3.1942 \(\int \frac {(a d e+(c d^2+a e^2) x+c d e x^2)^{5/2}}{(d+e x)^7} \, dx\)

Optimal. Leaf size=54 \[ \frac {2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{7/2}}{7 (d+e x)^7 \left (c d^2-a e^2\right )} \]

[Out]

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

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Rubi [A]  time = 0.02, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {650} \[ \frac {2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{7/2}}{7 (d+e x)^7 \left (c d^2-a e^2\right )} \]

Antiderivative was successfully verified.

[In]

Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^7,x]

[Out]

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

Rule 650

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[(e*(d + e*x)^m*(a +
b*x + c*x^2)^(p + 1))/((p + 1)*(2*c*d - b*e)), x] /; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c, 0] &&
EqQ[c*d^2 - b*d*e + a*e^2, 0] &&  !IntegerQ[p] && EqQ[m + 2*p + 2, 0]

Rubi steps

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

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Mathematica [A]  time = 0.04, size = 43, normalized size = 0.80 \[ \frac {2 ((d+e x) (a e+c d x))^{7/2}}{7 (d+e x)^7 \left (c d^2-a e^2\right )} \]

Antiderivative was successfully verified.

[In]

Integrate[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^7,x]

[Out]

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

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fricas [B]  time = 8.12, size = 170, normalized size = 3.15 \[ \frac {2 \, {\left (c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{2} e x^{2} + 3 \, a^{2} c d e^{2} x + a^{3} e^{3}\right )} \sqrt {c d e x^{2} + a d e + {\left (c d^{2} + a e^{2}\right )} x}}{7 \, {\left (c d^{6} - a d^{4} e^{2} + {\left (c d^{2} e^{4} - a e^{6}\right )} x^{4} + 4 \, {\left (c d^{3} e^{3} - a d e^{5}\right )} x^{3} + 6 \, {\left (c d^{4} e^{2} - a d^{2} e^{4}\right )} x^{2} + 4 \, {\left (c d^{5} e - a d^{3} e^{3}\right )} x\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^7,x, algorithm="fricas")

[Out]

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

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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((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^7,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-15*exp(1)^6*(sqrt(a*d*exp(1)+a*x*ex
p(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^6*exp(2)^6-90*c*d^2*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)
+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^5*exp(2)^5+180*c*d^2*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^5*exp(2)^4-225*c^2*d^4*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d
^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^4*exp(2)^4+720*c^2*d^4*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^4*exp(2)^3-720*c^2*d^4*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^4*exp(2)^2+2772*c^3*d^6*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^3*exp(2)^3-8136*c^3*d^6*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^3*exp(2)^2+7776*c^3*d^6*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d
^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^3*exp(2)-2112*c^3*d^6*exp(1)^12*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^3-225*c^4*d^8*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^
2*exp(1))-sqrt(c*d*exp(1))*x)^11*a^2*exp(2)^2+720*c^4*d^8*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2
*exp(1))-sqrt(c*d*exp(1))*x)^11*a^2*exp(2)-720*c^4*d^8*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*e
xp(1))-sqrt(c*d*exp(1))*x)^11*a^2-90*c^5*d^10*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqr
t(c*d*exp(1))*x)^11*a*exp(2)+180*c^5*d^10*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*
d*exp(1))*x)^11*a-15*c^6*d^12*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)
^11+165*d*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10
*a^6*exp(2)^6+990*c*d^3*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d
*exp(1))*x)^10*a^5*exp(2)^5-1980*c*d^3*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*e
xp(1))-sqrt(c*d*exp(1))*x)^10*a^5*exp(2)^4-6741*c^2*d^5*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+
c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^4*exp(2)^4+19728*c^2*d^5*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*
exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^4*exp(2)^3-19728*c^2*d^5*exp(1)^9*sqrt(c*d*
exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^4*exp(2)^2+9216*c^2*d^5*e
xp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^4*exp(2
)-21276*c^3*d^7*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))
*x)^10*a^3*exp(2)^3+61848*c^3*d^7*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1)
)-sqrt(c*d*exp(1))*x)^10*a^3*exp(2)^2-57888*c^3*d^7*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^3*exp(2)+14016*c^3*d^7*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1
)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^3+2475*c^4*d^9*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a
*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^2*exp(2)^2-7920*c^4*d^9*exp(1)^7*sqrt(c*
d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^2*exp(2)+7920*c^4*d^9*e
xp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a^2+990*c^
5*d^11*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^10*a*
exp(2)-1980*c^5*d^11*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*ex
p(1))*x)^10*a+165*c^6*d^13*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(
c*d*exp(1))*x)^10-85*d*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^7*
exp(2)^7+85*d*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^7*exp(2)^6-
1335*c*d^3*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^6*exp(2)^6+153
0*c*d^3*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^6*exp(2)^5-1020*c
*d^3*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^6*exp(2)^4+9135*c^2*
d^5*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^5*exp(2)^5-30825*c^2*
d^5*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^5*exp(2)^4+37920*c^2*
d^5*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^5*exp(2)^3-11280*c^2*
d^5*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^5*exp(2)^2+52485*c^3
*d^7*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)^4-157380*c^
3*d^7*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)^3+161160*c
^3*d^7*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)^2-68320*c
^3*d^7*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)-320*c^3*
d^7*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4+74385*c^4*d^9*exp(
1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)^3-211725*c^4*d^9*exp
(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)^2+189120*c^4*d^9*ex
p(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)-35280*c^4*d^9*exp(
1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3-12885*c^5*d^11*exp(1)^5*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2*exp(2)^2+41130*c^5*d^11*exp(1)^7*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2*exp(2)-40620*c^5*d^11*exp(1)^9*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2-5035*c^6*d^13*exp(1)^5*(sqrt(a*d*e
xp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a*exp(2)+9985*c^6*d^13*exp(1)^7*(sqrt(a*d*exp(1
)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a-825*c^7*d^15*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)
+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9+765*d^2*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c
*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^7*exp(2)^7-765*d^2*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a
*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^7*exp(2)^6-8295*c*d^4*exp(1)^4*sqrt(c*d*exp(1))*(sqr
t(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^6*exp(2)^6+32310*c*d^4*exp(1)^6*sqrt(c
*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^6*exp(2)^5-36900*c*d^4*
exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^6*exp(2)
^4+15360*c*d^4*exp(1)^10*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))
*x)^8*a^6*exp(2)^3-65835*c^2*d^6*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))
-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^5+198585*c^2*d^6*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2
*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^4-203040*c^2*d^6*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1
)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^3+55440*c^2*d^6*exp(1)^10*sqrt(c*d*exp(1
))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^2-177975*c^3*d^8*exp(1
)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4*exp(2)^4+54
8100*c^3*d^8*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)
^8*a^4*exp(2)^3-582120*c^3*d^8*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-s
qrt(c*d*exp(1))*x)^8*a^4*exp(2)^2+246240*c^3*d^8*exp(1)^10*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*
x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4*exp(2)+2880*c^3*d^8*exp(1)^12*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*
x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4-154065*c^4*d^10*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d
*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp(2)^3+418725*c^4*d^10*exp(1)^6*sqrt(c*
d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp(2)^2-334080*c^4*d^
10*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp
(2)+19920*c^4*d^10*exp(1)^10*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp
(1))*x)^8*a^3+41715*c^5*d^12*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqr
t(c*d*exp(1))*x)^8*a^2*exp(2)^2-132570*c^5*d^12*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+
c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^2*exp(2)+127980*c^5*d^12*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*
x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^2+15615*c^6*d^14*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*
exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a*exp(2)-30465*c^6*d^14*exp(1)^6*sqrt(c*d*exp(
1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a+2475*c^7*d^16*exp(1)^4*sqrt(c*
d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8-198*d^2*exp(1)^4*(sqrt(a*d
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exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^8*exp(2)^6+4968*c*d^4*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp
(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^7*exp(2)^7-19836*c*d^4*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2
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d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^7*exp(2)^4+50520*c^2*d^6*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
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c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^6*exp(2)^4-20640*c^2*d^6*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)
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p(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5*exp(2)^3-285840*c^3*d^8*exp(1)^10*(sqrt(a*d*exp(1)+a*x*
exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5*exp(2)^2+66240*c^3*d^8*exp(1)^12*(sqrt(a*d*exp(1)+a*x
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xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5+368460*c^4*d^10*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c
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p(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^4*exp(2)^2-514080*c^4*d^10*exp(1)^10*(sqrt(a*d*exp(1)+a*x
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p(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3*exp(2)+118920*c^5*d^12*exp(1)^10*(sqrt(a*d*exp(1)+a*x*e
xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3-92808*c^6*d^14*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2*exp(2)^2+293076*c^6*d^14*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+
c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2*exp(2)-274518*c^6*d^14*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+
c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2-32760*c^7*d^16*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+
c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a*exp(2)+62460*c^7*d^16*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d
*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a-4950*c^8*d^18*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1)
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-sqrt(c*d*exp(1))*x)^6*a^8*exp(2)^8+6444*d^3*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d
*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^8*exp(2)^7-7830*d^3*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)
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(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^7*exp(2)^7+66092*c*d^5*exp(1)^5*sq
rt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^7*exp(2)^6-44436*c*
d^5*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^7*ex
p(2)^5-8440*c*d^5*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)^6*a^7*exp(2)^4+10240*c*d^5*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1)
)-sqrt(c*d*exp(1))*x)^6*a^7*exp(2)^3-129120*c^2*d^7*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^6+390060*c^2*d^7*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^5-406650*c^2*d^7*exp(1)^7*sqrt(c*d*exp(
1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^4+175200*c^2*d^7*exp(
1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^3-5
3280*c^2*d^7*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x
)^6*a^6*exp(2)^2+30720*c^2*d^7*exp(1)^13*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-
sqrt(c*d*exp(1))*x)^6*a^6*exp(2)-376560*c^3*d^9*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+
c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^5*exp(2)^5+1265580*c^3*d^9*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+
a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^5*exp(2)^4-1596120*c^3*d^9*exp(1)^7*sqrt(c*d*exp(1)
)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^5*exp(2)^3+935280*c^3*d^9*exp(1)
^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^5*exp(2)^2-279
360*c^3*d^9*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)
^6*a^5*exp(2)+9600*c^3*d^9*exp(1)^13*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt
(c*d*exp(1))*x)^6*a^5-510700*c^4*d^11*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*ex
p(1))-sqrt(c*d*exp(1))*x)^6*a^4*exp(2)^4+1612900*c^4*d^11*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2
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a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^4*exp(2)^2+563680*c^4*d^11*exp(1)^9*sqrt
(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^4*exp(2)+147680*c^4*d
^11*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^4-1
51488*c^5*d^13*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*
x)^6*a^3*exp(2)^3+234468*c^5*d^13*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1)
)-sqrt(c*d*exp(1))*x)^6*a^3*exp(2)^2+175788*c^5*d^13*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d
^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^3*exp(2)-397368*c^5*d^13*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^3+148176*c^6*d^15*exp(1)^3*sqrt(c*d*exp(1))*(sqr
t(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^2*exp(2)^2-463932*c^6*d^15*exp(1)^5*sq
rt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^2*exp(2)+419706*c^6
*d^15*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^2+
48720*c^7*d^17*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*
x)^6*a*exp(2)-90300*c^7*d^17*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqr
t(c*d*exp(1))*x)^6*a+6930*c^8*d^19*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1
))-sqrt(c*d*exp(1))*x)^6+198*d^3*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))
*x)^5*a^9*exp(2)^9-594*d^3*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*
a^9*exp(2)^8+594*d^3*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^9*ex
p(2)^7-198*d^3*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^9*exp(2)^6
+6246*c*d^5*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^8*exp(2)^8-16
056*c*d^5*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^8*exp(2)^7+6534
*c*d^5*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^8*exp(2)^6+10116*c
*d^5*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^8*exp(2)^5-6840*c*d^
5*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^8*exp(2)^4+53328*c^2*d
^7*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^7-159816*c^2*
d^7*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^6+171018*c^2
*d^7*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^5-105330*c^
2*d^7*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^4+59520*c^
2*d^7*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^3-18720*c
^2*d^7*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^7*exp(2)^2+223680
*c^3*d^9*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)^6-78084
0*c^3*d^9*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)^5+1090
350*c^3*d^9*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)^4-82
0200*c^3*d^9*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)^3+3
98160*c^3*d^9*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)^2
-112320*c^3*d^9*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6*exp(2)
-5760*c^3*d^9*exp(1)^15*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^6+500940*c
^4*d^11*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp(2)^5-180846
0*c^4*d^11*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp(2)^4+249
0390*c^4*d^11*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp(2)^3-
1592010*c^4*d^11*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp(2)
^2+406080*c^4*d^11*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp
(2)+44640*c^4*d^11*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5+474
684*c^5*d^13*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^4*exp(2)^4-1
429512*c^5*d^13*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^4*exp(2)^
3+1291122*c^5*d^13*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^4*exp(
2)^2-61404*c^5*d^13*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^4*exp
(2)-378840*c^5*d^13*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^4+23
136*c^6*d^15*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^3*exp(2)^3+2
31480*c^6*d^15*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^3*exp(2)^2
-776178*c^6*d^15*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^3*exp(2)
+660162*c^6*d^15*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^3-172368
*c^7*d^17*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^2*exp(2)^2+5337
36*c^7*d^17*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^2*exp(2)-4653
18*c^7*d^17*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^2-52290*c^8*d
^19*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a*exp(2)+93870*c^8*d^19
*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a-6930*c^9*d^21*exp(1)^3*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5-990*d^4*exp(1)^2*sqrt(c*d*exp(1))*(sq
rt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^9*exp(2)^9+2970*d^4*exp(1)^4*sqrt(c*d
*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^9*exp(2)^8-2970*d^4*exp(1
)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^9*exp(2)^7+99
0*d^4*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^9*
exp(2)^6-14370*c*d^6*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*ex
p(1))*x)^4*a^8*exp(2)^8+46560*c*d^6*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)^4*a^8*exp(2)^7-61890*c*d^6*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2
*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^8*exp(2)^6+56940*c*d^6*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a
*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^8*exp(2)^5-42600*c*d^6*exp(1)^10*sqrt(c*d*exp(1))*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^8*exp(2)^4+15360*c*d^6*exp(1)^12*sqr
t(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^8*exp(2)^3-85440*c^2
*d^8*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*e
xp(2)^7+314400*c^2*d^8*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*
exp(1))*x)^4*a^7*exp(2)^6-487530*c^2*d^8*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2
*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*exp(2)^5+431850*c^2*d^8*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(
2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*exp(2)^4-220800*c^2*d^8*exp(1)^10*sqrt(c*d*exp(1))*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*exp(2)^3+47520*c^2*d^8*exp(1)^12*sqrt(
c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*exp(2)^2-276720*c^3*
d^10*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^6*e
xp(2)^6+1102320*c^3*d^10*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*
d*exp(1))*x)^4*a^6*exp(2)^5-1810530*c^3*d^10*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d
*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^6*exp(2)^4+1581000*c^3*d^10*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*
x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^6*exp(2)^3-766800*c^3*d^10*exp(1)^10*sqrt(c*d*exp(1))
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^6*exp(2)^2+146880*c^3*d^10*exp(1)
^12*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^6*exp(2)+2880
0*c^3*d^10*exp(1)^14*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^
4*a^6-453900*c^4*d^12*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*e
xp(1))*x)^4*a^5*exp(2)^5+1684500*c^4*d^12*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^
2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^5*exp(2)^4-2319870*c^4*d^12*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*e
xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^5*exp(2)^3+1322130*c^4*d^12*exp(1)^8*sqrt(c*d*exp(1))*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^5*exp(2)^2-81600*c^4*d^12*exp(1)^10*
sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^5*exp(2)-180960*c
^4*d^12*exp(1)^12*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a
^5-274020*c^5*d^14*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(
1))*x)^4*a^4*exp(2)^4+677760*c^5*d^14*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*ex
p(1))-sqrt(c*d*exp(1))*x)^4*a^4*exp(2)^3-186390*c^5*d^14*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)
+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^4*exp(2)^2-719220*c^5*d^14*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*
d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^4*exp(2)+576120*c^5*d^14*exp(1)^10*sqrt(c*
d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^4+85200*c^6*d^16*exp(1)^
2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^3*exp(2)^3-5493
60*c^6*d^16*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^
4*a^3*exp(2)^2+1063170*c^6*d^16*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-
sqrt(c*d*exp(1))*x)^4*a^3*exp(2)-698010*c^6*d^16*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x
+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^3+145440*c^7*d^18*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(
2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^2*exp(2)^2-444240*c^7*d^18*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^2*exp(2)+373050*c^7*d^18*exp(1)^6*sqrt(c
*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^2+40410*c^8*d^20*exp(1)
^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a*exp(2)-70110*c
^8*d^20*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a+
4950*c^9*d^22*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x
)^4+85*d^4*exp(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^10*exp(2)^10-3
40*d^4*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^10*exp(2)^9+510*d^
4*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^10*exp(2)^8-340*d^4*exp
(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^10*exp(2)^7+85*d^4*exp(1)^10
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^10*exp(2)^6+2490*c*d^6*exp(1)^2*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^9-9000*c*d^6*exp(1)^4*(sqr
t(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^8+13080*c*d^6*exp(1)^6*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^7-10140*c*d^6*exp(1)^8*(sqrt(a*
d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^6+4590*c*d^6*exp(1)^10*(sqrt(a*d*
exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^5-1020*c*d^6*exp(1)^12*(sqrt(a*d*ex
p(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^4+21585*c^2*d^8*exp(1)^2*(sqrt(a*d*ex
p(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^8-85440*c^2*d^8*exp(1)^4*(sqrt(a*d*ex
p(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^7+143400*c^2*d^8*exp(1)^6*(sqrt(a*d*e
xp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^6-129060*c^2*d^8*exp(1)^8*(sqrt(a*d*
exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^5+50475*c^2*d^8*exp(1)^10*(sqrt(a*d
*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^4+10320*c^2*d^8*exp(1)^12*(sqrt(a*
d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^3-11280*c^2*d^8*exp(1)^14*(sqrt(a
*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^2+95320*c^3*d^10*exp(1)^2*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^7-412720*c^3*d^10*exp(1)^4*(sqr
t(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^6+765000*c^3*d^10*exp(1)^6*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^5-782700*c^3*d^10*exp(1)^8*
(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^4+461700*c^3*d^10*exp(1)^
10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^3-151080*c^3*d^10*exp(
1)^12*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)^2+24800*c^3*d^10*ex
p(1)^14*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7*exp(2)-320*c^3*d^10*exp(
1)^16*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^7+229530*c^4*d^12*exp(1)^2*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)^6-983880*c^4*d^12*exp(1)^4
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)^5+1712100*c^4*d^12*exp(1
)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)^4-1502460*c^4*d^12*ex
p(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)^3+618075*c^4*d^12*
exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)^2-6960*c^4*d^12
*exp(1)^12*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6*exp(2)-68880*c^4*d^12
*exp(1)^14*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^6+261180*c^5*d^14*exp(1
)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)^5-928320*c^5*d^14*exp
(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)^4+1091880*c^5*d^14*
exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)^3-234900*c^5*d^1
4*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)^2-461010*c^5*d
^14*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)+286020*c^5*
d^14*exp(1)^12*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5+71130*c^6*d^16*ex
p(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^4+7200*c^6*d^16*ex
p(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^3-623160*c^6*d^16*
exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^2+1053300*c^6*d^
16*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)-545595*c^6*d^
16*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4-104040*c^7*d^18*exp
(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)^3+511920*c^7*d^18*e
xp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)^2-848520*c^7*d^18
*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)+490140*c^7*d^18
*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^3-86895*c^8*d^20*exp(1)^
2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)^2+261180*c^8*d^20*exp(1
)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)-211410*c^8*d^20*exp(1
)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^2-21990*c^9*d^22*exp(1)^2*(sqr
t(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a*exp(2)+36840*c^9*d^22*exp(1)^4*(sqrt(a
*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a-2475*c^10*d^24*exp(1)^2*(sqrt(a*d*exp(1)+
a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3-255*d^5*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*
exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^10*exp(2)^10+1020*d^5*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a
*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^10*exp(2)^9-1530*d^5*exp(1)^5*sqrt(c*d*ex
p(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^10*exp(2)^8+1020*d^5*exp(1)^
7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^10*exp(2)^7-255
*d^5*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^10*
exp(2)^6-3510*c*d^7*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)^2*a^9*exp(2)^9+15120*c*d^7*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))
-sqrt(c*d*exp(1))*x)^2*a^9*exp(2)^8-27360*c*d^7*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+
c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^9*exp(2)^7+26460*c*d^7*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*
exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^9*exp(2)^6-13770*c*d^7*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^9*exp(2)^5+3060*c*d^7*exp(1)^11*sqrt(c*d
*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^9*exp(2)^4-20763*c^2*d^9*
exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^8
+97056*c^2*d^9*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*
x)^2*a^8*exp(2)^7-196128*c^2*d^9*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))
-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^6+220860*c^2*d^9*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2
*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^5-149985*c^2*d^9*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1
)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^4+70416*c^2*d^9*exp(1)^11*sqrt(c*d*exp(1
))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^3-30672*c^2*d^9*exp(1)
^13*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^2+92
16*c^2*d^9*exp(1)^15*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^
2*a^8*exp(2)-68232*c^3*d^11*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c
*d*exp(1))*x)^2*a^7*exp(2)^7+328944*c^3*d^11*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d
*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^7*exp(2)^6-675792*c^3*d^11*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x
*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^7*exp(2)^5+757980*c^3*d^11*exp(1)^7*sqrt(c*d*exp(1))*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^7*exp(2)^4-486540*c^3*d^11*exp(1)^9
*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^7*exp(2)^3+16178
4*c^3*d^11*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^
2*a^7*exp(2)^2-9888*c^3*d^11*exp(1)^13*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sq
rt(c*d*exp(1))*x)^2*a^7*exp(2)-8256*c^3*d^11*exp(1)^15*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*
d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^7-115470*c^4*d^13*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^6*exp(2)^6+499320*c^4*d^13*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*e
xp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^6*exp(2)^5-832500*c^4*d^13*exp(1)^5*sqrt(c*d*
exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^6*exp(2)^4+598740*c^4*d^13
*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^6*exp(2
)^3-42705*c^4*d^13*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(
1))*x)^2*a^6*exp(2)^2-198000*c^4*d^13*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*e
xp(1))-sqrt(c*d*exp(1))*x)^2*a^6*exp(2)+91440*c^4*d^13*exp(1)^13*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+
c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^6-81540*c^5*d^15*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*
exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^5*exp(2)^5+225360*c^5*d^15*exp(1)^3*sqrt(c*d*exp(1))*(s
qrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^5*exp(2)^4-37440*c^5*d^15*exp(1)^5*s
qrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^5*exp(2)^3-480780*
c^5*d^15*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a
^5*exp(2)^2+611190*c^5*d^15*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt
(c*d*exp(1))*x)^2*a^5*exp(2)-241740*c^5*d^15*exp(1)^11*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*
d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^5+16290*c^6*d^17*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d
^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)^4-210240*c^6*d^17*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*ex
p(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)^3+627120*c^6*d^17*exp(1)^5*sqrt(c*d*e
xp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)^2-739980*c^6*d^17*
exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)
+319185*c^6*d^17*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1)
)*x)^2*a^4+60792*c^7*d^19*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d
*exp(1))*x)^2*a^3*exp(2)^3-272304*c^7*d^19*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x
^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^3*exp(2)^2+418032*c^7*d^19*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*e
xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^3*exp(2)-223020*c^7*d^19*exp(1)^7*sqrt(c*d*exp(1))*(sqrt
(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^3+34893*c^8*d^21*exp(1)*sqrt(c*d*exp(1)
)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)^2-102996*c^8*d^21*exp(1
)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)+8047
8*c^8*d^21*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2
*a^2+8010*c^9*d^23*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1)
)*x)^2*a*exp(2)-12960*c^9*d^23*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-s
qrt(c*d*exp(1))*x)^2*a+825*c^10*d^25*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1
))-sqrt(c*d*exp(1))*x)^2+15*d^5*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)
*a^11*exp(2)^11-75*d^5*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^11*e
xp(2)^10+150*d^5*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^11*exp(2)^
9-150*d^5*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^11*exp(2)^8+75*d^
5*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^11*exp(2)^7-15*d^5*exp(1)
^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^11*exp(2)^6+345*c*d^7*exp(1)*(sq
rt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^10-1650*c*d^7*exp(1)^3*(sqrt(
a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^9+3330*c*d^7*exp(1)^5*(sqrt(a*d*
exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^8-3720*c*d^7*exp(1)^7*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^7+2505*c*d^7*exp(1)^9*(sqrt(a*d*exp(1)+a
*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^6-990*c*d^7*exp(1)^11*(sqrt(a*d*exp(1)+a*x*e
xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^5+180*c*d^7*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2
)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^10*exp(2)^4+2745*c^2*d^9*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^9-13995*c^2*d^9*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^
2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^8+30960*c^2*d^9*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*
x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^7-38520*c^2*d^9*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+
c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^6+29295*c^2*d^9*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*
d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^5-14085*c^2*d^9*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d
*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^4+4320*c^2*d^9*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x
^2*exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^3-720*c^2*d^9*exp(1)^15*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*
exp(1))-sqrt(c*d*exp(1))*x)*a^9*exp(2)^2+11751*c^3*d^11*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp
(1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^8-63192*c^3*d^11*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^7+149136*c^3*d^11*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^6-201240*c^3*d^11*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^5+169605*c^3*d^11*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^4-90900*c^3*d^11*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^3+27048*c^3*d^11*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(
1))-sqrt(c*d*exp(1))*x)*a^8*exp(2)^2-96*c^3*d^11*exp(1)^15*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))
-sqrt(c*d*exp(1))*x)*a^8*exp(2)-2112*c^3*d^11*exp(1)^17*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sq
rt(c*d*exp(1))*x)*a^8+26454*c^4*d^13*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^7-132438*c^4*d^13*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^6+272844*c^4*d^13*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^5-283140*c^4*d^13*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^4+127665*c^4*d^13*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^3+22167*c^4*d^13*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)^2-50304*c^4*d^13*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)*a^7*exp(2)+16752*c^4*d^13*exp(1)^15*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))
*x)*a^7+28890*c^5*d^15*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(
2)^6-110700*c^5*d^15*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(
2)^5+123300*c^5*d^15*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(
2)^4+54600*c^5*d^15*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(2
)^3-239445*c^5*d^15*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(2
)^2+205650*c^5*d^15*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6*exp(
2)-62460*c^5*d^15*exp(1)^13*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^6+6930*c
^6*d^17*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^5+24210*c^6*
d^17*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^4-192960*c^6*
d^17*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^3+384840*c^6*
d^17*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^2-330795*c^6*
d^17*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)+108765*c^6*d^
17*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5-17010*c^7*d^19*exp(1)
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^4+112680*c^7*d^19*exp(1)^3
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^3-264960*c^7*d^19*exp(1)^5
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^2+273240*c^7*d^19*exp(1)^7
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)-106425*c^7*d^19*exp(1)^9*(
sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4-19029*c^8*d^21*exp(1)*(sqrt(a*d*exp
(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3+81153*c^8*d^21*exp(1)^3*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2-118674*c^8*d^21*exp(1)^5*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)+59850*c^8*d^21*exp(1)^7*(sqrt(a*d*exp(1)+
a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3-8451*c^9*d^23*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*
d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2+24462*c^9*d^23*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d
^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)-18486*c^9*d^23*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*
x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2-1755*c^10*d^25*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*ex
p(1))-sqrt(c*d*exp(1))*x)*a*exp(2)+2745*c^10*d^25*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))
-sqrt(c*d*exp(1))*x)*a-165*c^11*d^27*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1
))*x)-15*d^6*sqrt(c*d*exp(1))*a^11*exp(2)^11+75*d^6*exp(1)^2*sqrt(c*d*exp(1))*a^11*exp(2)^10-150*d^6*exp(1)^4*
sqrt(c*d*exp(1))*a^11*exp(2)^9+150*d^6*exp(1)^6*sqrt(c*d*exp(1))*a^11*exp(2)^8-75*d^6*exp(1)^8*sqrt(c*d*exp(1)
)*a^11*exp(2)^7+15*d^6*exp(1)^10*sqrt(c*d*exp(1))*a^11*exp(2)^6-175*c*d^8*sqrt(c*d*exp(1))*a^10*exp(2)^10+970*
c*d^8*exp(1)^2*sqrt(c*d*exp(1))*a^10*exp(2)^9-2310*c*d^8*exp(1)^4*sqrt(c*d*exp(1))*a^10*exp(2)^8+3040*c*d^8*ex
p(1)^6*sqrt(c*d*exp(1))*a^10*exp(2)^7-2335*c*d^8*exp(1)^8*sqrt(c*d*exp(1))*a^10*exp(2)^6+990*c*d^8*exp(1)^10*s
qrt(c*d*exp(1))*a^10*exp(2)^5-180*c*d^8*exp(1)^12*sqrt(c*d*exp(1))*a^10*exp(2)^4-933*c^2*d^10*sqrt(c*d*exp(1))
*a^9*exp(2)^9+5499*c^2*d^10*exp(1)^2*sqrt(c*d*exp(1))*a^9*exp(2)^8-14304*c^2*d^10*exp(1)^4*sqrt(c*d*exp(1))*a^
9*exp(2)^7+21408*c^2*d^10*exp(1)^6*sqrt(c*d*exp(1))*a^9*exp(2)^6-20115*c^2*d^10*exp(1)^8*sqrt(c*d*exp(1))*a^9*
exp(2)^5+12045*c^2*d^10*exp(1)^10*sqrt(c*d*exp(1))*a^9*exp(2)^4-4320*c^2*d^10*exp(1)^12*sqrt(c*d*exp(1))*a^9*e
xp(2)^3+720*c^2*d^10*exp(1)^14*sqrt(c*d*exp(1))*a^9*exp(2)^2-2565*c^3*d^12*sqrt(c*d*exp(1))*a^8*exp(2)^8+14232
*c^3*d^12*exp(1)^2*sqrt(c*d*exp(1))*a^8*exp(2)^7-33024*c^3*d^12*exp(1)^4*sqrt(c*d*exp(1))*a^8*exp(2)^6+39312*c
^3*d^12*exp(1)^6*sqrt(c*d*exp(1))*a^8*exp(2)^5-20655*c^3*d^12*exp(1)^8*sqrt(c*d*exp(1))*a^8*exp(2)^4-5196*c^3*
d^12*exp(1)^10*sqrt(c*d*exp(1))*a^8*exp(2)^3+14904*c^3*d^12*exp(1)^12*sqrt(c*d*exp(1))*a^8*exp(2)^2-9120*c^3*d
^12*exp(1)^14*sqrt(c*d*exp(1))*a^8*exp(2)+2112*c^3*d^12*exp(1)^16*sqrt(c*d*exp(1))*a^8-3622*c^4*d^14*sqrt(c*d*
exp(1))*a^7*exp(2)^7+16054*c^4*d^14*exp(1)^2*sqrt(c*d*exp(1))*a^7*exp(2)^6-22812*c^4*d^14*exp(1)^4*sqrt(c*d*ex
p(1))*a^7*exp(2)^5-3380*c^4*d^14*exp(1)^6*sqrt(c*d*exp(1))*a^7*exp(2)^4+48215*c^4*d^14*exp(1)^8*sqrt(c*d*exp(1
))*a^7*exp(2)^3-61671*c^4*d^14*exp(1)^10*sqrt(c*d*exp(1))*a^7*exp(2)^2+35392*c^4*d^14*exp(1)^12*sqrt(c*d*exp(1
))*a^7*exp(2)-8176*c^4*d^14*exp(1)^14*sqrt(c*d*exp(1))*a^7-1830*c^5*d^16*sqrt(c*d*exp(1))*a^6*exp(2)^6+540*c^5
*d^16*exp(1)^2*sqrt(c*d*exp(1))*a^6*exp(2)^5+27300*c^5*d^16*exp(1)^4*sqrt(c*d*exp(1))*a^6*exp(2)^4-81600*c^5*d
^16*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+104715*c^5*d^16*exp(1)^8*sqrt(c*d*exp(1))*a^6*exp(2)^2-65970*c^5*d^
16*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+16860*c^5*d^16*exp(1)^12*sqrt(c*d*exp(1))*a^6+1830*c^6*d^18*sqrt(c*d*
exp(1))*a^5*exp(2)^5-18450*c^6*d^18*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4+60720*c^6*d^18*exp(1)^4*sqrt(c*d*ex
p(1))*a^5*exp(2)^3-92880*c^6*d^18*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+69255*c^6*d^18*exp(1)^8*sqrt(c*d*exp(
1))*a^5*exp(2)-20565*c^6*d^18*exp(1)^10*sqrt(c*d*exp(1))*a^5+3622*c^7*d^20*sqrt(c*d*exp(1))*a^4*exp(2)^4-20776
*c^7*d^20*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+44496*c^7*d^20*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-42672*c
^7*d^20*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+15555*c^7*d^20*exp(1)^8*sqrt(c*d*exp(1))*a^4+2565*c^8*d^22*sqrt(c
*d*exp(1))*a^3*exp(2)^3-10593*c^8*d^22*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+14946*c^8*d^22*exp(1)^4*sqrt(c*d
*exp(1))*a^3*exp(2)-7218*c^8*d^22*exp(1)^6*sqrt(c*d*exp(1))*a^3+933*c^9*d^24*sqrt(c*d*exp(1))*a^2*exp(2)^2-264
6*c^9*d^24*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+1938*c^9*d^24*exp(1)^4*sqrt(c*d*exp(1))*a^2+175*c^10*d^26*sqrt
(c*d*exp(1))*a*exp(2)-265*c^10*d^26*exp(1)^2*sqrt(c*d*exp(1))*a+15*c^11*d^28*sqrt(c*d*exp(1)))/(-3072*d^3*exp(
1)^4*a^3*exp(2)^3+9216*d^3*exp(1)^6*a^3*exp(2)^2-9216*d^3*exp(1)^8*a^3*exp(2)+3072*d^3*exp(1)^10*a^3)/(-exp(1)
*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(
1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^6+(5*a^6*exp(2)^6+30*
c*d^2*a^5*exp(2)^5-60*c*d^2*exp(1)^2*a^5*exp(2)^4+75*c^2*d^4*a^4*exp(2)^4-240*c^2*d^4*exp(1)^2*a^4*exp(2)^3+24
0*c^2*d^4*exp(1)^4*a^4*exp(2)^2+100*c^3*d^6*a^3*exp(2)^3-360*c^3*d^6*exp(1)^2*a^3*exp(2)^2+480*c^3*d^6*exp(1)^
4*a^3*exp(2)-320*c^3*d^6*exp(1)^6*a^3+75*c^4*d^8*a^2*exp(2)^2-240*c^4*d^8*exp(1)^2*a^2*exp(2)+240*c^4*d^8*exp(
1)^4*a^2+30*c^5*d^10*a*exp(2)-60*c^5*d^10*exp(1)^2*a+5*c^6*d^12)/2/(512*d^3*exp(1)^3*a^3*exp(2)^3-1536*d^3*exp
(1)^5*a^3*exp(2)^2+1536*d^3*exp(1)^7*a^3*exp(2)-512*d^3*exp(1)^9*a^3)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*at
an((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-
a*d*exp(1)^3+a*d*exp(1)*exp(2))))

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maple [A]  time = 0.04, size = 58, normalized size = 1.07 \[ -\frac {2 \left (c d x +a e \right ) \left (c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right )^{\frac {5}{2}}}{7 \left (e x +d \right )^{6} \left (a \,e^{2}-c \,d^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^7,x)

[Out]

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

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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((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^7,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 zero or nonzero?

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mupad [B]  time = 3.76, size = 2156, normalized size = 39.93 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^7,x)

[Out]

(((d*((d*((16*c^6*d^7)/(105*e*(a*e^2 - c*d^2)^4) - (16*c^5*d^5*(4*a*e^2 - 3*c*d^2))/(35*e*(a*e^2 - c*d^2)^4)))
/e + (16*c^4*d^4*(56*a^2*e^4 + 35*c^2*d^4 - 88*a*c*d^2*e^2))/(105*e^2*(a*e^2 - c*d^2)^4)))/e - (16*a*c^3*d^3*(
45*a^2*e^4 + 35*c^2*d^4 - 79*a*c*d^2*e^2))/(105*e*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^
(1/2))/(d + e*x) - (((2*a^3*e^4)/(7*a*e^3 - 7*c*d^2*e) - (d*((d*((2*c^3*d^4)/(7*a*e^3 - 7*c*d^2*e) - (6*a*c^2*
d^2*e^2)/(7*a*e^3 - 7*c*d^2*e)))/e + (6*a^2*c*d*e^3)/(7*a*e^3 - 7*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c
*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((d*((4*c^4*d^5)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (4*c^3*d^3*(7
*a*e^2 - 4*c*d^2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (16*c^4*d^6 - 64*a*c^3*d^4*e^2 + 60*a^2*c^2
*d^2*e^4)/(7*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e - (4*a*c*d*(3*a*e^2 - 2*c*d^2)^2)/(7*(a*e^2 - c*d^2)
*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((4*c^4*d^5)/(7*e*(
a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - 3*c*d^2))/(7*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^
2*e))))/e + (16*c^4*d^6 - 62*a*c^3*d^4*e^2 + 66*a^2*c^2*d^2*e^4)/(35*e^2*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)
))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((216*c^6*d^9 - 280*a*c^5*d^7*e^2 - 208*a^2*c
^4*d^5*e^4 + 288*a^3*c^3*d^3*e^6)/(105*e^3*(a*e^2 - c*d^2)^4) - (d*((d*((16*c^6*d^7)/(105*e*(a*e^2 - c*d^2)^4)
- (8*c^5*d^5*(7*a*e^2 - 5*c*d^2))/(35*e*(a*e^2 - c*d^2)^4)))/e + (16*c^4*d^4*(41*a^2*e^4 + 23*c^2*d^4 - 61*a*
c*d^2*e^2))/(105*e^2*(a*e^2 - c*d^2)^4)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*(
(d*((8*c^5*d^6)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (8*c^4*d^4*(10*a*e^2 - 7*c*d^2))/(35*(a*e^2 - c
*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^3*d^3*(36*a^2*e^4 + 19*c^2*d^4 - 52*a*c*d^2*e^2))/(35*e*(a*e^2 - c*d
^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e - (8*a*c^2*d^2*(27*a^2*e^4 + 19*c^2*d^4 - 45*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2
)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((8*c^5*d^6)/(35
*e^2*(a*e^2 - c*d^2)^3) - (4*c^4*d^4*(15*a*e^2 - 11*c*d^2))/(35*e^2*(a*e^2 - c*d^2)^3)))/e + (4*c^3*d^3*(27*a^
2*e^4 + 14*c^2*d^4 - 39*a*c*d^2*e^2))/(35*e^3*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2
))/(d + e*x) - (((d*((d*((4*c^4*d^5)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - c*d^2))
/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (2*c^2*d^2*(9*a^2*e^4 + c^2*d^4 - 4*a*c*d^2*e^2))/(7*e*(a*e^2
- c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e - (2*c^4*d^7 - 4*a*c^3*d^5*e^2 + 6*a^3*c*d*e^6)/(7*e^2*(a*e^2 - c*d^2)*(5
*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((d*((8*c^5*d^6)/(35*(
a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (12*c^4*d^4*(5*a*e^2 - 3*c*d^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*
c*d^2*e))))/e + (4*c^3*d^3*(37*a^2*e^4 + 13*c^2*d^4 - 44*a*c*d^2*e^2))/(35*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*
d^2*e))))/e - (36*c^5*d^8 - 56*a*c^4*d^6*e^2 - 32*a^2*c^3*d^4*e^4 + 60*a^3*c^2*d^2*e^6)/(35*e^2*(a*e^2 - c*d^2
)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((6*c^4*d^5 - 26*a*c
^3*d^3*e^2)/(35*e^3*(a*e^2 - c*d^2)^2) + (4*c^4*d^5)/(7*e^3*(a*e^2 - c*d^2)^2))*(x*(a*e^2 + c*d^2) + a*d*e + c
*d*e*x^2)^(1/2))/(d + e*x)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (\left (d + e x\right ) \left (a e + c d x\right )\right )^{\frac {5}{2}}}{\left (d + e x\right )^{7}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**7,x)

[Out]

Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x)**7, x)

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