3.17.3 \(\int \frac {\sqrt {a d e+(c d^2+a e^2) x+c d e x^2}}{(d+e x)^6} \, dx\)
Optimal. Leaf size=231 \[ \frac {32 c^3 d^3 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{315 (d+e x)^3 \left (c d^2-a e^2\right )^4}+\frac {16 c^2 d^2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{105 (d+e x)^4 \left (c d^2-a e^2\right )^3}+\frac {4 c d \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{21 (d+e x)^5 \left (c d^2-a e^2\right )^2}+\frac {2 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{9 (d+e x)^6 \left (c d^2-a e^2\right )} \]
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Rubi [A] time = 0.12, antiderivative size = 231, normalized size of antiderivative = 1.00,
number of steps used = 4, 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 {32 c^3 d^3 \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{315 (d+e x)^3 \left (c d^2-a e^2\right )^4}+\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 )^{3/2}}{105 (d+e x)^4 \left (c d^2-a e^2\right )^3}+\frac {4 c d \left (x \left (a e^2+c d^2\right )+a d e+c d e x^2\right )^{3/2}}{21 (d+e x)^5 \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 )^{3/2}}{9 (d+e x)^6 \left (c d^2-a e^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^6,x]
[Out]
(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^6) + (4*c*d*(a*d*e + (c*d^2 + a
*e^2)*x + c*d*e*x^2)^(3/2))/(21*(c*d^2 - a*e^2)^2*(d + e*x)^5) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*
e*x^2)^(3/2))/(105*(c*d^2 - a*e^2)^3*(d + e*x)^4) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))
/(315*(c*d^2 - a*e^2)^4*(d + e*x)^3)
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 {\sqrt {a d e+\left (c d^2+a e^2\right ) x+c d e x^2}}{(d+e x)^6} \, dx &=\frac {2 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^6}+\frac {(2 c d) \int \frac {\sqrt {a d e+\left (c d^2+a e^2\right ) x+c d e x^2}}{(d+e x)^5} \, dx}{3 \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 )^{3/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^6}+\frac {4 c d \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{21 \left (c d^2-a e^2\right )^2 (d+e x)^5}+\frac {\left (8 c^2 d^2\right ) \int \frac {\sqrt {a d e+\left (c d^2+a e^2\right ) x+c d e x^2}}{(d+e x)^4} \, dx}{21 \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 )^{3/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^6}+\frac {4 c d \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{21 \left (c d^2-a e^2\right )^2 (d+e x)^5}+\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 )^{3/2}}{105 \left (c d^2-a e^2\right )^3 (d+e x)^4}+\frac {\left (16 c^3 d^3\right ) \int \frac {\sqrt {a d e+\left (c d^2+a e^2\right ) x+c d e x^2}}{(d+e x)^3} \, dx}{105 \left (c d^2-a e^2\right )^3}\\ &=\frac {2 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{9 \left (c d^2-a e^2\right ) (d+e x)^6}+\frac {4 c d \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{21 \left (c d^2-a e^2\right )^2 (d+e x)^5}+\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 )^{3/2}}{105 \left (c d^2-a e^2\right )^3 (d+e x)^4}+\frac {32 c^3 d^3 \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{3/2}}{315 \left (c d^2-a e^2\right )^4 (d+e x)^3}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 180, normalized size = 0.78 \begin {gather*} \frac {2 \sqrt {(d+e x) (a e+c d x)} \left (-35 a^4 e^7+5 a^3 c d e^5 (27 d-e x)+3 a^2 c^2 d^2 e^3 \left (-63 d^2+9 d e x+2 e^2 x^2\right )+a c^3 d^3 e \left (105 d^3-63 d^2 e x-36 d e^2 x^2-8 e^3 x^3\right )+c^4 d^4 x \left (105 d^3+126 d^2 e x+72 d e^2 x^2+16 e^3 x^3\right )\right )}{315 (d+e x)^5 \left (c d^2-a e^2\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^6,x]
[Out]
(2*Sqrt[(a*e + c*d*x)*(d + e*x)]*(-35*a^4*e^7 + 5*a^3*c*d*e^5*(27*d - e*x) + 3*a^2*c^2*d^2*e^3*(-63*d^2 + 9*d*
e*x + 2*e^2*x^2) + a*c^3*d^3*e*(105*d^3 - 63*d^2*e*x - 36*d*e^2*x^2 - 8*e^3*x^3) + c^4*d^4*x*(105*d^3 + 126*d^
2*e*x + 72*d*e^2*x^2 + 16*e^3*x^3)))/(315*(c*d^2 - a*e^2)^4*(d + e*x)^5)
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IntegrateAlgebraic [B] time = 31.65, size = 9547, normalized size = 41.33 \begin {gather*} \text {Result too large to show} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^6,x]
[Out]
Result too large to show
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fricas [B] time = 8.80, size = 572, normalized size = 2.48 \begin {gather*} \frac {2 \, {\left (16 \, c^{4} d^{4} e^{3} x^{4} + 105 \, a c^{3} d^{6} e - 189 \, a^{2} c^{2} d^{4} e^{3} + 135 \, a^{3} c d^{2} e^{5} - 35 \, a^{4} e^{7} + 8 \, {\left (9 \, c^{4} d^{5} e^{2} - a c^{3} d^{3} e^{4}\right )} x^{3} + 6 \, {\left (21 \, c^{4} d^{6} e - 6 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right )} x^{2} + {\left (105 \, c^{4} d^{7} - 63 \, a c^{3} d^{5} e^{2} + 27 \, a^{2} c^{2} d^{3} e^{4} - 5 \, a^{3} c d e^{6}\right )} x\right )} \sqrt {c d e x^{2} + a d e + {\left (c d^{2} + a e^{2}\right )} x}}{315 \, {\left (c^{4} d^{13} - 4 \, a c^{3} d^{11} e^{2} + 6 \, a^{2} c^{2} d^{9} e^{4} - 4 \, a^{3} c d^{7} e^{6} + a^{4} d^{5} e^{8} + {\left (c^{4} d^{8} e^{5} - 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} - 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right )} x^{5} + 5 \, {\left (c^{4} d^{9} e^{4} - 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} - 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right )} x^{4} + 10 \, {\left (c^{4} d^{10} e^{3} - 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} - 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right )} x^{3} + 10 \, {\left (c^{4} d^{11} e^{2} - 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} - 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right )} x^{2} + 5 \, {\left (c^{4} d^{12} e - 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} - 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9}\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)^(1/2)/(e*x+d)^6,x, algorithm="fricas")
[Out]
2/315*(16*c^4*d^4*e^3*x^4 + 105*a*c^3*d^6*e - 189*a^2*c^2*d^4*e^3 + 135*a^3*c*d^2*e^5 - 35*a^4*e^7 + 8*(9*c^4*
d^5*e^2 - a*c^3*d^3*e^4)*x^3 + 6*(21*c^4*d^6*e - 6*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^2 + (105*c^4*d^7 - 63*a*
c^3*d^5*e^2 + 27*a^2*c^2*d^3*e^4 - 5*a^3*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^4*d^13 - 4
*a*c^3*d^11*e^2 + 6*a^2*c^2*d^9*e^4 - 4*a^3*c*d^7*e^6 + a^4*d^5*e^8 + (c^4*d^8*e^5 - 4*a*c^3*d^6*e^7 + 6*a^2*c
^2*d^4*e^9 - 4*a^3*c*d^2*e^11 + a^4*e^13)*x^5 + 5*(c^4*d^9*e^4 - 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 - 4*a^3*c
*d^3*e^10 + a^4*d*e^12)*x^4 + 10*(c^4*d^10*e^3 - 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 - 4*a^3*c*d^4*e^9 + a^4*d
^2*e^11)*x^3 + 10*(c^4*d^11*e^2 - 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 - 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x^2 +
5*(c^4*d^12*e - 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 - 4*a^3*c*d^6*e^7 + a^4*d^4*e^9)*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)^(1/2)/(e*x+d)^6,x, algorithm="giac")
[Out]
Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((105*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)^9*a^5*exp(2)^5+75*c*d^2*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)^4-600*c*d^2*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)^3-30*c^2*d^4*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+360*c^2*d^4*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+720*c^2*d^4*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^3*exp(2)+30*c^3*d^6*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^2*exp(2)^2-360*c^3*d^6*exp(1)^7*(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)^9*a^2*exp(2)-720*c^3*d^6*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^2-75*c^4*d^8*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*e
xp(1))*x)^9*a*exp(2)+600*c^4*d^8*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-105*c^5*d^10*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)^9-945*d*
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)
^5-675*c*d^3*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+5400*c*d^3*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+270*c^2*d^5*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)^3-3240*c^2*d^5*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)^2-6480*c^2*d^5*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)-270*c^3*d^7*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^2*exp(2)^2+3240*c^3*d^7*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)+6480*c
^3*d^7*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
+675*c^4*d^9*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)-5400*c^4*d^9*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+945*c^5*d^11*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))-sq
rt(c*d*exp(1))*x)^8+490*d*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
^6*exp(2)^6-490*d*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^6*exp(2
)^5+4130*c*d^3*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^5*exp(2)^5
-3150*c*d^3*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^5*exp(2)^4+28
00*c*d^3*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^5*exp(2)^3+2560*
c^2*d^5*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^4*exp(2)^4-19780*
c^2*d^5*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^4*exp(2)^3+1680*c
^2*d^5*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^4*exp(2)^2-3360*c^
2*d^5*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^4*exp(2)-940*c^3*d
^7*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^3*exp(2)^3+11140*c^3*d
^7*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^3*exp(2)^2+24240*c^3*d
^7*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^3*exp(2)+3360*c^3*d^7*
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^3+730*c^4*d^9*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)^2-9810*c^4*d^9*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)^7*a^2*exp(2)-28720*c^4*d^9*exp(1)^8*(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)^7*a^2-3190*c^5*d^11*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)+22090*c^5*d^11*exp(1)^6*(sqrt(a*d*exp(1)
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c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^6+3430*d^2*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)
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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)^5+22050*c*d^4*exp(1)^5*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)^6*a^5*exp(2)^4-19600*c*d
^4*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+2360*c^2*d^6*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+6940*c^2*d^6*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^4*exp(2)^3+34320*c^2*d^6*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^4*exp(2)^2-7200*c^2*d^6*exp(1)^9*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)
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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^4+1540*c^3*d^8*exp(1)^3*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)^6*a^3*exp(2)^3-17500*c^3*d^8*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-
48720*c^3*d^8*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)-23520*c^3*d^8*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)^6*a^3-70*c^4*d^10*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+8190*c^4*d^10*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)+80080*c^4*d^10*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)
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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)-53830*c^5*d^12*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)^6*a+8820*c^6*d^14*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+896*d^2*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)^7-1792*d^2*exp(1)^5*(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)^5*a^7*exp(2)^6+896*d^2*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+10930*c*d^4*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)^6-16690*c*d^4*exp(1)^5*(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)^5*a^6*exp(2)^5+10880*c*d^4*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)^4-5120*c*d^4*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)
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c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^5*a^5*exp(2)^5+23450*c^2*d^6*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)^4-70480*c^2*d^6*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+76800*c^2*d^6*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)^2-15360*c^2*d^6*exp(1)^11*(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)^5*a^4*exp(2)^4+57340*c^3*d^8*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)^3-111920*c^3*d^8*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+36960*c^3*d^8*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)-30720*c^3*d^8*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^4-1480*c^4*d^10*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+13540*c^4*d^10*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+44560*c^4*d^10*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)+75680*c^4*d^10*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^3-4466*c^5*d^12*exp(1)^3*(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)^5*a^2*exp(2)^2+22582*c^5*d^12*exp(1)^5*(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)^5*a^2*exp(2)-150416*c^5*d^12*exp(1)^7*(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)^5*a^2-19740*c^6*d^14*exp(1)^3*(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)^5*a*exp(2)+85890*c^6*d^14*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-13230*c^7*d^16*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)^5-4480*d^3*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*exp(2)^7+8960*d^3*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)^4*a^7*exp(2)^6-4480*d^3*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+3970*c*d^5*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)^6-48130*c*d^5*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+91520*c*d^5*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)^4-71680*c*d^5*exp(1)^8*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)^4*a^6*exp(2)^3+24320*c
*d^5*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+32120*c^2*d^7*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)^5-130390*c^2*d^7*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+230960*c^2*d^7*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)^3-163840*c^2*d^7*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+15360*c^2*d^7*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)+2560*c^2*d^7*e
xp(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+26170*
c^3*d^9*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)^4-98180*c^3*d^9*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+131920*c^3*d^9*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)^2-56480*c^3*d^9*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)+62720*c^3*d^9*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+2080*c^4*d^11*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)^3-13660*c^4*d^11*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+22480
*c^4*d^11*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)-143200*c^4*d^11*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+12950*c^5*d^13*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)^2-73850*c^5*d^13*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)+193200*c^5*d^13*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+26600*c^6*d^15*exp(1)^2*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*exp(2)-92750*c^6*d^15*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+13230*c^7*d^17*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+790*d^3*exp(1)^2*(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^8*exp(2)^8-2370*d^3*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^8*exp(2)^7+2370*d^3*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^8*exp(2)^6-790*d^3*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)^5-4190*c*d^5*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+30730*c*d^5*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^7*exp(2)^6-58090*c*d^5*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^7*exp(2)^5+40750*c*d^5*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)^4-9200*c*d^5*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)^3-26230*c^2*d^7*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+113870*c^2*d^7*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)^5-165580*c^2*d^7*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)
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c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^5*exp(2)^5+150410*c^3*d^9*exp(1)^4*(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^5*exp(2)^2+4560*c^3*d^9*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)+1760*c^3*d^9*exp(1)^12*(sqrt(a*d*exp(1)+a*x*exp(2)
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x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^3-86630*c^4*d^11*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+77170*c^4*d^11*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)-88080*c^4*d^11*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^4-4810*c^5*d^13*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+32910*c^5*d^13*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)^2-109490*c^5*d^13*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)+169590*c^5*d^13*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^3-18690*c^6*d^15*exp(1)^2*(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)^3*a^2*exp(2)^2+97930*c^6*d^15*exp(1)^4*(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)^3*a^2*exp(2)-167440*c^6*d^15*exp(1)^6*(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)^3*a^2-23450*c^7*d^17*exp(1)^2*(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)^3*a*exp(2)+67550*c^7*d^17*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-8820*c^8*d^19*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+1470*d^4*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)^8-8250*d^4*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+15930*d^4*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*e
xp(1))-sqrt(c*d*exp(1))*x)^2*a^8*exp(2)^6-12990*d^4*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+3840*d^4*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+10010*c*d^6*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)^7-40990*c*d^6*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+48830*c*d^6*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-
9610*c*d^6*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)^4-13360*c*d^6*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+5120*c*d^6*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+22570*c^2*d^8*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)^6-85810*c^2*d^8*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+117860*c^2*d^8*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^6*exp(2)^4-63340*c^2*d^8*ex
p(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
-4240*c^2*d^8*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+10400*c^2*d^8*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^6*exp(2)+2560*c^2*d^8*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+21290*c^3*d^10*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)^5-80950*c^3*d^10*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^5*exp(2)^4+113900*c^3*d^10*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^5*exp(2)^3-49300*c^3*d^10*e
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)^2*a^5*exp(2)^
2+6800*c^3*d^10*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)-15520*c^3*d^10*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+8150*c^4*d^12*exp(1)*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^4*exp(2)^4-34510*c^4*d^12*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^4*exp(2)^3+60530*c^4*d^12*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)^2-99030*c^4*d^12*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)+83760*c^4*d^12*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)^2*a^4+6910*c^
5*d^14*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*e
xp(2)^3-45850*c^5*d^14*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+125270*c^5*d^14*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)-124130*c^5*d^14*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+15230*c^6*d^16*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)^2-71110*c^6*d^16*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)+93680*c^6*d^16*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^2+12990*c^7*d^18*e
xp(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)-3189
0*c^7*d^18*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+3780*c^8*d^20*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^4*exp(1)*(sqrt(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+420*d
^4*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)^8-630*d^4*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+420*d^4*exp(1)^7*(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)*a^9*exp(2)^6-105*d^4*exp(1)^9*(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)*a^9*exp(2)^5-1545*c*d^6*exp(1)*(sqrt(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+5310*c*d^6*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)^7-3420*c*d^6*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)^6-6150*c*d^6*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+9045*c*d^6*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)^4-3240*c*d^6*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)^3-5500*c^2*d^8*exp(1)*(sqrt(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+20030*c^2*d^8*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)^6-24250*c^2*d^8*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+12770*c^2*d^8*exp(1)^7*(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^7*exp(2)^4-6130*c^2*d^8*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+3800*c^2*d^8*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)^2-720*c^2*d^8*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*e
xp(1))*x)*a^7*exp(2)-8340*c^3*d^10*exp(1)*(sqrt(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+31710*c^3*d^10*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)^5-45160*c^3*d^10*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+24340*c^3*d^10*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+690*c^3*d^10*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+1160*c^3*d^10*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)-4400*c^3*d^10*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^6-59
10*c^4*d^12*exp(1)*(sqrt(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+23030*
c^4*d^12*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)^4-33770*c
^4*d^12*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+27480*c^
4*d^12*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)^2-28645*c^4
*d^12*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)+18760*c^4*d^
12*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^5-2990*c^5*d^14*exp(1)*
(sqrt(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+17130*c^5*d^14*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)^3-46300*c^5*d^14*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)*a^4*exp(2)^2+73970*c^5*d^14*exp(1)^7*(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^4*exp(2)-46535*c^5*d^14*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^4-4860*c^6*d^16*exp(1)*(sqrt(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+29610*c^6*d^16*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)^2-66790*c^6*d^16*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)+51490*c^6*d^16*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^3-6660*c^7*d^18*exp(1)*(sqrt(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+27770*c^7*d^18*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)-30560*c^7*d^18*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^2-4105*c^8*d^20*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)*a*exp(2)+8830*c^8*d^20*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-945*c^9*d^22*exp(1)*(sqrt(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^5*sqrt(c*d*exp(1))*a^9*exp(2)^9-420*d^5*exp(1)^2*sqrt(c*d*exp(1))*a^9*exp(2)^8+630*d^5*exp(1)^4*sqrt(c*d*exp
(1))*a^9*exp(2)^7-420*d^5*exp(1)^6*sqrt(c*d*exp(1))*a^9*exp(2)^6+105*d^5*exp(1)^8*sqrt(c*d*exp(1))*a^9*exp(2)^
5+565*c*d^7*sqrt(c*d*exp(1))*a^8*exp(2)^8-2370*c*d^7*exp(1)^2*sqrt(c*d*exp(1))*a^8*exp(2)^7+4320*c*d^7*exp(1)^
4*sqrt(c*d*exp(1))*a^8*exp(2)^6-5670*c*d^7*exp(1)^6*sqrt(c*d*exp(1))*a^8*exp(2)^5+6315*c*d^7*exp(1)^8*sqrt(c*d
*exp(1))*a^8*exp(2)^4-4440*c*d^7*exp(1)^10*sqrt(c*d*exp(1))*a^8*exp(2)^3+1280*c*d^7*exp(1)^12*sqrt(c*d*exp(1))
*a^8*exp(2)^2+1216*c^2*d^9*sqrt(c*d*exp(1))*a^7*exp(2)^7-5162*c^2*d^9*exp(1)^2*sqrt(c*d*exp(1))*a^7*exp(2)^6+9
446*c^2*d^9*exp(1)^4*sqrt(c*d*exp(1))*a^7*exp(2)^5-10630*c^2*d^9*exp(1)^6*sqrt(c*d*exp(1))*a^7*exp(2)^4+8210*c
^2*d^9*exp(1)^8*sqrt(c*d*exp(1))*a^7*exp(2)^3-4312*c^2*d^9*exp(1)^10*sqrt(c*d*exp(1))*a^7*exp(2)^2+1744*c^2*d^
9*exp(1)^12*sqrt(c*d*exp(1))*a^7*exp(2)-512*c^2*d^9*exp(1)^14*sqrt(c*d*exp(1))*a^7+1320*c^3*d^11*sqrt(c*d*exp(
1))*a^6*exp(2)^6-5570*c^3*d^11*exp(1)^2*sqrt(c*d*exp(1))*a^6*exp(2)^5+9680*c^3*d^11*exp(1)^4*sqrt(c*d*exp(1))*
a^6*exp(2)^4-9420*c^3*d^11*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+8110*c^3*d^11*exp(1)^8*sqrt(c*d*exp(1))*a^6*
exp(2)^2-7240*c^3*d^11*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+3120*c^3*d^11*exp(1)^12*sqrt(c*d*exp(1))*a^6+890*
c^4*d^13*sqrt(c*d*exp(1))*a^5*exp(2)^5-4450*c^4*d^13*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4+10530*c^4*d^13*exp
(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3-16800*c^4*d^13*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+17285*c^4*d^13*exp(1
)^8*sqrt(c*d*exp(1))*a^5*exp(2)-7560*c^4*d^13*exp(1)^10*sqrt(c*d*exp(1))*a^5+890*c^5*d^15*sqrt(c*d*exp(1))*a^4
*exp(2)^4-5910*c^5*d^15*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+16400*c^5*d^15*exp(1)^4*sqrt(c*d*exp(1))*a^4*ex
p(2)^2-22030*c^5*d^15*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+11175*c^5*d^15*exp(1)^8*sqrt(c*d*exp(1))*a^4+1320*c
^6*d^17*sqrt(c*d*exp(1))*a^3*exp(2)^3-7310*c^6*d^17*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+14210*c^6*d^17*exp(
1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-9270*c^6*d^17*exp(1)^6*sqrt(c*d*exp(1))*a^3+1216*c^7*d^19*sqrt(c*d*exp(1))*a^
2*exp(2)^2-4582*c^7*d^19*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+4416*c^7*d^19*exp(1)^4*sqrt(c*d*exp(1))*a^2+565*
c^8*d^21*sqrt(c*d*exp(1))*a*exp(2)-1090*c^8*d^21*exp(1)^2*sqrt(c*d*exp(1))*a+105*c^9*d^23*sqrt(c*d*exp(1)))/(-
3840*d^4*exp(1)^2*a^4*exp(2)^4+15360*d^4*exp(1)^4*a^4*exp(2)^3-23040*d^4*exp(1)^6*a^4*exp(2)^2+15360*d^4*exp(1
)^8*a^4*exp(2)-3840*d^4*exp(1)^10*a^4)/(-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+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*e
xp(2)+d*exp(1)^2*a-c*d^3)^5+(7*a^5*exp(2)^5+5*c*d^2*a^4*exp(2)^4-40*c*d^2*exp(1)^2*a^4*exp(2)^3-2*c^2*d^4*a^3*
exp(2)^3+24*c^2*d^4*exp(1)^2*a^3*exp(2)^2+48*c^2*d^4*exp(1)^4*a^3*exp(2)+2*c^3*d^6*a^2*exp(2)^2-24*c^3*d^6*exp
(1)^2*a^2*exp(2)-48*c^3*d^6*exp(1)^4*a^2-5*c^4*d^8*a*exp(2)+40*c^4*d^8*exp(1)^2*a-7*c^5*d^10)/2/(128*d^4*exp(1
)*a^4*exp(2)^4-512*d^4*exp(1)^3*a^4*exp(2)^3+768*d^4*exp(1)^5*a^4*exp(2)^2-512*d^4*exp(1)^7*a^4*exp(2)+128*d^4
*exp(1)^9*a^4)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-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 = 217, normalized size = 0.94 \begin {gather*} -\frac {2 \left (c d x +a e \right ) \left (-16 c^{3} d^{3} e^{3} x^{3}+24 a \,c^{2} d^{2} e^{4} x^{2}-72 c^{3} d^{4} e^{2} x^{2}-30 a^{2} c d \,e^{5} x +108 a \,c^{2} d^{3} e^{3} x -126 c^{3} d^{5} e x +35 a^{3} e^{6}-135 a^{2} c \,d^{2} e^{4}+189 a \,c^{2} d^{4} e^{2}-105 c^{3} d^{6}\right ) \sqrt {c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{315 \left (e x +d \right )^{5} \left (a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right )} \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)^(1/2)/(e*x+d)^6,x)
[Out]
-2/315*(c*d*x+a*e)*(-16*c^3*d^3*e^3*x^3+24*a*c^2*d^2*e^4*x^2-72*c^3*d^4*e^2*x^2-30*a^2*c*d*e^5*x+108*a*c^2*d^3
*e^3*x-126*c^3*d^5*e*x+35*a^3*e^6-135*a^2*c*d^2*e^4+189*a*c^2*d^4*e^2-105*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+
a*d*e)^(1/2)/(e*x+d)^5/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)
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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)^(1/2)/(e*x+d)^6,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 = 2.58, size = 1192, normalized size = 5.16 \begin {gather*} \frac {\left (\frac {4\,c^2\,d^3}{9\,\left (a\,e^2-c\,d^2\right )\,\left (7\,a\,e^3-7\,c\,d^2\,e\right )}-\frac {4\,a\,c\,d\,e^2}{9\,\left (a\,e^2-c\,d^2\right )\,\left (7\,a\,e^3-7\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^4}-\frac {\left (\frac {2\,a\,e^2}{9\,a\,e^3-9\,c\,d^2\,e}-\frac {2\,c\,d^2}{9\,a\,e^3-9\,c\,d^2\,e}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^5}+\frac {\left (\frac {4\,c^3\,d^4+4\,a\,c^2\,d^2\,e^2}{63\,{\left (a\,e^2-c\,d^2\right )}^2\,\left (5\,a\,e^3-5\,c\,d^2\,e\right )}-\frac {8\,c^3\,d^4}{63\,{\left (a\,e^2-c\,d^2\right )}^2\,\left (5\,a\,e^3-5\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^3}+\frac {\left (\frac {8\,c^4\,d^5+8\,a\,c^3\,d^3\,e^2}{315\,{\left (a\,e^2-c\,d^2\right )}^3\,\left (3\,a\,e^3-3\,c\,d^2\,e\right )}-\frac {16\,c^4\,d^5}{315\,{\left (a\,e^2-c\,d^2\right )}^3\,\left (3\,a\,e^3-3\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^2}+\frac {\left (\frac {16\,c^5\,d^6+16\,a\,c^4\,d^4\,e^2}{945\,e\,{\left (a\,e^2-c\,d^2\right )}^5}-\frac {32\,c^5\,d^6}{945\,e\,{\left (a\,e^2-c\,d^2\right )}^5}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{d+e\,x}+\frac {\left (\frac {2\,c^2\,d^3+2\,a\,c\,d\,e^2}{9\,\left (a\,e^2-c\,d^2\right )\,\left (7\,a\,e^3-7\,c\,d^2\,e\right )}-\frac {4\,c^2\,d^3}{9\,\left (a\,e^2-c\,d^2\right )\,\left (7\,a\,e^3-7\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^4}+\frac {\left (\frac {8\,c^3\,d^4}{63\,{\left (a\,e^2-c\,d^2\right )}^2\,\left (5\,a\,e^3-5\,c\,d^2\,e\right )}-\frac {8\,a\,c^2\,d^2\,e^2}{63\,{\left (a\,e^2-c\,d^2\right )}^2\,\left (5\,a\,e^3-5\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^3}+\frac {\left (\frac {16\,c^4\,d^5}{315\,{\left (a\,e^2-c\,d^2\right )}^3\,\left (3\,a\,e^3-3\,c\,d^2\,e\right )}-\frac {16\,a\,c^3\,d^3\,e^2}{315\,{\left (a\,e^2-c\,d^2\right )}^3\,\left (3\,a\,e^3-3\,c\,d^2\,e\right )}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{{\left (d+e\,x\right )}^2}+\frac {\left (\frac {32\,c^5\,d^6}{945\,e\,{\left (a\,e^2-c\,d^2\right )}^5}-\frac {32\,a\,c^4\,d^4\,e}{945\,{\left (a\,e^2-c\,d^2\right )}^5}\right )\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{d+e\,x}-\frac {8\,c^3\,d^3\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{63\,{\left (a\,e^2-c\,d^2\right )}^2\,\left (3\,a\,e^3-3\,c\,d^2\,e\right )\,{\left (d+e\,x\right )}^2}+\frac {16\,c^2\,d^2\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{63\,\left (a\,e^2-c\,d^2\right )\,\left (5\,a\,e^3-5\,c\,d^2\,e\right )\,{\left (d+e\,x\right )}^3}+\frac {16\,c^4\,d^4\,\sqrt {c\,d\,e\,x^2+\left (c\,d^2+a\,e^2\right )\,x+a\,d\,e}}{135\,e\,{\left (a\,e^2-c\,d^2\right )}^4\,\left (d+e\,x\right )} \end {gather*}
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)^(1/2)/(d + e*x)^6,x)
[Out]
(((4*c^2*d^3)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*a*c*d*e^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 - (((2*a*e^2)/(9*a*e^3 - 9*c*d^2*e) - (2*c*d^2
)/(9*a*e^3 - 9*c*d^2*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((4*c^3*d^4 + 4*a*c^2*d
^2*e^2)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (8*c^3*d^4)/(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 + (((8*c^4*d^5 + 8*a*c^3*d^3*e^2)/(315*(a*e^2 -
c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (16*c^4*d^5)/(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 + (((16*c^5*d^6 + 16*a*c^4*d^4*e^2)/(945*e*(a*e^2 - c*d^2)^5) - (32
*c^5*d^6)/(945*e*(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) + (((2*c^2*d^3 +
2*a*c*d*e^2)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*c^2*d^3)/(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 + (((8*c^3*d^4)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 -
5*c*d^2*e)) - (8*a*c^2*d^2*e^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 + (((16*c^4*d^5)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (16*a*c^3*d^3*e^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 +
(((32*c^5*d^6)/(945*e*(a*e^2 - c*d^2)^5) - (32*a*c^4*d^4*e)/(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) - (8*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(63*(a*e^2 - c*d^2
)^2*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) + (16*c^2*d^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(63*(a*e^2
- c*d^2)*(5*a*e^3 - 5*c*d^2*e)*(d + e*x)^3) + (16*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(135
*e*(a*e^2 - c*d^2)^4*(d + e*x))
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {\left (d + e x\right ) \left (a e + c d x\right )}}{\left (d + e x\right )^{6}}\, 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)**(1/2)/(e*x+d)**6,x)
[Out]
Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x)**6, x)
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