3.17.15 \(\int \frac {(a d e+(c d^2+a e^2) x+c d e x^2)^{3/2}}{(d+e x)^7} \, dx\)

Optimal. Leaf size=171 \[ \frac {16 c^2 d^2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{315 (d+e x)^5 \left (c d^2-a e^2\right )^3}+\frac {8 c d \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{63 (d+e x)^6 \left (c d^2-a e^2\right )^2}+\frac {2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{9 (d+e x)^7 \left (c d^2-a e^2\right )} \]

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Rubi [A]  time = 0.08, antiderivative size = 171, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {658, 650} \begin {gather*} \frac {16 c^2 d^2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{315 (d+e x)^5 \left (c d^2-a e^2\right )^3}+\frac {8 c d \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{63 (d+e x)^6 \left (c d^2-a e^2\right )^2}+\frac {2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{5/2}}{9 (d+e x)^7 \left (c d^2-a e^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^7) + (8*c*d*(a*d*e + (c*d^2 + a
*e^2)*x + c*d*e*x^2)^(5/2))/(63*(c*d^2 - a*e^2)^2*(d + e*x)^6) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*
e*x^2)^(5/2))/(315*(c*d^2 - a*e^2)^3*(d + e*x)^5)

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]

Rule 658

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))/((m + p + 1)*(2*c*d - b*e)), x] + Dist[(c*Simplify[m + 2*p + 2])/((m + p + 1)*(2*c*d -
b*e)), Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p, x], 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] && ILtQ[Simplify[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 )^{3/2}}{(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 )^{5/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^7}+\frac {(4 c d) \int \frac {\left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{(d+e x)^6} \, dx}{9 \left (c d^2-a e^2\right )}\\ &=\frac {2 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{5/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^7}+\frac {8 c d \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{5/2}}{63 \left (c d^2-a e^2\right )^2 (d+e x)^6}+\frac {\left (8 c^2 d^2\right ) \int \frac {\left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{(d+e x)^5} \, dx}{63 \left (c d^2-a e^2\right )^2}\\ &=\frac {2 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{5/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^7}+\frac {8 c d \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{5/2}}{63 \left (c d^2-a e^2\right )^2 (d+e x)^6}+\frac {16 c^2 d^2 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{5/2}}{315 \left (c d^2-a e^2\right )^3 (d+e x)^5}\\ \end {align*}

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Mathematica [A]  time = 0.07, size = 94, normalized size = 0.55 \begin {gather*} \frac {2 ((d+e x) (a e+c d x))^{5/2} \left (35 a^2 e^4-10 a c d e^2 (9 d+2 e x)+c^2 d^2 \left (63 d^2+36 d e x+8 e^2 x^2\right )\right )}{315 (d+e x)^7 \left (c d^2-a e^2\right )^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

(2*((a*e + c*d*x)*(d + e*x))^(5/2)*(35*a^2*e^4 - 10*a*c*d*e^2*(9*d + 2*e*x) + c^2*d^2*(63*d^2 + 36*d*e*x + 8*e
^2*x^2)))/(315*(c*d^2 - a*e^2)^3*(d + e*x)^7)

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IntegrateAlgebraic [F]  time = 180.04, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

$Aborted

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fricas [B]  time = 11.32, size = 472, normalized size = 2.76 \begin {gather*} \frac {2 \, {\left (8 \, c^{4} d^{4} e^{2} x^{4} + 63 \, a^{2} c^{2} d^{4} e^{2} - 90 \, a^{3} c d^{2} e^{4} + 35 \, a^{4} e^{6} + 4 \, {\left (9 \, c^{4} d^{5} e - a c^{3} d^{3} e^{3}\right )} x^{3} + 3 \, {\left (21 \, c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right )} x^{2} + 2 \, {\left (63 \, a c^{3} d^{5} e - 72 \, a^{2} c^{2} d^{3} e^{3} + 25 \, a^{3} c d e^{5}\right )} x\right )} \sqrt {c d e x^{2} + a d e + {\left (c d^{2} + a e^{2}\right )} x}}{315 \, {\left (c^{3} d^{11} - 3 \, a c^{2} d^{9} e^{2} + 3 \, a^{2} c d^{7} e^{4} - a^{3} d^{5} e^{6} + {\left (c^{3} d^{6} e^{5} - 3 \, a c^{2} d^{4} e^{7} + 3 \, a^{2} c d^{2} e^{9} - a^{3} e^{11}\right )} x^{5} + 5 \, {\left (c^{3} d^{7} e^{4} - 3 \, a c^{2} d^{5} e^{6} + 3 \, a^{2} c d^{3} e^{8} - a^{3} d e^{10}\right )} x^{4} + 10 \, {\left (c^{3} d^{8} e^{3} - 3 \, a c^{2} d^{6} e^{5} + 3 \, a^{2} c d^{4} e^{7} - a^{3} d^{2} e^{9}\right )} x^{3} + 10 \, {\left (c^{3} d^{9} e^{2} - 3 \, a c^{2} d^{7} e^{4} + 3 \, a^{2} c d^{5} e^{6} - a^{3} d^{3} e^{8}\right )} x^{2} + 5 \, {\left (c^{3} d^{10} e - 3 \, a c^{2} d^{8} e^{3} + 3 \, a^{2} c d^{6} e^{5} - a^{3} d^{4} e^{7}\right )} x\right )}} \end {gather*}

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)^(3/2)/(e*x+d)^7,x, algorithm="fricas")

[Out]

2/315*(8*c^4*d^4*e^2*x^4 + 63*a^2*c^2*d^4*e^2 - 90*a^3*c*d^2*e^4 + 35*a^4*e^6 + 4*(9*c^4*d^5*e - a*c^3*d^3*e^3
)*x^3 + 3*(21*c^4*d^6 - 6*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x^2 + 2*(63*a*c^3*d^5*e - 72*a^2*c^2*d^3*e^3 + 25*a
^3*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^3*d^11 - 3*a*c^2*d^9*e^2 + 3*a^2*c*d^7*e^4 - a^3
*d^5*e^6 + (c^3*d^6*e^5 - 3*a*c^2*d^4*e^7 + 3*a^2*c*d^2*e^9 - a^3*e^11)*x^5 + 5*(c^3*d^7*e^4 - 3*a*c^2*d^5*e^6
+ 3*a^2*c*d^3*e^8 - a^3*d*e^10)*x^4 + 10*(c^3*d^8*e^3 - 3*a*c^2*d^6*e^5 + 3*a^2*c*d^4*e^7 - a^3*d^2*e^9)*x^3
+ 10*(c^3*d^9*e^2 - 3*a*c^2*d^7*e^4 + 3*a^2*c*d^5*e^6 - a^3*d^3*e^8)*x^2 + 5*(c^3*d^10*e - 3*a*c^2*d^8*e^3 + 3
*a^2*c*d^6*e^5 - a^3*d^4*e^7)*x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^7,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-105*exp(1)^6*(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)^11*a^6*exp(2)^6-270*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+900*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)^4-135*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)^3-2160*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+60*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)^3-360*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+1440*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)+960*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^3-135*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)-2160*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^2-270*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))-sq
rt(c*d*exp(1))*x)^11*a*exp(2)+900*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-105*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+1155*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+2970*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)^5-9900*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*exp(1))-sqrt(c*d*exp(1))*x)^10*a^5*exp(2)^4+1485*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)^4-7920*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+23760*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)^2-660*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+3960*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)^2-15840*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)-10560*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+1485*c^4*d^9*exp(1)^5*sqrt(c*d*exp(1))*(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)^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)+23760*c^4*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)^10*a^2+2970*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)-9900*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*exp(1))*x)^10*a+
1155*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
)^10-595*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+595
*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)^6-7305*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+6630*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)^5-5100*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)^4-15615*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+54345*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)^4-16320*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+12240*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+13395*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)^4-44700*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+14280*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)^2-84640*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)+15040*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+2535*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)^3-14955*c^4*d^9*exp(1)^7*(sqrt(
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5*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+115095*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
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d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^3+197040*c^2*d^6*exp(1)^10*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*
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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)^8*a^5*exp(2)-88305*c^3*d^8*exp(1)^4*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)^8*a^4*exp(2)^4+332700*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)^3-380520*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))-sqrt(c*d
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^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4*exp(2)-58560*c^3*d^8*exp(1)^12*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(
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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)^8*a^3*exp(2)^2-90720*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)-268560
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xp(1))-sqrt(c*d*exp(1))*x)^8*a^2*exp(2)+402300*c^5*d^12*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+
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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+17325*c^7*d^16*exp(1)^4*sqrt(c*d*exp(1
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xp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^8*exp(2)^6-37712*c*d^5*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a
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xp(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*exp(2)^
5+367400*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)^4-112640*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)^3-292800*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+1219380*c^2*d^7*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1
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(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-
36960*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)^2-61440*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)-516960*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
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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^5*exp(2)^3+1836720*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)^2-5
57760*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)-113280*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^5-292660*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*exp(1))-sqrt(c*d*exp(1))*x)^6*a^4*exp(2)^4+1131580*c^4*d^11*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)^6*a^4*exp(2)^3-1547430*c^4*d^11*exp(1)^7*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)^6*a^4*exp(2)^2+1118560*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)+317600*
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+61488*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)^3-373716*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*ex
p(1))-sqrt(c*d*exp(1))*x)^6*a^3*exp(2)^2+896868*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)-1554840*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+200592*c^6*d^15*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^2*exp(2)^2-908964*c^6*d^15*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^2*exp(2)+14360
22*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+174720*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*e
xp(1))*x)^6*a*exp(2)-465780*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))-sqrt(c*d*exp(1))*x)^6*a+48510*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)^6-1686*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+5058*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*ex
p(1))*x)^5*a^9*exp(2)^8-5058*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*exp(2)^7+1686*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+23610*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)^8-142536*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+256842*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)^6-180516*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+42600*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*e
xp(2)^4+202176*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)^7-830952*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+1101366*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)^5-465390*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)^4-135360*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+128160*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+540720*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)^6-2071800*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+2912850*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)^4-1504920*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*ex
p(1))*x)^5*a^6*exp(2)^3+87120*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*e
xp(1))*x)^5*a^6*exp(2)^2-37440*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)+24960*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*e
xp(1))*x)^5*a^6+620580*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)^5-2414820*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+3515130*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*ex
p(1))*x)^5*a^5*exp(2)^3-2360550*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+647040*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)+283680*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+244596*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*ex
p(1))*x)^5*a^4*exp(2)^4-888888*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+1030878*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)^2-121476*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)-992760*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))-sqr
t(c*d*exp(1))*x)^5*a^4-145200*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*e
xp(1))*x)^5*a^3*exp(2)^3+848376*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)^2-1969902*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)+2236926*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^3-284256*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*ex
p(1))*x)^5*a^2*exp(2)^2+1226232*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)-1669626*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^2-199710*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)+490770*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-48510*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)^5-6930
*d^4*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^9*e
xp(2)^9+36150*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)^8-66870*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))-s
qrt(c*d*exp(1))*x)^4*a^9*exp(2)^7+53010*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)^6-15360*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)^4*a^9*exp(2)^5-76830*c*d^6*exp(1)^2*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)^4*a^8*exp(2)^8+292320*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)^7-306030*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)^6-19
020*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+171000*c*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)^4*a^8*exp(2)^4-61440*c*d^6*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^8*exp(2)^3-300720*c^2*d^8*exp(1)^2*sqrt(c*d*exp(1))*(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)^4*a^7*exp(2)^7+1115760*c^2*d^8*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)^4*a^7*exp(2)^6-1429110*c^2*d^8*exp(1)^6*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)^4*a^7*exp(2)^5+700950*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)^4-91200*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+96480*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
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p(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^4*a^7*exp(2)-551040*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*exp(2)^6+2142960*c^3*d^10*exp(1)^4*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^6*exp(2)^5-3167550*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+2105400*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)^3-834000*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+371520*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)-32640*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^6-480900*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*exp(1))*x)^4*a^5*exp(2)^5+1907580*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*e
xp(2)^4-2829330*c^4*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)^4*a^5*exp(2)^3+1918110*c^4*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)^4*a^5*exp(2)^2-192000*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)-531360*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^5-107340*c^5*d^14*exp(1)^2*sqrt(c*d
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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^4*exp(
2)^3+276390*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*ex
p(1))*x)^4*a^4*exp(2)^2-1451820*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)+1562520*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+209760*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)^3-1182240*c^6*d^16*exp(1)^4*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)^4*a^3*exp(2)^2+2562750*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)
-2283270*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+285840*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)^2-1170000*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)+1403910*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+164070*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)-371970*c^8*d^20*exp(1)^4*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)^4*a+34650*c^9*d^22*exp(1)^2*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+595*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)^10-2380*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+3570*d^4*exp(1)^6*(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^10*exp(2)^8-2380*d^4*exp(1)^8*(sqrt(a*d*exp(1)
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exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^9-52800*c*d^6*exp(1)^4*(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)^3*a^9*exp(2)^8+40440*c*d^6*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(
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c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^9*exp(2)^5+25620*c*d^6*exp(1)^12*(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)^3*a^8*exp(2)^7+463320*c^2*d^8*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)
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(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^8*exp(2)^4-206640*c^2*d^8*exp(1)^12*(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)^3*a^8*exp(2)^3+58320*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+262600*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)^7-1047760*c^3*d^10*exp(1)^4*(sqrt(a*d*exp(1)
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(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)^5-1469700*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+914700*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)^3-498120*c^3*d^10*exp(1)^12*(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)^2+146720*c^3*d^10*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^7*exp(2)+15040*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+368310*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)^6-1532760*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+2545500*c^4*d^12*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^6*exp(2)^4-2192100*c^4*d^12*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^6*exp(2)^3+1189725*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)^2-335280*c^4*d^12*ex
p(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)-60720*c^4*d^12*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^6+245460*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)^5-962640*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+1321800*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)^3-513660*c^5*d^14*e
xp(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)^2-693270*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)+706260*c^5*d^1
4*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^5-14730*c^6*d^16*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^4*exp(2)^4+312000*c^6*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)^3*a^4*exp(2)^3-1280520*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+2238060*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)-1514685*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^4-195960*c^7*d^18*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^3*exp(2)^3+1063440*c^7*d^18
*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^3*exp(2)^2-2140200*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)+1619220*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^3-199305*c^8*d^20*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^2*exp(2)^2+772740*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)-833310*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^2-94530*c^9*d^22*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*exp(2)+198480*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-17325*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)^3-1785*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+7140*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)^9-10710*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)^2*a^10*exp(2)^8+7140*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)^7-1785*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)^6-18450*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))-sqr
t(c*d*exp(1))*x)^2*a^9*exp(2)^9+75240*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)^8-130320*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+154740*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)^6-157950*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+107460*c*d^7*ex
p(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)^
4-30720*c*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)^2*a^9*exp(2)^3-73341*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))-sq
rt(c*d*exp(1))*x)^2*a^8*exp(2)^8+317952*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)^7-598176*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+682980*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)^5-497895*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+17755
2*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+3216*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)^2-12288*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)-147864*c^3*d^11*exp(1)*sqrt(c*d*exp(1))*(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)^2*a^7*exp(2)^7+663888*c^3*d^11*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)^2*a^7*exp(2)^6-1266624*c^3*d^11*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^7*exp(2)^5+1370100
*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)^4-966180*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))-sqr
t(c*d*exp(1))*x)^2*a^7*exp(2)^3+444888*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)^2-65376*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))-sqrt(c*d*exp(1))*x)^2*a^7*exp(2)-32832*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^7-160290*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+708840*c^4*d^1
3*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^6*exp(
2)^5-1261260*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*e
xp(1))*x)^2*a^6*exp(2)^4+1138380*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)^3-467415*c^4*d^13*exp(1)^9*sqrt(c*d*exp(1))*(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)^2*a^6*exp(2)^2-111600*c^4*d^13*exp(1)^11*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)^2*a^6*exp(2)+159120*c^4*d^13*exp(1)^13*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)^2*a^6-70380*c^5*d^15*ex
p(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+2
20320*c^5*d^15*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^5*exp(2)^4-58320*c^5*d^15*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^5*exp(2)^3-622980*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+1089090*c^5*d^15*exp(1)^9*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^5*exp(2)-592380*c^5*d^15*exp(1)^11*sqrt(c*d*ex
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exp(2)^3+1216080*c^6*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))-sqrt(c
*d*exp(1))*x)^2*a^4*exp(2)^2-1686420*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)+916695*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+115944*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)^3-604368*c^7*d^19*exp(1)^3*sqrt(c*d*ex
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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^3*exp(2)
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)*x)^2*a^3+91611*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)^2-336492*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)+331506*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+36270*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)-70920*c^9*d^23*exp(1)^3*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)^2*a+5775*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+105*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)^11-525*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*exp(2)^10+1050*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)^9-1050*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+525*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)^7-105*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+2055*c*d^7*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)*a^10*exp(2)^10-9390*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+17910*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)^8-18840*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+12135*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)^6-4770*c*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
)*a^10*exp(2)^5+900*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+11655*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*e
xp(2)^9-55845*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+116640*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)^7-136440*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+79905*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+5445*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-
34560*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+1
3200*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+31
857*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)^8-15722
4*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+33907
2*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)^6-41508
0*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+30211
5*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)^4-12788
4*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+3568
8*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)^2-9504
*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)+960*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))-sqrt(c*d*exp(1))*x)*a^8+48378*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)^7-237306*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+496548*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)^5-577260*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+397575*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)^3-124911*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)^2-36768*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)+33744*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+38790*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)^6-168660*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+265500*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)^4-117480*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)^3-183915*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+294030*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)-129420*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+3150*c^6*d^17*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)*a^5*exp(2)^5+42030*c^6*d^17*exp(1)^3*(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)*a^5*exp(2)^4-274320*c^6*d^17*exp(1)^5*(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)*a^5*exp(2)^3+625320*c^6*d^17*exp(1)^7*(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)*a^5*exp(2)^2-667125*c^6*d^17*exp(1)^9*(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)*a^5*exp(2)+277875*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^5-31230*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+209880*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)^3-550800*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+674280*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)-319455*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^4-39603*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+197991*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)^2-347598*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)+212310*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^3-24957*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+86994*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)-79362*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^2-8325*c^10*d^25*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*exp(2)
+15255*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-1155*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)-105*d^6*sqrt(c*d*exp(1))*a
^11*exp(2)^11+525*d^6*exp(1)^2*sqrt(c*d*exp(1))*a^11*exp(2)^10-1050*d^6*exp(1)^4*sqrt(c*d*exp(1))*a^11*exp(2)^
9+1050*d^6*exp(1)^6*sqrt(c*d*exp(1))*a^11*exp(2)^8-525*d^6*exp(1)^8*sqrt(c*d*exp(1))*a^11*exp(2)^7+105*d^6*exp
(1)^10*sqrt(c*d*exp(1))*a^11*exp(2)^6-865*c*d^8*sqrt(c*d*exp(1))*a^10*exp(2)^10+4630*c*d^8*exp(1)^2*sqrt(c*d*e
xp(1))*a^10*exp(2)^9-10770*c*d^8*exp(1)^4*sqrt(c*d*exp(1))*a^10*exp(2)^8+14080*c*d^8*exp(1)^6*sqrt(c*d*exp(1))
*a^10*exp(2)^7-10945*c*d^8*exp(1)^8*sqrt(c*d*exp(1))*a^10*exp(2)^6+4770*c*d^8*exp(1)^10*sqrt(c*d*exp(1))*a^10*
exp(2)^5-900*c*d^8*exp(1)^12*sqrt(c*d*exp(1))*a^10*exp(2)^4-3051*c^2*d^10*sqrt(c*d*exp(1))*a^9*exp(2)^9+16773*
c^2*d^10*exp(1)^2*sqrt(c*d*exp(1))*a^9*exp(2)^8-40848*c^2*d^10*exp(1)^4*sqrt(c*d*exp(1))*a^9*exp(2)^7+57456*c^
2*d^10*exp(1)^6*sqrt(c*d*exp(1))*a^9*exp(2)^6-51405*c^2*d^10*exp(1)^8*sqrt(c*d*exp(1))*a^9*exp(2)^5+33507*c^2*
d^10*exp(1)^10*sqrt(c*d*exp(1))*a^9*exp(2)^4-20736*c^2*d^10*exp(1)^12*sqrt(c*d*exp(1))*a^9*exp(2)^3+11376*c^2*
d^10*exp(1)^14*sqrt(c*d*exp(1))*a^9*exp(2)^2-3072*c^2*d^10*exp(1)^16*sqrt(c*d*exp(1))*a^9*exp(2)-5955*c^3*d^12
*sqrt(c*d*exp(1))*a^8*exp(2)^8+32424*c^3*d^12*exp(1)^2*sqrt(c*d*exp(1))*a^8*exp(2)^7-77328*c^3*d^12*exp(1)^4*s
qrt(c*d*exp(1))*a^8*exp(2)^6+105264*c^3*d^12*exp(1)^6*sqrt(c*d*exp(1))*a^8*exp(2)^5-88905*c^3*d^12*exp(1)^8*sq
rt(c*d*exp(1))*a^8*exp(2)^4+46380*c^3*d^12*exp(1)^10*sqrt(c*d*exp(1))*a^8*exp(2)^3-11208*c^3*d^12*exp(1)^12*sq
rt(c*d*exp(1))*a^8*exp(2)^2-2784*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^8-6634*c^4*d^14*sqrt(c*d*exp(1))*a^7*exp(2)^7+33178*c^4*d^14*exp(1)^2*sqrt(c*d*exp(1))*a^7*exp(2)
^6-66804*c^4*d^14*exp(1)^4*sqrt(c*d*exp(1))*a^7*exp(2)^5+62020*c^4*d^14*exp(1)^6*sqrt(c*d*exp(1))*a^7*exp(2)^4
-6895*c^4*d^14*exp(1)^8*sqrt(c*d*exp(1))*a^7*exp(2)^3-46497*c^4*d^14*exp(1)^10*sqrt(c*d*exp(1))*a^7*exp(2)^2+4
7584*c^4*d^14*exp(1)^12*sqrt(c*d*exp(1))*a^7*exp(2)-15952*c^4*d^14*exp(1)^14*sqrt(c*d*exp(1))*a^7-2970*c^5*d^1
6*sqrt(c*d*exp(1))*a^6*exp(2)^6+7140*c^5*d^16*exp(1)^2*sqrt(c*d*exp(1))*a^6*exp(2)^5+15900*c^5*d^16*exp(1)^4*s
qrt(c*d*exp(1))*a^6*exp(2)^4-86880*c^5*d^16*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+148005*c^5*d^16*exp(1)^8*sq
rt(c*d*exp(1))*a^6*exp(2)^2-119790*c^5*d^16*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+38700*c^5*d^16*exp(1)^12*sqr
t(c*d*exp(1))*a^6+2970*c^6*d^18*sqrt(c*d*exp(1))*a^5*exp(2)^5-28110*c^6*d^18*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp
(2)^4+99840*c^6*d^18*exp(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3-175680*c^6*d^18*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(
2)^2+156105*c^6*d^18*exp(1)^8*sqrt(c*d*exp(1))*a^5*exp(2)-55755*c^6*d^18*exp(1)^10*sqrt(c*d*exp(1))*a^5+6634*c
^7*d^20*sqrt(c*d*exp(1))*a^4*exp(2)^4-41752*c^7*d^20*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+101952*c^7*d^20*ex
p(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-114384*c^7*d^20*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+49125*c^7*d^20*exp(1
)^8*sqrt(c*d*exp(1))*a^4+5955*c^8*d^22*sqrt(c*d*exp(1))*a^3*exp(2)^3-28551*c^8*d^22*exp(1)^2*sqrt(c*d*exp(1))*
a^3*exp(2)^2+47262*c^8*d^22*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-26766*c^8*d^22*exp(1)^6*sqrt(c*d*exp(1))*a^3+
3051*c^9*d^24*sqrt(c*d*exp(1))*a^2*exp(2)^2-10122*c^9*d^24*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+8646*c^9*d^24*
exp(1)^4*sqrt(c*d*exp(1))*a^2+865*c^10*d^26*sqrt(c*d*exp(1))*a*exp(2)-1495*c^10*d^26*exp(1)^2*sqrt(c*d*exp(1))
*a+105*c^11*d^28*sqrt(c*d*exp(1)))/(-15360*d^4*exp(1)^3*a^4*exp(2)^4+61440*d^4*exp(1)^5*a^4*exp(2)^3-92160*d^4
*exp(1)^7*a^4*exp(2)^2+61440*d^4*exp(1)^9*a^4*exp(2)-15360*d^4*exp(1)^11*a^4)/(-exp(1)*(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)^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+(7*a^6*exp(2)^6+18*c*d^2*a^5*exp(2)^5-60*c*
d^2*exp(1)^2*a^5*exp(2)^4+9*c^2*d^4*a^4*exp(2)^4-48*c^2*d^4*exp(1)^2*a^4*exp(2)^3+144*c^2*d^4*exp(1)^4*a^4*exp
(2)^2-4*c^3*d^6*a^3*exp(2)^3+24*c^3*d^6*exp(1)^2*a^3*exp(2)^2-96*c^3*d^6*exp(1)^4*a^3*exp(2)-64*c^3*d^6*exp(1)
^6*a^3+9*c^4*d^8*a^2*exp(2)^2-48*c^4*d^8*exp(1)^2*a^2*exp(2)+144*c^4*d^8*exp(1)^4*a^2+18*c^5*d^10*a*exp(2)-60*
c^5*d^10*exp(1)^2*a+7*c^6*d^12)/2/(512*d^4*exp(1)^2*a^4*exp(2)^4-2048*d^4*exp(1)^4*a^4*exp(2)^3+3072*d^4*exp(1
)^6*a^4*exp(2)^2-2048*d^4*exp(1)^8*a^4*exp(2)+512*d^4*exp(1)^10*a^4)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*ata
n((-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 = 0.05, size = 146, normalized size = 0.85 \begin {gather*} -\frac {2 \left (c d x +a e \right ) \left (8 c^{2} d^{2} e^{2} x^{2}-20 a c d \,e^{3} x +36 c^{2} d^{3} e x +35 a^{2} e^{4}-90 a c \,d^{2} e^{2}+63 c^{2} d^{4}\right ) \left (c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right )^{\frac {3}{2}}}{315 \left (e x +d \right )^{6} \left (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 )} \end {gather*}

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)^(3/2)/(e*x+d)^7,x)

[Out]

-2/315*(c*d*x+a*e)*(8*c^2*d^2*e^2*x^2-20*a*c*d*e^3*x+36*c^2*d^3*e*x+35*a^2*e^4-90*a*c*d^2*e^2+63*c^2*d^4)*(c*d
*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(e*x+d)^6/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)

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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((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(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 = 3.85, size = 2067, normalized size = 12.09

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)^(3/2)/(d + e*x)^7,x)

[Out]

(((d*((4*c^3*d^4)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (2*c^2*d^2*(5*a*e^2 - c*d^2))/(9*(a*e^2 - c*d^2)
*(7*a*e^3 - 7*c*d^2*e))))/e + (2*a*c^2*d^3*e^2 - 2*c^3*d^5 + 4*a^2*c*d*e^4)/(9*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*
c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((148*c^4*d^5 - 188*a*c^3*d^3*e^2)/(3
15*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) + (8*c^4*d^5)/(63*e*(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*((16*c^5*d^6)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3
- 3*c*d^2*e)) - (32*c^4*d^4*(7*a*e^2 - 6*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (16*a*c^3
*d^3*e*(13*a*e^2 - 12*c*d^2))/(315*(a*e^2 - c*d^2)^3*(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 - (((18*c^3*d^4 - 46*a*c^2*d^2*e^2)/(63*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) + (
4*c^3*d^4)/(9*e*(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 - (((16*c^5*d^6)/(315*e^2*(a*e^2 - c*d^2)^4) - (8*c^4*d^4*(47*a*e^2 - 41*c*d^2))/(945*e^2*(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) - (((d*((72*c^4*d^5 - 88*a*c^3*d^3*e^2)/(63*(a*e
^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) + (8*c^4*d^5)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (8*a*c^2
*d^2*e*(10*a*e^2 - 9*c*d^2))/(63*(a*e^2 - c*d^2)^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*((32*c^6*d^7)/(945*e*(a*e^2 - c*d^2)^5) - (16*c^5*d^5*(29*a*e^2 - 25*c*d^2))/(9
45*e*(a*e^2 - c*d^2)^5)))/e + (16*c^4*d^4*(14*a^2*e^4 - 13*c^2*d^4 + a*c*d^2*e^2))/(945*e^2*(a*e^2 - c*d^2)^5)
)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((16*c^5*d^6)/(315*(a*e^2 - c*d^2)^3*(3*a*e^
3 - 3*c*d^2*e)) - (8*c^4*d^4*(23*a*e^2 - 19*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^3
*d^3*(11*a^2*e^4 - 10*c^2*d^4 + a*c*d^2*e^2))/(315*e*(a*e^2 - c*d^2)^3*(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 - (((2*a^2*e^3)/(9*a*e^3 - 9*c*d^2*e) + (d*((2*c^2*d^3)/(9*a*e^3 -
9*c*d^2*e) - (4*a*c*d*e^2)/(9*a*e^3 - 9*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
)^5 - (((d*((32*c^6*d^7)/(945*e*(a*e^2 - c*d^2)^5) - (64*c^5*d^5*(8*a*e^2 - 7*c*d^2))/(945*e*(a*e^2 - c*d^2)^5
)))/e + (32*a*c^4*d^4*(15*a*e^2 - 14*c*d^2))/(945*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^
(1/2))/(d + e*x) - (((d*((20*c^3*d^4 - 28*a*c^2*d^2*e^2)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) + (4*c^3*d^
4)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (4*a*c*d*e*(6*a*e^2 - 5*c*d^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3
- 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((8*c^4*d^5)/(63*(a*e^2 - c*
d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (4*c^3*d^3*(15*a*e^2 - 11*c*d^2))/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))
))/e + (4*a*c^3*d^4*e^2 - 24*c^4*d^6 + 28*a^2*c^2*d^2*e^4)/(63*e*(a*e^2 - c*d^2)^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 - (8*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(
1/2))/(45*e^2*(a*e^2 - c*d^2)^3*(d + e*x)) - (44*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(315*e
*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (\left (d + e x\right ) \left (a e + c d x\right )\right )^{\frac {3}{2}}}{\left (d + e x\right )^{7}}\, dx \end {gather*}

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)**(3/2)/(e*x+d)**7,x)

[Out]

Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**7, x)

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