*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-4*a^5*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)^4+4*a^5*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)^5+8*
a^5*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-8*a^5*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)^5+128*a^4*c^6*d^10*exp(1)^8-128*a^4*c^6*d^10*exp(1)
^6*exp(2)+48*a^4*c^6*d^10*exp(1)^4*exp(2)^2-64*a^4*c^6*d^10*exp(1)^2*exp(2)^3+16*a^4*c^6*d^10*exp(2)^4+64*a^4*
c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)
*exp(1)^8-64*a^4*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*
d*exp(2))*sqrt(2)*exp(1)^6*exp(2)+24*a^4*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^
2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-32*a^4*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+8*a^4*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)^4+32*a^4*c
^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*
exp(1)^6*exp(2)+24*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-64*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2
*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+8*a^4*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)^4+20*a^4*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)^2-
24*a^4*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)^3+4*a^4*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)^4-40*a^4*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*ex
p(2))*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp
(2)^3-8*a^4*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)^4-192*a^3*c^7*d^12*exp(1
)^6+288*a^3*c^7*d^12*exp(1)^4*exp(2)-120*a^3*c^7*d^12*exp(1)^2*exp(2)^2+24*a^3*c^7*d^12*exp(2)^3-96*a^3*c^6*d^
11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(
1)^6+144*a^3*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*e
xp(2))*sqrt(2)*exp(1)^4*exp(2)-60*a^3*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+12*a^3*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)^3-32*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*
sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-24*a^3*c^6*d^10*
sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^
4*exp(2)+64*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*
d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-8*a^3*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(2)^3-16*a^3*c^6*d^9*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)^6+8*a^3*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*exp(2)+8*a^3*c^6*d^9*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)^2*e
xp(2)^2+32*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-16*a^3*c^5*d^8*(c^2
*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1
)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^8*d^14*exp(1)^4-96*a^2*c^8*d^14*exp(1)^2*exp(2)+
24*a^2*c^8*d^14*exp(2)^2+36*a^2*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*
d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-48*a^2*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a
^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+12*a^2*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)^2+40*a^2*c^7*d^12*sqrt(-c^
2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-40*a^2
*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*exp(1)^2*exp(2)+20*a^2*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*ex
p(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-24*a^2*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*exp(2)+4*a^2*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)^2-40*a^2*c^6*d^10*(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*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))*ex
p(2)^2-8*a*c^9*d^16*exp(1)^2+8*a*c^9*d^16*exp(2)-4*a*c^8*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^
2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^8*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-8*a*c^8*d^14*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+8*a*c^8*d^14*sqrt(
-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-4*a*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)
*exp(1)^2+4*a*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)*exp(2)+8*a*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^
7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)-4*a^7*c^4*d^4*exp(2)^7
+2*a^7*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)^7+32*a^6*c^5*d^6*exp(1)^2*exp(2)
^5-4*a^6*c^5*d^6*exp(2)^6-16*a^6*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)^5+2*a^6*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)^6-4*a^6*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)^6-72*a^5*c^6*d^8*exp(1)^4*exp(2)^3-16*a^5*c^6*d^8*exp(1)^2*
exp(2)^4+4*a^5*c^6*d^8*exp(2)^5+36*a^5*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)^3+8*a^5*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)^4-2*a^5*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)^5+16*a^5*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(1)^2*exp(2)^4+8*a^5*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*e
xp(2))*exp(2)^5+2*a^5*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)^5+4*a^5*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)^5+32*a^4*c^7*d^10*exp(1)^6*exp(2)+120*a^4*c^7
*d^10*exp(1)^4*exp(2)^2-16*a^4*c^7*d^10*exp(1)^2*exp(2)^3+4*a^4*c^7*d^10*exp(2)^4-16*a^4*c^5*d^8*sqrt(-c^2*d^3
-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-60*a^4*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)^2+8*a^4*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))*ex
p(1)^2*exp(2)^3-2*a^4*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)^4-8*a^4*c^5*d^7*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(1)^4*exp(2)^2-48*a^4*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)^3-4*a^4*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(2)^4-8*a^4*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*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)^2*exp(2)^3-2
*a^4*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))*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(2)^4-16*a^4*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)^3-4*a^4*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)^4-32*a^3*c^8*d^12*exp(1)^6-120*a^3*c^8*d^12*exp(1)^4*exp(2)+16*a^3*c^8*d^12*exp(
1)^2*exp(2)^2-4*a^3*c^8*d^12*exp(2)^3+16*a^3*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*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)^6+60*a^3*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)^4*exp(2)-8*a^3*c^6*d^1
0*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*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^6*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(2)^3+16*a^3*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*e
xp(2))*exp(1)^4*exp(2)+64*a^3*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)^
2+4*a^3*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)^4*exp(2)+16*a^3*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)^2+8*a^3*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)^4*exp(2)+32*a^3*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)^2+72*a^2*c^9*d^14*exp(1)^4+16*a^2*c^9*d^14*exp(1)^2*exp(2)-4*a^2*c^9*d^14*exp(2)^2-3
6*a^2*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)^4-8*a^2*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*exp(2)+2*a^2*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)^2-8*a^2*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)^4-48*
a^2*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))*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)^2*exp(2)-4*a^2*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)^2-4*a^2*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)^4-16*a^2*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*exp(
2)-8*a^2*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)^4-32*a^2*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*exp(2)-32*a*c^10*d^16*exp(1)^2+4*a*c^10*d^16*exp(2
)+16*a*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))*exp(1)^2-2*a*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))*exp(2)+16*a*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*e
xp(2))*exp(1)^2+8*a*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))*exp(2)+8*a*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))*exp(1)^2+2*a*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))*exp(2)+16*a*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))*exp(1)^2+4*
a*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))*exp(2)+4*c^11*d^18-2*c^9*d^16*sqrt(-c^2*
d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(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^9*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2
*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(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^9*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))*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))-4*c^9*d^14*(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^5*d^6*exp(1)^2*exp(2)^4-8*a^5*c^5*d^6*exp(2)^5-64*a^4*c^6*d^8*exp(1)^4
*exp(2)^2+96*a^4*c^6*d^8*exp(1)^2*exp(2)^3-32*a^4*c^6*d^8*exp(2)^4-16*a^4*c^6*d^7*exp(1)^2*exp(2)^3+16*a^4*c^6
*d^7*exp(2)^4+128*a^3*c^7*d^10*exp(1)^6-256*a^3*c^7*d^10*exp(1)^4*exp(2)+176*a^3*c^7*d^10*exp(1)^2*exp(2)^2-48
*a^3*c^7*d^10*exp(2)^3+64*a^3*c^7*d^9*exp(1)^4*exp(2)-80*a^3*c^7*d^9*exp(1)^2*exp(2)^2+16*a^3*c^7*d^9*exp(2)^3
+8*a^3*c^7*d^8*exp(1)^2*exp(2)^2-8*a^3*c^7*d^8*exp(2)^3-64*a^2*c^8*d^12*exp(1)^4+96*a^2*c^8*d^12*exp(1)^2*exp(
2)-32*a^2*c^8*d^12*exp(2)^2-64*a^2*c^8*d^11*exp(1)^4+80*a^2*c^8*d^11*exp(1)^2*exp(2)-16*a^2*c^8*d^11*exp(2)^2-
32*a^2*c^8*d^10*exp(1)^4+48*a^2*c^8*d^10*exp(1)^2*exp(2)-16*a^2*c^8*d^10*exp(2)^2+8*a*c^9*d^14*exp(1)^2-8*a*c^
9*d^14*exp(2)+16*a*c^9*d^13*exp(1)^2-16*a*c^9*d^13*exp(2)+8*a*c^9*d^12*exp(1)^2-8*a*c^9*d^12*exp(2))/c^2/d^2*a
tan(sqrt(d+x*exp(1))/sqrt(-(d^7*c^6-d^5*c^5*a*exp(2)+sqrt((-d^7*c^6+d^5*c^5*a*exp(2))*(-d^7*c^6+d^5*c^5*a*exp(
2))-4*d^6*c^6*(d^6*exp(1)^2*c^5*a-d^6*c^5*a*exp(2))))/2/d^6/c^6))-((4*a^7*c^2*d^2*exp(2)^7-2*a^7*sqrt(-c^2*d^3
+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^7-40*a^6*c^3*d^4*exp(1)^2*exp(2)^5+12*a^6*c^3*d^4*exp(2)^6+2
0*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))*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)^5-6*a^6*c*d^2*sqrt(-c^2*d^
3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+4*a^6*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)
^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))*exp(2)^6+128*a^5*c^4*d^6*exp(1)^4*exp(2)^3-56*a^5*c^4*d^6*exp(1)^2*exp(2)^4+12*a^5*c^4*d^6*exp(2)^5-6
4*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*s
qrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+28*a^5*c^2*d^4*sqrt(-c
^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4
*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-6*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^
4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*
exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-24*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp
(1)^2*exp(2)^4-2*a^5*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+
a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c^2*d^2*(c
^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-128*a^4*c^5*d^8*exp(1)^6*exp(2)-16*a^4*c^5*d
^8*exp(1)^2*exp(2)^3+4*a^4*c^5*d^8*exp(2)^4+64*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a
^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp
(2))*exp(1)^6*exp(2)+8*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*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)^2*exp(2)^3-2
*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))*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(2)^4+32*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+32*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(
2)^4+12*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp
(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^4*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)^4+24*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)^3-4*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+16*a^3*c^6*d^10*exp(1)^2*exp(2)^2-4*a^3*c^6*d^10*exp(2)^3-64*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)*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)^6-8*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^
2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)
^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2
*exp(2))*exp(2)^3-64*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(
2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^
3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(
2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-16*a^3*c^4*d^6*sqrt(-c^2*d
^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-4*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*
c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-32*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)-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(1)^2*exp(2)^2-
128*a^2*c^7*d^12*exp(1)^4+56*a^2*c^7*d^12*exp(1)^2*exp(2)-12*a^2*c^7*d^12*exp(2)^2+64*a^2*c^5*d^10*sqrt(-c^2*d
^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c
*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-28*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2
*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*
a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+
2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^
2+32*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2)
)*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+32*a^2*c^5*d^9*sqrt(-c^2*d^3
+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d
^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2
+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+4*
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))*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)+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+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(1)^2*exp(2)+40*a*c^8*d^14*exp(1)^2-12*a*c^8*d^14*exp(2)-20*a*c^6*d^12*sqrt(-c^2*d^3+c*
d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^
2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*
exp(2))*exp(2)-24*a*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+
a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-12*a*c^6*d^10*sq
rt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a
*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2
)^2+2*a*c*d^2*exp(2))*exp(2)-24*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
+4*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)-4*c^9*d^16+2*c^7*d^14*sqrt(-c^
2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*
a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*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)*sqrt(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^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))+4*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2
+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(-8*a^7*c^3*d^4*exp(1)^2*exp(2)^6+8*a^7*c^3*d^4*exp(2)^7+4*a^7*c^2*d^
3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1
)^2*exp(2)^6-4*a^7*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)^7+72*a^6*c^4*d^6*exp(1)^4*exp(2)^4-96*a^6*c^4*d^6*exp(1)^2*exp(2)^5+24*a^6*c^4*d^6*
exp(2)^6-36*a^6*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d
*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+48*a^6*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)
^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-12*a^6*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)^6-8*a^6*c^3*d^4*sqrt(-c^2*d^3+c*d*
sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+8*a^6*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)^6-192*a^5*c^5*d^8*exp(1)^6*exp(2)^2+288*a^5*c^5*d^8*exp(1)^4*exp(2)^3-120*a^5*c^5*d^8*exp(1)^2*exp(2)^4
+24*a^5*c^5*d^8*exp(2)^5+96*a^5*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d
^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-144*a^5*c^4*d^7*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)^4*exp(2)^3+60*a^5*c^4*d^7*sqrt(-c^2*d^3+c*d
*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-12*a^5
*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)^5+40*a^5*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c
*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-40*a^5*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(
2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+4*a^5*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)^4-4*a^5*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)^5+8*a^5*
c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-8*a^5*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)^5+128*a^4*c^6*d^10*exp(1)^8-128*a^4*c^6*d^10*exp(1)^6*e
xp(2)+48*a^4*c^6*d^10*exp(1)^4*exp(2)^2-64*a^4*c^6*d^10*exp(1)^2*exp(2)^3+16*a^4*c^6*d^10*exp(2)^4-64*a^4*c^5*
d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp
(1)^8+64*a^4*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*ex
p(2))*sqrt(2)*exp(1)^6*exp(2)-24*a^4*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*
a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+32*a^4*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^
2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-8*a^4*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)^4-32*a^4*c^5*d
^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(
1)^6*exp(2)-24*a^4*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*
c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+64*a^4*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-8*a^4*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)^4-20*a^4*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)^2+24*a
^4*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)^3-4*a^4*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*e
xp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-40*a^4*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)
)*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^
3-8*a^4*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)^4-192*a^3*c^7*d^12*exp(1)^6+
288*a^3*c^7*d^12*exp(1)^4*exp(2)-120*a^3*c^7*d^12*exp(1)^2*exp(2)^2+24*a^3*c^7*d^12*exp(2)^3+96*a^3*c^6*d^11*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
-144*a^3*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2
))*sqrt(2)*exp(1)^4*exp(2)+60*a^3*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-12*a^3*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)^3+32*a^3*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt
(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+24*a^3*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*ex
p(2)-64*a^3*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*ex
p(2))*sqrt(2)*exp(1)^2*exp(2)^2+8*a^3*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(2)^3+16*a^3*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)^6-8*a^3*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*exp(2)-8*a^3*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
)^2+32*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-16*a^3*c^5*d^8*(c^2*d^4
-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+
a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^8*d^14*exp(1)^4-96*a^2*c^8*d^14*exp(1)^2*exp(2)+24*a
^2*c^8*d^14*exp(2)^2-36*a^2*c^7*d^13*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*
exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+48*a^2*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*e
xp(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^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)^2-40*a^2*c^7*d^12*sqrt(-c^2*d^
3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+40*a^2*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)*e
xp(1)^2*exp(2)-20*a^2*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)^4+24*a^2*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*exp(2)-4*a^2*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)^2-40*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*
exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*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)
^2-8*a*c^9*d^16*exp(1)^2+8*a*c^9*d^16*exp(2)+4*a*c^8*d^15*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^
2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^8*d^15*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*
d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^8*d^14*sqrt(-c^2*d^3+c*d*sqrt(c
^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-8*a*c^8*d^14*sqrt(-c^2
*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+4*a*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)*exp
(1)^2-4*a*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)*exp(2)+8*a*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^7*d^
12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)-4*a^7*c^4*d^4*exp(2)^7+2*a
^7*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)^7+32*a^6*c^5*d^6*exp(1)^2*exp(2)^5-4
*a^6*c^5*d^6*exp(2)^6-16*a^6*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)^5
+2*a^6*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)^6-4*a^6*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)^6-72*a^5*c^6*d^8*exp(1)^4*exp(2)^3-16*a^5*c^6*d^8*exp(1)^2*exp(
2)^4+4*a^5*c^6*d^8*exp(2)^5+36*a^5*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*ex
p(2)^3+8*a^5*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*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)^2*exp(2)^4-2*a^5*c^4*d^6*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+16*a^5*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*ex
p(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+8*a^5*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)^5+2*a^5*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)^5+4*a^5*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)^5+32*a^4*c^7*d^10*exp(1)^6*exp(2)+120*a^4*c^7*d^1
0*exp(1)^4*exp(2)^2-16*a^4*c^7*d^10*exp(1)^2*exp(2)^3+4*a^4*c^7*d^10*exp(2)^4-16*a^4*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*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-60*a^4*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)^2+8*a^4*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)^3-2*a^4*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)^4-8*a^4*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)^4*exp(2)^2-48*a^4*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)^3-4*a^4*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(2)^4-8*a^4*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)^3-2*a^4
*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(2)^4-16*a^4*c^5*d^6*(c^2*d^4-4*a*c*d^2*ex
p(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*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)^4-32*a^3*c^8*d^12*exp(1)^6-120*a^3*c^8*d^12*exp(1)^4*exp(2)+16*a^3*c^8*d^12*exp(1)^2
*exp(2)^2-4*a^3*c^8*d^12*exp(2)^3+16*a^3*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)^6+60*a^3*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*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)^4*exp(2)-8*a^3*c^6*d^10*sq
rt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*
d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*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)^3+16*a^3*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)^4*exp(2)+64*a^3*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)^2+4*
a^3*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))*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)^4*exp(2)+16*a^3*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)^2+8*a^3*c^6*d^8*(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)+32*a^3*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*ex
p(2))*exp(1)^2*exp(2)^2+72*a^2*c^9*d^14*exp(1)^4+16*a^2*c^9*d^14*exp(1)^2*exp(2)-4*a^2*c^9*d^14*exp(2)^2-36*a^
2*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)^4-8*a^2*c^7*d^12*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)^2*exp(2)+2*a^2*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*e
xp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*
c*d^2*exp(2))*exp(2)^2-8*a^2*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)^4-48*a^2*
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*exp(2)-4*a^2*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)^2-4*a^2*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)^4-16*a^2*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*exp(2)-8
*a^2*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)^4-32*a^2*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*exp(2)-32*a*c^10*d^16*exp(1)^2+4*a*c^10*d^16*exp(2)+16
*a*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))*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^8*d^14*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)+16*a*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
))*exp(1)^2+8*a*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))*exp(2)+8*a*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))*exp(1)^2+2*a*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))*exp(2)+16*a*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))*exp(1)^2+4*a*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))*exp(2)+4*c^11*d^18-2*c^9*d^16*sqrt(-c^2*d^3+
c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(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^9*d^15*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp
(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(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^9*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^9*d^14*(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)))/(8*a^5*c^5*d^6*exp(1)^2*exp(2)^4-8*a^5*c^5*d^6*exp(2)^5-64*a^4*c^6*d^8*exp(1)^4*exp
(2)^2+96*a^4*c^6*d^8*exp(1)^2*exp(2)^3-32*a^4*c^6*d^8*exp(2)^4-16*a^4*c^6*d^7*exp(1)^2*exp(2)^3+16*a^4*c^6*d^7
*exp(2)^4+128*a^3*c^7*d^10*exp(1)^6-256*a^3*c^7*d^10*exp(1)^4*exp(2)+176*a^3*c^7*d^10*exp(1)^2*exp(2)^2-48*a^3
*c^7*d^10*exp(2)^3+64*a^3*c^7*d^9*exp(1)^4*exp(2)-80*a^3*c^7*d^9*exp(1)^2*exp(2)^2+16*a^3*c^7*d^9*exp(2)^3+8*a
^3*c^7*d^8*exp(1)^2*exp(2)^2-8*a^3*c^7*d^8*exp(2)^3-64*a^2*c^8*d^12*exp(1)^4+96*a^2*c^8*d^12*exp(1)^2*exp(2)-3
2*a^2*c^8*d^12*exp(2)^2-64*a^2*c^8*d^11*exp(1)^4+80*a^2*c^8*d^11*exp(1)^2*exp(2)-16*a^2*c^8*d^11*exp(2)^2-32*a
^2*c^8*d^10*exp(1)^4+48*a^2*c^8*d^10*exp(1)^2*exp(2)-16*a^2*c^8*d^10*exp(2)^2+8*a*c^9*d^14*exp(1)^2-8*a*c^9*d^
14*exp(2)+16*a*c^9*d^13*exp(1)^2-16*a*c^9*d^13*exp(2)+8*a*c^9*d^12*exp(1)^2-8*a*c^9*d^12*exp(2))/c^2/d^2*atan(
sqrt(d+x*exp(1))/sqrt(-(d^7*c^6-d^5*c^5*a*exp(2)-sqrt((-d^7*c^6+d^5*c^5*a*exp(2))*(-d^7*c^6+d^5*c^5*a*exp(2))-
4*d^6*c^6*(d^6*exp(1)^2*c^5*a-d^6*c^5*a*exp(2))))/2/d^6/c^6))+(2/5*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^4*c^4+2/3
*sqrt(d+x*exp(1))*(d+x*exp(1))*d^5*c^4-2/3*sqrt(d+x*exp(1))*(d+x*exp(1))*d^3*c^3*a*exp(2)+2*sqrt(d+x*exp(1))*d
^6*c^4-2*sqrt(d+x*exp(1))*d^4*exp(1)^2*c^3*a-2*sqrt(d+x*exp(1))*d^4*c^3*a*exp(2)+2*sqrt(d+x*exp(1))*d^2*c^2*a^
2*exp(2)^2)/d^5/c^5

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maple [B]  time = 0.06, size = 324, normalized size = 2.20 \begin {gather*} -\frac {2 a^{3} e^{6} \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^{3} d^{3}}+\frac {6 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}-\frac {6 a d \,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^{3} \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^{2} e^{4}}{c^{3} d^{3}}-\frac {4 \sqrt {e x +d}\, a \,e^{2}}{c^{2} d}+\frac {2 \sqrt {e x +d}\, d}{c}-\frac {2 \left (e x +d \right )^{\frac {3}{2}} a \,e^{2}}{3 c^{2} d^{2}}+\frac {2 \left (e x +d \right )^{\frac {3}{2}}}{3 c}+\frac {2 \left (e x +d \right )^{\frac {5}{2}}}{5 c d} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)

[Out]

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

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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((e*x+d)^(7/2)/(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 = 0.65, size = 165, normalized size = 1.12 \begin {gather*} \frac {2\,{\left (d+e\,x\right )}^{5/2}}{5\,c\,d}+\frac {2\,{\left (a\,e^2-c\,d^2\right )}^2\,\sqrt {d+e\,x}}{c^3\,d^3}-\frac {2\,\left (a\,e^2-c\,d^2\right )\,{\left (d+e\,x\right )}^{3/2}}{3\,c^2\,d^2}-\frac {2\,\mathrm {atan}\left (\frac {\sqrt {c}\,\sqrt {d}\,{\left (a\,e^2-c\,d^2\right )}^{5/2}\,\sqrt {d+e\,x}}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}\right )\,{\left (a\,e^2-c\,d^2\right )}^{5/2}}{c^{7/2}\,d^{7/2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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