3.7.55 \(\int \frac {(d^2-e^2 x^2)^{7/2}}{(d+e x)^{12}} \, dx\)

Optimal. Leaf size=133 \[ -\frac {\left (d^2-e^2 x^2\right )^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{6435 d^4 e (d+e x)^9}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{715 d^3 e (d+e x)^{10}} \]

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Rubi [A]  time = 0.06, antiderivative size = 133, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {659, 651} \begin {gather*} -\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{6435 d^4 e (d+e x)^9}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{715 d^3 e (d+e x)^{10}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x]

[Out]

-(d^2 - e^2*x^2)^(9/2)/(15*d*e*(d + e*x)^12) - (d^2 - e^2*x^2)^(9/2)/(65*d^2*e*(d + e*x)^11) - (2*(d^2 - e^2*x
^2)^(9/2))/(715*d^3*e*(d + e*x)^10) - (2*(d^2 - e^2*x^2)^(9/2))/(6435*d^4*e*(d + e*x)^9)

Rule 651

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

Rule 659

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

Rubi steps

\begin {align*} \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{12}} \, dx &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}}+\frac {\int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{11}} \, dx}{5 d}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{65 d^2 e (d+e x)^{11}}+\frac {2 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{10}} \, dx}{65 d^2}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{715 d^3 e (d+e x)^{10}}+\frac {2 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^9} \, dx}{715 d^3}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{15 d e (d+e x)^{12}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{715 d^3 e (d+e x)^{10}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{6435 d^4 e (d+e x)^9}\\ \end {align*}

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Mathematica [A]  time = 0.08, size = 71, normalized size = 0.53 \begin {gather*} -\frac {(d-e x)^4 \sqrt {d^2-e^2 x^2} \left (548 d^3+141 d^2 e x+24 d e^2 x^2+2 e^3 x^3\right )}{6435 d^4 e (d+e x)^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x]

[Out]

-1/6435*((d - e*x)^4*Sqrt[d^2 - e^2*x^2]*(548*d^3 + 141*d^2*e*x + 24*d*e^2*x^2 + 2*e^3*x^3))/(d^4*e*(d + e*x)^
8)

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IntegrateAlgebraic [A]  time = 0.95, size = 107, normalized size = 0.80 \begin {gather*} \frac {\sqrt {d^2-e^2 x^2} \left (-548 d^7+2051 d^6 e x-2748 d^5 e^2 x^2+1440 d^4 e^3 x^3-120 d^3 e^4 x^4-57 d^2 e^5 x^5-16 d e^6 x^6-2 e^7 x^7\right )}{6435 d^4 e (d+e x)^8} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x]

[Out]

(Sqrt[d^2 - e^2*x^2]*(-548*d^7 + 2051*d^6*e*x - 2748*d^5*e^2*x^2 + 1440*d^4*e^3*x^3 - 120*d^3*e^4*x^4 - 57*d^2
*e^5*x^5 - 16*d*e^6*x^6 - 2*e^7*x^7))/(6435*d^4*e*(d + e*x)^8)

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fricas [B]  time = 0.82, size = 269, normalized size = 2.02 \begin {gather*} -\frac {548 \, e^{8} x^{8} + 4384 \, d e^{7} x^{7} + 15344 \, d^{2} e^{6} x^{6} + 30688 \, d^{3} e^{5} x^{5} + 38360 \, d^{4} e^{4} x^{4} + 30688 \, d^{5} e^{3} x^{3} + 15344 \, d^{6} e^{2} x^{2} + 4384 \, d^{7} e x + 548 \, d^{8} + {\left (2 \, e^{7} x^{7} + 16 \, d e^{6} x^{6} + 57 \, d^{2} e^{5} x^{5} + 120 \, d^{3} e^{4} x^{4} - 1440 \, d^{4} e^{3} x^{3} + 2748 \, d^{5} e^{2} x^{2} - 2051 \, d^{6} e x + 548 \, d^{7}\right )} \sqrt {-e^{2} x^{2} + d^{2}}}{6435 \, {\left (d^{4} e^{9} x^{8} + 8 \, d^{5} e^{8} x^{7} + 28 \, d^{6} e^{7} x^{6} + 56 \, d^{7} e^{6} x^{5} + 70 \, d^{8} e^{5} x^{4} + 56 \, d^{9} e^{4} x^{3} + 28 \, d^{10} e^{3} x^{2} + 8 \, d^{11} e^{2} x + d^{12} e\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x, algorithm="fricas")

[Out]

-1/6435*(548*e^8*x^8 + 4384*d*e^7*x^7 + 15344*d^2*e^6*x^6 + 30688*d^3*e^5*x^5 + 38360*d^4*e^4*x^4 + 30688*d^5*
e^3*x^3 + 15344*d^6*e^2*x^2 + 4384*d^7*e*x + 548*d^8 + (2*e^7*x^7 + 16*d*e^6*x^6 + 57*d^2*e^5*x^5 + 120*d^3*e^
4*x^4 - 1440*d^4*e^3*x^3 + 2748*d^5*e^2*x^2 - 2051*d^6*e*x + 548*d^7)*sqrt(-e^2*x^2 + d^2))/(d^4*e^9*x^8 + 8*d
^5*e^8*x^7 + 28*d^6*e^7*x^6 + 56*d^7*e^6*x^5 + 70*d^8*e^5*x^4 + 56*d^9*e^4*x^3 + 28*d^10*e^3*x^2 + 8*d^11*e^2*
x + d^12*e)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: (454164480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^54*exp(2)^2+1135411200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^13*exp(1)^52*exp(2)^3+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*
exp(1)^50*exp(2)^4+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^48*exp(2)^
5+1192181760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^46*exp(2)^6+596090880*(-1/2
*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^44*exp(2)^7+212889600*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^42*exp(2)^8+53222400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^19*exp(1)^40*exp(2)^9+8870400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20
*exp(1)^38*exp(2)^10+887040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^36*exp(2)^11
[phone]*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^54*exp(2)^2+1776287744*(-1/2*
(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^52*exp(2)^3+4440719360*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^50*exp(2)^4+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^14*exp(1)^48*exp(2)^5+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^15*exp(1)^46*exp(2)^6+4662755328*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^44*e
xp(2)^7+2331377664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^42*exp(2)^8+832634880
*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^40*exp(2)^9+208158720*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^38*exp(2)^10+35481600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^20*exp(1)^36*exp(2)^11+3548160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^21*exp(1)^34*exp(2)^12+454164480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^5
4*exp(2)^2+2162163712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^52*exp(2)^3+451172
7616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^50*exp(2)^4+5318410240*(-1/2*(-2*d*
exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^48*exp(2)^5+3719823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^46*exp(2)^6+1335459840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^15*exp(1)^44*exp(2)^7-78532608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*ex
p(1)^42*exp(2)^8-358600704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^40*exp(2)^9-2
06384640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^38*exp(2)^10-62684160*(-1/2*(-2
*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^36*exp(2)^11-8870400*(-1/2*(-2*d*exp(1)-2*sqrt(d^
2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^34*exp(2)^12-887040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1)
)/x/exp(2))^21*exp(1)^32*exp(2)^13+1776287744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*e
xp(1)^52*exp(2)^3+6917718016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^50*exp(2)^4
[phone]*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^48*exp(2)^5-356843520*(-1/2*
(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^46*exp(2)^6-17187962880*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^44*exp(2)^7-26513473536*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^15*exp(1)^42*exp(2)^8-22500065280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^16*exp(1)^40*exp(2)^9-12498984960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^
38*exp(2)^10-4761630720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^36*exp(2)^11-123
4759680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^34*exp(2)^12-212889600*(-1/2*(-2
*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^32*exp(2)^13-21288960*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^30*exp(2)^14+1135411200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^9*exp(1)^52*exp(2)^3+4511727616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^1
0*exp(1)^50*exp(2)^4+5745688576*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^48*exp(2
)^5-2968379392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^46*exp(2)^6-20440330240*(
-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^44*exp(2)^7-34036992000*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^42*exp(2)^8-33879926784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2
*exp(2))*exp(1))/x/exp(2))^15*exp(1)^40*exp(2)^9-23075103744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))
/x/exp(2))^16*exp(1)^38*exp(2)^10-11227974912*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*e
xp(1)^36*exp(2)^11-3885826560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^34*exp(2)^
12-960368640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^32*exp(2)^13-177408000*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^30*exp(2)^14-17740800*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^28*exp(2)^15+4440719360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^9*exp(1)^50*exp(2)^4+9182773248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^10*exp(1)^48*exp(2)^5-9332719616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^46*
exp(2)^6-49010475008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^44*exp(2)^7-6236831
7440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^42*exp(2)^8-27230945280*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^40*exp(2)^9+17769185280*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^38*exp(2)^10+33476653056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^16*exp(1)^36*exp(2)^11+23880772608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^17*exp(1)^34*exp(2)^12+10327511040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^32
*exp(2)^13+2847989760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^30*exp(2)^14+49674
2400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^28*exp(2)^15+49674240*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^26*exp(2)^16+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^50*exp(2)^4+5318410240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^9*exp(1)^48*exp(2)^5-2968379392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*ex
p(1)^46*exp(2)^6-35817684992*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^44*exp(2)^7
-64475744256*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^42*exp(2)^8-42059888640*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^40*exp(2)^9+22106726400*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^38*exp(2)^10+68256933888*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^15*exp(1)^36*exp(2)^11+66571760640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))
/x/exp(2))^16*exp(1)^34*exp(2)^12+39114620160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*e
xp(1)^32*exp(2)^13+15179028480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^30*exp(2)
^14+4016517120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^28*exp(2)^15+745113600*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^26*exp(2)^16+74511360*(-1/2*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^24*exp(2)^17+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^8*exp(1)^48*exp(2)^5-356843520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^9*exp(1)^46*exp(2)^6-49010475008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^44
*exp(2)^7-72072658944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^42*exp(2)^8+876735
6928*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^40*exp(2)^9+117226700800*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^38*exp(2)^10+131142696960*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^36*exp(2)^11+64189390848*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^15*exp(1)^34*exp(2)^12+5202075648*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^16*exp(1)^32*exp(2)^13-12890228736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^
30*exp(2)^14-8908247040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^28*exp(2)^15-284
7989760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^26*exp(2)^16-496742400*(-1/2*(-2
*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^24*exp(2)^17-49674240*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^22*exp(2)^18+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^7*exp(1)^48*exp(2)^5+3719823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8
*exp(1)^46*exp(2)^6-20440330240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^44*exp(2)
^7-63794497536*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^42*exp(2)^8-17358155776*(
-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^40*exp(2)^9+158830318592*(-1/2*(-2*d*exp(
1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^38*exp(2)^10+291600826880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^36*exp(2)^11+235916820480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^14*exp(1)^34*exp(2)^12+81697228800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^15*exp(1)^32*exp(2)^13-19857159168*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^30*e
xp(2)^14-37614872064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^28*exp(2)^15-203206
08000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^26*exp(2)^16-6340857600*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^24*exp(2)^17-1282216320*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^22*exp(2)^18-132612480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^21*exp(1)^20*exp(2)^19+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^7*exp(1)^46*exp(2)^6-17187962880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^44*exp(
2)^7-62368317440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^42*exp(2)^8+9221521408*(
-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^40*exp(2)^9+182305046528*(-1/2*(-2*d*exp(
1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^38*exp(2)^10+227689549824*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^36*exp(2)^11+91490150400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^13*exp(1)^34*exp(2)^12-41117429760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
14*exp(1)^32*exp(2)^13-65572294656*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^30*ex
p(2)^14-33956837376*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^28*exp(2)^15-6894547
968*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^26*exp(2)^16+1311045120*(-1/2*(-2*d*
exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^24*exp(2)^17+729146880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^22*exp(2)^18+55883520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^20*exp(1)^20*exp(2)^19+2661120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp
(1)^18*exp(2)^20+1192181760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^46*exp(2)^6+1
335459840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^44*exp(2)^7-33961297920*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^42*exp(2)^8-40621701120*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^40*exp(2)^9+187660301312*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^10*exp(1)^38*exp(2)^10+661171017728*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^11*exp(1)^36*exp(2)^11+1139388811264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(
1)^34*exp(2)^12+1437707054080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^32*exp(2)^
13+1446173963520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^30*exp(2)^14+1129292879
616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^28*exp(2)^15+661664217984*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^26*exp(2)^16+284922023232*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^24*exp(2)^17+87622143840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^18*exp(1)^22*exp(2)^18+18573176160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^19*exp(1)^20*exp(2)^19+2608285680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^
18*exp(2)^20+195758640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^16*exp(2)^21+4662
755328*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^44*exp(2)^7-26513473536*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^42*exp(2)^8-27306639360*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^40*exp(2)^9+118627041280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^9*exp(1)^38*exp(2)^10+244616638464*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2)
)^10*exp(1)^36*exp(2)^11+216680093696*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^34
*exp(2)^12+274274874368*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^32*exp(2)^13+534
142906880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^30*exp(2)^14+715047125760*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^28*exp(2)^15+616167121152*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^26*exp(2)^16+359634667392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^
2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^24*exp(2)^17+143475304896*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^17*exp(1)^22*exp(2)^18+38859115680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^1
8*exp(1)^20*exp(2)^19+7463221920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^18*exp(
2)^20+1042770960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^16*exp(2)^21+75675600*(
-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^14*exp(2)^22+596090880*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^44*exp(2)^7-78532608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^6*exp(1)^42*exp(2)^8-33804232704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^7*exp(1)^40*exp(2)^9+23081287680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^38*
exp(2)^10+416467673600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^36*exp(2)^11+15310
47130624*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^34*exp(2)^12+3982697569664*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^32*exp(2)^13+7284266417472*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^30*exp(2)^14+9203026467360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^28*exp(2)^15+8206226368560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^14*exp(1)^26*exp(2)^16+5289016449552*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^15*exp(1)^24*exp(2)^17+2486297206008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)
^22*exp(2)^18+844771953564*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^20*exp(2)^19+
202034870730*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^18*exp(2)^20+32067251370*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^16*exp(2)^21+2912128065*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^14*exp(2)^22+99643005*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^21*exp(1)^12*exp(2)^23+2331377664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^5*exp(1)^42*exp(2)^8-22545481728*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^
40*exp(2)^9+17784324096*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^38*exp(2)^10+1337
54142720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^36*exp(2)^11+162136381440*(-1/2*
(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^34*exp(2)^12+460633699328*(-1/2*(-2*d*exp(1)-2*
sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^32*exp(2)^13+1616341433344*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^11*exp(1)^30*exp(2)^14+3127058195712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^12*exp(1)^28*exp(2)^15+3734080120320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
13*exp(1)^26*exp(2)^16+3037287665280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^24*
exp(2)^17+1766118009216*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^22*exp(2)^18+749
884640736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^20*exp(2)^19+234915571968*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^18*exp(2)^20+53196213840*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^16*exp(2)^21+7711463760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^19*exp(1)^14*exp(2)^22+502757640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^20*exp(1)^12*exp(2)^23-2079000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^1
0*exp(2)^24+212889600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^42*exp(2)^8-3586007
04*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^40*exp(2)^9-23084565504*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^38*exp(2)^10+69250418688*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^36*exp(2)^11+482417548800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^8*exp(1)^34*exp(2)^12+2724212508160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^9*exp(1)^32*exp(2)^13+9472929694272*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^30*
exp(2)^14+19350572769792*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^28*exp(2)^15+25
598852857776*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^26*exp(2)^16+23592220283280
*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^24*exp(2)^17+15820453405680*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^22*exp(2)^18+7912063010544*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^20*exp(2)^19+2997196470114*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp
(2))*exp(1))/x/exp(2))^16*exp(1)^18*exp(2)^20+867038842362*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^17*exp(1)^16*exp(2)^21+189604915500*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*ex
p(1)^14*exp(2)^22+29957673900*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^12*exp(2)^
23+3081459150*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^10*exp(2)^24+156028950*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^8*exp(2)^25+832634880*(-1/2*(-2*d*exp(1)-2*
sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^40*exp(2)^9-12521693184*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^5*exp(1)^38*exp(2)^10+33945956352*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^6*exp(1)^36*exp(2)^11+65862230016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^3
4*exp(2)^12+96428175360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^32*exp(2)^13+1109
540917760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^30*exp(2)^14+3968752710912*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^28*exp(2)^15+7270703692032*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^26*exp(2)^16+8465368196736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^24*exp(2)^17+6883484741760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^13*exp(1)^22*exp(2)^18+4099326443520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^14*exp(1)^20*exp(2)^19+1839581872128*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)
^18*exp(2)^20+632133148416*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^16*exp(2)^21+
166288539648*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^14*exp(2)^22+33523459200*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^12*exp(2)^23+5359939200*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^10*exp(2)^24+655300800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^20*exp(1)^8*exp(2)^25+42356160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^21*exp(1)^6*exp(2)^26+53222400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^40*e
xp(2)^9-194219520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^38*exp(2)^10-1125095347
2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^36*exp(2)^11+67897564416*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^34*exp(2)^12+367698490368*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^32*exp(2)^13+3673216081920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^8*exp(1)^30*exp(2)^14+14772098652960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^9*exp(1)^28*exp(2)^15+31419134327856*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)
^26*exp(2)^16+42396423122064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^24*exp(2)^1
7+39751916476272*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^22*exp(2)^18+2721573845
7600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^20*exp(2)^19+14012361510840*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^18*exp(2)^20+5511812033112*(-1/2*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^16*exp(2)^21+1655351957259*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2
*exp(2))*exp(1))/x/exp(2))^16*exp(1)^14*exp(2)^22+372509841627*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^17*exp(1)^12*exp(2)^23+61178779200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18
*exp(1)^10*exp(2)^24+7217918400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^8*exp(2)
^25+600304320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^6*exp(2)^26+29050560*(-1/2
*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^4*exp(2)^27+208158720*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^38*exp(2)^10-4739328000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^4*exp(1)^36*exp(2)^11+24081970176*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^5*exp(1)^34*exp(2)^12+4297396224*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^32*e
xp(2)^13+101884096512*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^30*exp(2)^14+165969
9106560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^28*exp(2)^15+5693835333120*(-1/2*
(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^26*exp(2)^16+10230921968256*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^24*exp(2)^17+11858184167808*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x
^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^22*exp(2)^18+9686219794944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^12*exp(1)^20*exp(2)^19+5843280051840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^13*exp(1)^18*exp(2)^20+2674721945280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^
16*exp(2)^21+939024934848*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^14*exp(2)^22+2
52073307640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^12*exp(2)^23+51100055160*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^10*exp(2)^24+7371893760*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^8*exp(2)^25+587811840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp
(2))*exp(1))/x/exp(2))^19*exp(1)^6*exp(2)^26+1774080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^20*exp(1)^4*exp(2)^27-1774080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(2)^29+8870
400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^38*exp(2)^10-59642880*(-1/2*(-2*d*exp
(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^36*exp(2)^11-3976346880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^
2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^34*exp(2)^12+39913302528*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1)
)/x/exp(2))^5*exp(1)^32*exp(2)^13+200086694016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*e
xp(1)^30*exp(2)^14+3629638096128*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^28*exp(2
)^15+15859133872560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^26*exp(2)^16+34723986
836880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^24*exp(2)^17+47553391585392*(-1/2*
(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^22*exp(2)^18+44897428318512*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^20*exp(2)^19+30781188709656*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^18*exp(2)^20+15760443514200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^13*exp(1)^16*exp(2)^21+6083022847440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^14*exp(1)^14*exp(2)^22+1758996058512*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1
)^12*exp(2)^23+376638595410*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^10*exp(2)^24
[phone]*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^8*exp(2)^25+6652800000*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^6*exp(2)^26+452390400*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^4*exp(2)^27+9757440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^20*exp(2)^29+33904640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^3
6*exp(2)^11-1227212800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^34*exp(2)^12+10143
288320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^32*exp(2)^13-13066234368*(-1/2*(-2
*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^30*exp(2)^14+103501085952*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^28*exp(2)^15+1619490614016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^7*exp(1)^26*exp(2)^16+5515441176960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^8*exp(1)^24*exp(2)^17+9922689722880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(
1)^22*exp(2)^18+11513672030784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^20*exp(2)
^19+9382029163584*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^18*exp(2)^20+561201039
9072*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^16*exp(2)^21+2516004876000*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^14*exp(2)^22+845530667520*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^12*exp(2)^23+208676160000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^15*exp(1)^10*exp(2)^24+35609259840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^16*exp(1)^8*exp(2)^25+3447554880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1
)^6*exp(2)^26+49674240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^4*exp(2)^27-14192
640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(2)^29-13587200*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^34*exp(2)^12-977102720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^3*exp(1)^32*exp(2)^13+15674655040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2)
)^4*exp(1)^30*exp(2)^14+81449114208*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^28*ex
p(2)^15+2595069253392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^26*exp(2)^16+122628
76848816*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^24*exp(2)^17+27774124028640*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^22*exp(2)^18+38466510676440*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^20*exp(2)^19+36155903422716*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^18*exp(2)^20+24327275207004*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^11*exp(1)^16*exp(2)^21+12005263564602*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^12*exp(1)^14*exp(2)^22+4367011523490*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(
1)^12*exp(2)^23+1166716615680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^10*exp(2)^
24+227853373440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^8*exp(2)^25+31663114560*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^6*exp(2)^26+2748271680*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^4*exp(2)^27+97574400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^18*exp(2)^29-205534208*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*e
xp(1)^32*exp(2)^13+2792739840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^30*exp(2)^1
4-8017194240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^28*exp(2)^15+67054834176*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^26*exp(2)^16+1103053260672*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^24*exp(2)^17+3861234976896*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x
^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^18+7041552788160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^8*exp(1)^20*exp(2)^19+8163372201600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^9*exp(1)^18*exp(2)^20+6547070752992*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^16*
exp(2)^21+3783632995296*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^14*exp(2)^22+159
2787958608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^12*exp(2)^23+479963206800*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^10*exp(2)^24+97858252800*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^8*exp(2)^25+11491307520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^15*exp(1)^6*exp(2)^26+345945600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^16*exp(1)^4*exp(2)^27+80640*exp(1)^34*exp(2)^12-47900160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^17*exp(2)^29-142780352*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^30*
exp(2)^14+4097139200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^28*exp(2)^15+2496430
3760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^26*exp(2)^16+1336479168816*(-1/2*(-2
*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)^17+7043646076368*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^18+16622627859024*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^19+23174285016300*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))
/x/exp(2))^8*exp(1)^18*exp(2)^20+21429023971740*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*
exp(1)^16*exp(2)^21+13863225053832*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^14*ex
p(2)^22+6407351713224*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^12*exp(2)^23+21287
52052812*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^10*exp(2)^24+509009816700*(-1/2
*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^8*exp(2)^25+85915146240*(-1/2*(-2*d*exp(1)-2*
sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^6*exp(2)^26+9196830720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^15*exp(1)^4*exp(2)^27+315392*exp(1)^32*exp(2)^13+439084800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(2)^29+492600064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^2*exp(1)^28*exp(2)^15-2620048640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^26*e
xp(2)^16+27595680640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^24*exp(2)^17+5445085
70496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^18+2019689861376*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^19+3762148355328*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^20+4330930866240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^8*exp(1)^16*exp(2)^21+3361913163840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/
x/exp(2))^9*exp(1)^14*exp(2)^22+1820707730688*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*e
xp(1)^12*exp(2)^23+683666742528*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^10*exp(2
)^24+169585282944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^8*exp(2)^25+2434170816
0*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^6*exp(2)^26+1192181760*(-1/2*(-2*d*exp
(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^4*exp(2)^27-106112*exp(1)^30*exp(2)^14-85155840*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(2)^29+644381584*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^2*exp(1)^26*exp(2)^16+5764912560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^3*exp(1)^24*exp(2)^17+492231350160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(
1)^22*exp(2)^18+3050419446624*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^1
9+7555261758264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^20+105699180372
72*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^21+9496853205510*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^22+5774643837270*(-1/2*(-2*d*exp(1)-2*sqrt
(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^23+2431356947712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^10*exp(1)^10*exp(2)^24+717950483712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^11*exp(1)^8*exp(2)^25+147580304256*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1
)^6*exp(2)^26+19326384000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^4*exp(2)^27-19
17696*exp(1)^28*exp(2)^15+1170892800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(2)^29-
532481664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^24*exp(2)^17+7784064640*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^18+195295767040*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^19+798639355008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp
(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^20+1532034634944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^6*exp(1)^16*exp(2)^21+1738292309952*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp
(1)^14*exp(2)^22+1278053280240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^
23+621232199280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^24+192978745344
*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*exp(2)^25+34424248320*(-1/2*(-2*d*exp
(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^6*exp(2)^26+2458874880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^
2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^4*exp(2)^27-1450096*exp(1)^26*exp(2)^16-74511360*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(2)^29+1022256752*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))
/x/exp(2))^2*exp(1)^22*exp(2)^18+126715146800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*ex
p(1)^20*exp(2)^19+991927905320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^
20+2618246107752*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^21+36768746768
16*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^22+3156426726288*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^23+1757209463460*(-1/2*(-2*d*exp(1)-2*sqrt
(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^24+657521407620*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^25+167422058496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^10*exp(1)^6*exp(2)^26+27047623680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^4*
exp(2)^27+4592896*exp(1)^24*exp(2)^17+2049062400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^1
2*exp(2)^29+1488955424*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^19+49144
450080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^20+239105848080*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^21+477342259152*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^22+527876405760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(
2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^23+355008360960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^7*exp(1)^10*exp(2)^24+144723553920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)
^8*exp(2)^25+33032039040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^26+3278
499840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^4*exp(2)^27+6388392*exp(1)^22*exp
(2)^18+21644961866*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^20+236106883
210*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^21+691189098325*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^22+972412454673*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^23+777789450240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^24+387216614400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^7*exp(1)^8*exp(2)^25+126206720640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*e
xp(2)^26+25752988800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^27-4907936*
exp(1)^20*exp(2)^19+2458874880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^29+820531
1312*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^21+53803948880*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^22+112859480360*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^23+119300392200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^24+69289144320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^6*exp(1)^8*exp(2)^25+21293690880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp
(2)^26+2905943040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^27-1501054*exp
(1)^18*exp(2)^20+74511360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^29+38952089132*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^22+137910558060*(-1/2*(-2*d*exp
(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^23+191329440390*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^24+139186067790*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^5*exp(1)^8*exp(2)^25+61517998080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*
exp(1)^6*exp(2)^26+16562810880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^2
7+7267392*exp(1)^16*exp(2)^21+2049062400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^
29+8680194688*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^23+19757105280*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^24+19397991360*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^25+8846819520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^26+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^6*exp(1)^4*exp(2)^27+110317087*exp(1)^14*exp(2)^22+85155840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^7*exp(2)^29+20153994432*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^1
0*exp(2)^24+26864819520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^25+17967
660480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^26+6911593920*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^27+41673368*exp(1)^12*exp(2)^23+1170892800*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^29+2513009664*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^25+2144271360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^3*exp(1)^6*exp(2)^26+633346560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*ex
p(1)^4*exp(2)^27+184776042*exp(1)^10*exp(2)^24+47900160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^5*exp(2)^29+2606478336*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^26+
1694246400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^27+39657024*exp(1)^8*
exp(2)^25+439084800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^29+134830080*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^27+96376896*exp(1)^6*exp(2)^26+14192640*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^29+12418560*exp(1)^4*exp(2)^27+97574400*(
-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^29+9757440*exp(2)^29+82575360*(-1/2*(-2*d*
exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^56*exp(2)-887040*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))*exp(2)^29/x/exp(2)-92806560*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^27/x/exp(2)-1
15426080*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^26/x/exp(2)-982131381*(-2*d*exp(1)-2*sqrt
(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^25/x/exp(2)-437266764*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp
(1)^10*exp(2)^24/x/exp(2)-3965429919/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^23/x/exp(2
)-420569248*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^22/x/exp(2)-1115608637*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^21/x/exp(2)-78610752*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1)
)*exp(1)^18*exp(2)^20/x/exp(2)-49794646*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^19/x/exp(
2)[phone]*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^18/x/exp(2)-33016632*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^17/x/exp(2)-25684736*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*
exp(1)^26*exp(2)^16/x/exp(2)+7080656*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^28*exp(2)^15/x/exp(2)+
10450176*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^30*exp(2)^14/x/exp(2)+723712*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))*exp(1)^32*exp(2)^13/x/exp(2)-1695232*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)
^34*exp(2)^12/x/exp(2)-443520*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^36*exp(2)^11/x/exp(2))/((-1/2
*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+
exp(2))^11/(443520*d^4*exp(1)^37-443520*d^4*exp(1)^33*exp(2)^2-10644480*d^4*exp(1)^31*exp(2)^3-8870400*d^4*exp
(1)^29*exp(2)^4+24837120*d^4*exp(1)^27*exp(2)^5+37255680*d^4*exp(1)^25*exp(2)^6-24837120*d^4*exp(1)^23*exp(2)^
7-68302080*d^4*exp(1)^21*exp(2)^8+68302080*d^4*exp(1)^17*exp(2)^10+24837120*d^4*exp(1)^15*exp(2)^11-37255680*d
^4*exp(1)^13*exp(2)^12-24837120*d^4*exp(1)^11*exp(2)^13+8870400*d^4*exp(1)^9*exp(2)^14+10644480*d^4*exp(1)^7*e
xp(2)^15+443520*d^4*exp(1)^5*exp(2)^16+1774080*d^4*exp(1)^35*exp(2)-2217600*d^4*exp(1)*exp(2)^18)+1/2*(-1152*e
xp(1)^20*exp(2)^9-768*exp(1)^18*exp(2)^10-17072*exp(1)^16*exp(2)^11-7504*exp(1)^14*exp(2)^12-50261*exp(1)^12*e
xp(2)^13-13736*exp(1)^10*exp(2)^14-39910*exp(1)^8*exp(2)^15-6080*exp(1)^6*exp(2)^16-8128*exp(1)^4*exp(2)^17-76
8*exp(2)^19)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-
exp(1)^4+exp(2)^2)/(-64*d^4*exp(1)^37+64*d^4*exp(1)^33*exp(2)^2+1536*d^4*exp(1)^31*exp(2)^3+1280*d^4*exp(1)^29
*exp(2)^4-3584*d^4*exp(1)^27*exp(2)^5-5376*d^4*exp(1)^25*exp(2)^6+3584*d^4*exp(1)^23*exp(2)^7+9856*d^4*exp(1)^
21*exp(2)^8-9856*d^4*exp(1)^17*exp(2)^10-3584*d^4*exp(1)^15*exp(2)^11+5376*d^4*exp(1)^13*exp(2)^12+3584*d^4*ex
p(1)^11*exp(2)^13-1280*d^4*exp(1)^9*exp(2)^14-1536*d^4*exp(1)^7*exp(2)^15-64*d^4*exp(1)^5*exp(2)^16-256*d^4*ex
p(1)^35*exp(2)+320*d^4*exp(1)*exp(2)^18)

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maple [A]  time = 0.04, size = 66, normalized size = 0.50 \begin {gather*} -\frac {\left (-e x +d \right ) \left (2 e^{3} x^{3}+24 e^{2} x^{2} d +141 x \,d^{2} e +548 d^{3}\right ) \left (-e^{2} x^{2}+d^{2}\right )^{\frac {7}{2}}}{6435 \left (e x +d \right )^{11} d^{4} e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x)

[Out]

-1/6435*(-e*x+d)*(2*e^3*x^3+24*d*e^2*x^2+141*d^2*e*x+548*d^3)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^11/d^4/e

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maxima [B]  time = 1.69, size = 932, normalized size = 7.01 \begin {gather*} -\frac {{\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {7}{2}}}{4 \, {\left (e^{12} x^{11} + 11 \, d e^{11} x^{10} + 55 \, d^{2} e^{10} x^{9} + 165 \, d^{3} e^{9} x^{8} + 330 \, d^{4} e^{8} x^{7} + 462 \, d^{5} e^{7} x^{6} + 462 \, d^{6} e^{6} x^{5} + 330 \, d^{7} e^{5} x^{4} + 165 \, d^{8} e^{4} x^{3} + 55 \, d^{9} e^{3} x^{2} + 11 \, d^{10} e^{2} x + d^{11} e\right )}} + \frac {7 \, {\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {5}{2}} d}{20 \, {\left (e^{11} x^{10} + 10 \, d e^{10} x^{9} + 45 \, d^{2} e^{9} x^{8} + 120 \, d^{3} e^{8} x^{7} + 210 \, d^{4} e^{7} x^{6} + 252 \, d^{5} e^{6} x^{5} + 210 \, d^{6} e^{5} x^{4} + 120 \, d^{7} e^{4} x^{3} + 45 \, d^{8} e^{3} x^{2} + 10 \, d^{9} e^{2} x + d^{10} e\right )}} - \frac {7 \, {\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {3}{2}} d^{2}}{24 \, {\left (e^{10} x^{9} + 9 \, d e^{9} x^{8} + 36 \, d^{2} e^{8} x^{7} + 84 \, d^{3} e^{7} x^{6} + 126 \, d^{4} e^{6} x^{5} + 126 \, d^{5} e^{5} x^{4} + 84 \, d^{6} e^{4} x^{3} + 36 \, d^{7} e^{3} x^{2} + 9 \, d^{8} e^{2} x + d^{9} e\right )}} + \frac {7 \, \sqrt {-e^{2} x^{2} + d^{2}} d^{3}}{60 \, {\left (e^{9} x^{8} + 8 \, d e^{8} x^{7} + 28 \, d^{2} e^{7} x^{6} + 56 \, d^{3} e^{6} x^{5} + 70 \, d^{4} e^{5} x^{4} + 56 \, d^{5} e^{4} x^{3} + 28 \, d^{6} e^{3} x^{2} + 8 \, d^{7} e^{2} x + d^{8} e\right )}} - \frac {7 \, \sqrt {-e^{2} x^{2} + d^{2}} d^{2}}{1560 \, {\left (e^{8} x^{7} + 7 \, d e^{7} x^{6} + 21 \, d^{2} e^{6} x^{5} + 35 \, d^{3} e^{5} x^{4} + 35 \, d^{4} e^{4} x^{3} + 21 \, d^{5} e^{3} x^{2} + 7 \, d^{6} e^{2} x + d^{7} e\right )}} - \frac {7 \, \sqrt {-e^{2} x^{2} + d^{2}} d}{2860 \, {\left (e^{7} x^{6} + 6 \, d e^{6} x^{5} + 15 \, d^{2} e^{5} x^{4} + 20 \, d^{3} e^{4} x^{3} + 15 \, d^{4} e^{3} x^{2} + 6 \, d^{5} e^{2} x + d^{6} e\right )}} - \frac {7 \, \sqrt {-e^{2} x^{2} + d^{2}}}{5148 \, {\left (e^{6} x^{5} + 5 \, d e^{5} x^{4} + 10 \, d^{2} e^{4} x^{3} + 10 \, d^{3} e^{3} x^{2} + 5 \, d^{4} e^{2} x + d^{5} e\right )}} - \frac {\sqrt {-e^{2} x^{2} + d^{2}}}{1287 \, {\left (d e^{5} x^{4} + 4 \, d^{2} e^{4} x^{3} + 6 \, d^{3} e^{3} x^{2} + 4 \, d^{4} e^{2} x + d^{5} e\right )}} - \frac {\sqrt {-e^{2} x^{2} + d^{2}}}{2145 \, {\left (d^{2} e^{4} x^{3} + 3 \, d^{3} e^{3} x^{2} + 3 \, d^{4} e^{2} x + d^{5} e\right )}} - \frac {2 \, \sqrt {-e^{2} x^{2} + d^{2}}}{6435 \, {\left (d^{3} e^{3} x^{2} + 2 \, d^{4} e^{2} x + d^{5} e\right )}} - \frac {2 \, \sqrt {-e^{2} x^{2} + d^{2}}}{6435 \, {\left (d^{4} e^{2} x + d^{5} e\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x, algorithm="maxima")

[Out]

-1/4*(-e^2*x^2 + d^2)^(7/2)/(e^12*x^11 + 11*d*e^11*x^10 + 55*d^2*e^10*x^9 + 165*d^3*e^9*x^8 + 330*d^4*e^8*x^7
+ 462*d^5*e^7*x^6 + 462*d^6*e^6*x^5 + 330*d^7*e^5*x^4 + 165*d^8*e^4*x^3 + 55*d^9*e^3*x^2 + 11*d^10*e^2*x + d^1
1*e) + 7/20*(-e^2*x^2 + d^2)^(5/2)*d/(e^11*x^10 + 10*d*e^10*x^9 + 45*d^2*e^9*x^8 + 120*d^3*e^8*x^7 + 210*d^4*e
^7*x^6 + 252*d^5*e^6*x^5 + 210*d^6*e^5*x^4 + 120*d^7*e^4*x^3 + 45*d^8*e^3*x^2 + 10*d^9*e^2*x + d^10*e) - 7/24*
(-e^2*x^2 + d^2)^(3/2)*d^2/(e^10*x^9 + 9*d*e^9*x^8 + 36*d^2*e^8*x^7 + 84*d^3*e^7*x^6 + 126*d^4*e^6*x^5 + 126*d
^5*e^5*x^4 + 84*d^6*e^4*x^3 + 36*d^7*e^3*x^2 + 9*d^8*e^2*x + d^9*e) + 7/60*sqrt(-e^2*x^2 + d^2)*d^3/(e^9*x^8 +
8*d*e^8*x^7 + 28*d^2*e^7*x^6 + 56*d^3*e^6*x^5 + 70*d^4*e^5*x^4 + 56*d^5*e^4*x^3 + 28*d^6*e^3*x^2 + 8*d^7*e^2*
x + d^8*e) - 7/1560*sqrt(-e^2*x^2 + d^2)*d^2/(e^8*x^7 + 7*d*e^7*x^6 + 21*d^2*e^6*x^5 + 35*d^3*e^5*x^4 + 35*d^4
*e^4*x^3 + 21*d^5*e^3*x^2 + 7*d^6*e^2*x + d^7*e) - 7/2860*sqrt(-e^2*x^2 + d^2)*d/(e^7*x^6 + 6*d*e^6*x^5 + 15*d
^2*e^5*x^4 + 20*d^3*e^4*x^3 + 15*d^4*e^3*x^2 + 6*d^5*e^2*x + d^6*e) - 7/5148*sqrt(-e^2*x^2 + d^2)/(e^6*x^5 + 5
*d*e^5*x^4 + 10*d^2*e^4*x^3 + 10*d^3*e^3*x^2 + 5*d^4*e^2*x + d^5*e) - 1/1287*sqrt(-e^2*x^2 + d^2)/(d*e^5*x^4 +
4*d^2*e^4*x^3 + 6*d^3*e^3*x^2 + 4*d^4*e^2*x + d^5*e) - 1/2145*sqrt(-e^2*x^2 + d^2)/(d^2*e^4*x^3 + 3*d^3*e^3*x
^2 + 3*d^4*e^2*x + d^5*e) - 2/6435*sqrt(-e^2*x^2 + d^2)/(d^3*e^3*x^2 + 2*d^4*e^2*x + d^5*e) - 2/6435*sqrt(-e^2
*x^2 + d^2)/(d^4*e^2*x + d^5*e)

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mupad [B]  time = 3.02, size = 228, normalized size = 1.71 \begin {gather*} \frac {320\,\sqrt {d^2-e^2\,x^2}}{1287\,e\,{\left (d+e\,x\right )}^5}-\frac {824\,d\,\sqrt {d^2-e^2\,x^2}}{715\,e\,{\left (d+e\,x\right )}^6}-\frac {\sqrt {d^2-e^2\,x^2}}{1287\,d\,e\,{\left (d+e\,x\right )}^4}-\frac {\sqrt {d^2-e^2\,x^2}}{2145\,d^2\,e\,{\left (d+e\,x\right )}^3}-\frac {2\,\sqrt {d^2-e^2\,x^2}}{6435\,d^3\,e\,{\left (d+e\,x\right )}^2}-\frac {2\,\sqrt {d^2-e^2\,x^2}}{6435\,d^4\,e\,\left (d+e\,x\right )}+\frac {368\,d^2\,\sqrt {d^2-e^2\,x^2}}{195\,e\,{\left (d+e\,x\right )}^7}-\frac {16\,d^3\,\sqrt {d^2-e^2\,x^2}}{15\,e\,{\left (d+e\,x\right )}^8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x)

[Out]

(320*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^5) - (824*d*(d^2 - e^2*x^2)^(1/2))/(715*e*(d + e*x)^6) - (d^2 -
e^2*x^2)^(1/2)/(1287*d*e*(d + e*x)^4) - (d^2 - e^2*x^2)^(1/2)/(2145*d^2*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(1
/2))/(6435*d^3*e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(1/2))/(6435*d^4*e*(d + e*x)) + (368*d^2*(d^2 - e^2*x^2)^(1
/2))/(195*e*(d + e*x)^7) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(15*e*(d + e*x)^8)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**12,x)

[Out]

Timed out

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