3.813 \(\int \frac {(d^2-e^2 x^2)^{7/2}}{(d+e x)^{11}} \, dx\)

Optimal. Leaf size=100 \[ -\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{143 d^2 e (d+e x)^{10}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{13 d e (d+e x)^{11}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{1287 d^3 e (d+e x)^9} \]

[Out]

-1/13*(-e^2*x^2+d^2)^(9/2)/d/e/(e*x+d)^11-2/143*(-e^2*x^2+d^2)^(9/2)/d^2/e/(e*x+d)^10-2/1287*(-e^2*x^2+d^2)^(9
/2)/d^3/e/(e*x+d)^9

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Rubi [A]  time = 0.04, antiderivative size = 100, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {659, 651} \[ -\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{1287 d^3 e (d+e x)^9}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{143 d^2 e (d+e x)^{10}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{13 d e (d+e x)^{11}} \]

Antiderivative was successfully verified.

[In]

Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^11,x]

[Out]

-(d^2 - e^2*x^2)^(9/2)/(13*d*e*(d + e*x)^11) - (2*(d^2 - e^2*x^2)^(9/2))/(143*d^2*e*(d + e*x)^10) - (2*(d^2 -
e^2*x^2)^(9/2))/(1287*d^3*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)^{11}} \, dx &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{13 d e (d+e x)^{11}}+\frac {2 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{10}} \, dx}{13 d}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{13 d e (d+e x)^{11}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{143 d^2 e (d+e x)^{10}}+\frac {2 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^9} \, dx}{143 d^2}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{13 d e (d+e x)^{11}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{143 d^2 e (d+e x)^{10}}-\frac {2 \left (d^2-e^2 x^2\right )^{9/2}}{1287 d^3 e (d+e x)^9}\\ \end {align*}

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Mathematica [A]  time = 0.07, size = 60, normalized size = 0.60 \[ -\frac {(d-e x)^4 \sqrt {d^2-e^2 x^2} \left (119 d^2+22 d e x+2 e^2 x^2\right )}{1287 d^3 e (d+e x)^7} \]

Antiderivative was successfully verified.

[In]

Integrate[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^11,x]

[Out]

-1/1287*((d - e*x)^4*Sqrt[d^2 - e^2*x^2]*(119*d^2 + 22*d*e*x + 2*e^2*x^2))/(d^3*e*(d + e*x)^7)

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fricas [B]  time = 1.20, size = 236, normalized size = 2.36 \[ -\frac {119 \, e^{7} x^{7} + 833 \, d e^{6} x^{6} + 2499 \, d^{2} e^{5} x^{5} + 4165 \, d^{3} e^{4} x^{4} + 4165 \, d^{4} e^{3} x^{3} + 2499 \, d^{5} e^{2} x^{2} + 833 \, d^{6} e x + 119 \, d^{7} + {\left (2 \, e^{6} x^{6} + 14 \, d e^{5} x^{5} + 43 \, d^{2} e^{4} x^{4} - 352 \, d^{3} e^{3} x^{3} + 628 \, d^{4} e^{2} x^{2} - 454 \, d^{5} e x + 119 \, d^{6}\right )} \sqrt {-e^{2} x^{2} + d^{2}}}{1287 \, {\left (d^{3} e^{8} x^{7} + 7 \, d^{4} e^{7} x^{6} + 21 \, d^{5} e^{6} x^{5} + 35 \, d^{6} e^{5} x^{4} + 35 \, d^{7} e^{4} x^{3} + 21 \, d^{8} e^{3} x^{2} + 7 \, d^{9} e^{2} x + d^{10} e\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x, algorithm="fricas")

[Out]

-1/1287*(119*e^7*x^7 + 833*d*e^6*x^6 + 2499*d^2*e^5*x^5 + 4165*d^3*e^4*x^4 + 4165*d^4*e^3*x^3 + 2499*d^5*e^2*x
^2 + 833*d^6*e*x + 119*d^7 + (2*e^6*x^6 + 14*d*e^5*x^5 + 43*d^2*e^4*x^4 - 352*d^3*e^3*x^3 + 628*d^4*e^2*x^2 -
454*d^5*e*x + 119*d^6)*sqrt(-e^2*x^2 + d^2))/(d^3*e^8*x^7 + 7*d^4*e^7*x^6 + 21*d^5*e^6*x^5 + 35*d^6*e^5*x^4 +
35*d^7*e^4*x^3 + 21*d^8*e^3*x^2 + 7*d^9*e^2*x + d^10*e)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: (-20643840*(-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)^2-46448640*(-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)^3-61931520*(-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)^4-54190080*(-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)^5-3251
4048*(-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)^6-13547520*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^38*exp(2)^7-3870720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^17*exp(1)^36*exp(2)^8-725760*(-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)^9-80640*(-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)^10-16056320*(-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)^2-80281600*(-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)^3-180633600*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^44*exp(2)^4-240844800*(-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)^5-210739200*(-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)^6-126443520*(-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)^7-52684800*(-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)^8-15052800*(-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)^9-2903040*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^32*exp(2)^10-322560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^19*exp(1)^30*exp(2)^11-20643840*(-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)^2-91316224*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^46*exp(2)^3-
177889280*(-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)^4-198973440*(-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)^5-138854400*(-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)^6-60533760*(-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)^7-14644224*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*e
xp(1)^36*exp(2)^8+26880*(-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)^9+9408
00*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^32*exp(2)^10-80281600*(-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)^3-279445504*(-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)^4-313425920*(-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)^5+77537280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^4
0*exp(2)^6+595107840*(-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)^7+7552204
80*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^36*exp(2)^8+537427968*(-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)^9+246973440*(-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)^10+74296320*(-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)^11+14515200*(-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)^12+1612800*(-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)^13-46448
640*(-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)^3-177889280*(-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)^4-215736320*(-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)^5+115159040*(-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)^6+715545600*(-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)^7+1095306240*(-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)^8+98133
5040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^34*exp(2)^9+588758016*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^32*exp(2)^10+240844800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^30*exp(2)^11+68812800*(-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)^12+14515200*(-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)^13+1612800*(-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)^14-18
0633600*(-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)^4-313425920*(-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)^5+422338560*(-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)^6+1646469120*(-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)^7+1770455040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*e
xp(1)^36*exp(2)^8+598425600*(-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)^9-
465346560*(-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)^10-674365440*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^30*exp(2)^11-397931520*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^28*exp(2)^12-132357120*(-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)^13-26127360*(-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)^14-2903040*(-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
)^15-61931520*(-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)^4-198973440*(-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)^5+115159040*(-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)^6+1340556288*(-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)^7+2306288640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^11*exp(1)^36*exp(2)^8+1459737600*(-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)^9-446684160*(-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)^10-1527751680*
(-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)^11-1334516736*(-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)^12-660522240*(-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)^13-210147840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/
x/exp(2))^17*exp(1)^24*exp(2)^14-45682560*(-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)^15-5120640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^20*exp(2)^16-2408
44800*(-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)^5+77537280*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^40*exp(2)^6+1646469120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^
2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^38*exp(2)^7+2091868160*(-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)^8-266608640*(-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)^9-2666035200*(-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)^10-25
72124160*(-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)^11-1113584640*(-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)^12-63974400*(-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)^13+183939840*(-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)^14+83381760*(-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)^15+15281280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^20*exp(2
)^16+1653120*(-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)^17-54190080*(-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)^5-138854400*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^40*exp(2)^6+705223680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^8*exp(1)^38*exp(2)^7+2574658560*(-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)^8+3931833856*(-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)
^9+5765588480*(-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)^10+9392079360*(-
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)^11+11610393600*(-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)^12+9680697600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2
*exp(2))*exp(1))/x/exp(2))^14*exp(1)^26*exp(2)^13+5513211648*(-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)^14+2134265280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*ex
p(1)^22*exp(2)^15+555340800*(-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)^16
[phone]*(-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)^17+8900640*(-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)^18-210739200*(-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)^6+595107840*(-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)^7+1770455040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*e
xp(1)^36*exp(2)^8-60170240*(-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)^9-21
70340864*(-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)^10+1602798080*(-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)^11+8519468160*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^28*exp(2)^12+11073968640*(-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)^13+8103453120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^14*exp(1)^24*exp(2)^14+3717661248*(-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)^15+1083228720*(-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)^16+219
344160*(-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)^17+33906600*(-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)^18+2633400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^14*exp(2)^19-32514048*(-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)^6-60533760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)
^38*exp(2)^7+1081543680*(-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)^8+24476
31360*(-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)^9+10108536320*(-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)^10+40457686208*(-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)^11+86514758080*(-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)^12+111269384880*(-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)^13+94654328640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^2
4*exp(2)^14+55470311400*(-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)^15+224
79282840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^20*exp(2)^16+6179893650*(-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)^17+1086337980*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^16*exp(2)^18+101542455*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^18*exp(1)^14*exp(2)^19+2628045*(-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)^20-126443520*(-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)^7+760381440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^36*exp(2)^8+586383360*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^34*exp(2)^9-1919846400*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^32*exp(2)^10+4209082880*(-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)^11+26755826688*(-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)^12+50393422080*(-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)^13+55047522240*(-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)^14+40
366155840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^22*exp(2)^15+20944983360*(-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)^16+7899576384*(-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)^17+2136905400*(-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)^18+362884200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^17*exp(1)^14*exp(2)^19+26780040*(-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)^20-118440*(-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)^21-13547520*
(-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)^7-14644224*(-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)^8+978324480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^6*exp(1)^34*exp(2)^9+1083970560*(-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)^10+24253520640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^30*e
xp(2)^11+116188504000*(-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)^12+254208
548544*(-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)^13+335439553440*(-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)^14+298391784600*(-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)^15+188947512600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^13*exp(1)^20*exp(2)^16+88035931200*(-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)^17+30776130000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*ex
p(1)^16*exp(2)^18+8011963575*(-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)^1
9+1479769515*(-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)^20+174853350*(-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)^21+10051650*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^8*exp(2)^22-52684800*(-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)^8+540524544*(-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)^9-519106560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^32*exp(2)^
10-1245327360*(-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)^11+16963981440*(-
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)^12+64264147200*(-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)^13+113306286528*(-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)^14+126183988800*(-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)^15+97921447680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12
*exp(1)^20*exp(2)^16+55460126400*(-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)^17+23480456160*(-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)^18+744018576
0*(-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)^19+1764199080*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^12*exp(2)^20+324613800*(-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)^21+44775360*(-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)^22+3205440*(-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)^23-3870720*(-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)^8-1263360*
(-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)^9+589016064*(-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)^10-122949120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp
(2))*exp(1))/x/exp(2))^6*exp(1)^30*exp(2)^11+37102041600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^7*exp(1)^28*exp(2)^12+186497540400*(-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)^13+420044380320*(-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)^14+5
71857213480*(-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)^15+527275471800*(-
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)^16+349138365240*(-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)^17+171238240320*(-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)^18+62566778820*(-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)^19+16749708444*(-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)^20+3212326110*(-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)^21+436579710*(-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)^22+40985280*(-
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)^23+2157120*(-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)^24-15052800*(-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)^9+244823040*(-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)^10-703180800*(-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)
^11+356213760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^28*exp(2)^12+24671162880*(-
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)^13+86760331200*(-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)^14+156031755840*(-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)^15+179601334080*(-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)^16+143898726720*(-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)^17+83822178720*(-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)^18+36217732320*(-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)^19+116335800
00*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^12*exp(2)^20+2756628000*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^10*exp(2)^21+457195200*(-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)^22+41522880*(-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)^23+161280*(-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)^24-161280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(2)^26-725760*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^34*exp(2)^9+572160*(-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)^10+247751040*(-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)^11-437657088*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^
28*exp(2)^12+36265509120*(-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)^13+195
160422720*(-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)^14+459549124440*(-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)^15+643651208760*(-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)^16+604084895904*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^10*exp(1)^18*exp(2)^17+402507858480*(-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)^18+194842193700*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*
exp(1)^14*exp(2)^19+68562698820*(-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
)^20+17432262120*(-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)^21+3197425560
*(-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)^22+411848640*(-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)^23+31711680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^17*exp(1)^4*exp(2)^24+806400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^18*exp(2)^26-2741760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^32*exp(2)^10+7347
4560*(-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)^11-385388160*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^28*exp(2)^12+862863360*(-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)^13+21675620160*(-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)^14+79226477760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*e
xp(1)^22*exp(2)^15+148387918560*(-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)
^16+174258416640*(-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)^17+13978684440
0*(-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)^18+80002777680*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^14*exp(2)^19+33107004000*(-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)^20+9782892000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^13*exp(1)^10*exp(2)^21+1957536000*(-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)^22+219959040*(-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)
^23+4032000*(-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)^24-1128960*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(2)^26+475200*(-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)^11+70175040*(-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)^12-274782960*(-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)^13+23551000704*(-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)^14+143622197
880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^15+357091177800*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^16+510820922220*(-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)^17+478585375800*(-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)^18+310291370298*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^10*exp(1)^14*exp(2)^19+141983838990*(-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)^20+46149466440*(-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)^21+10
704641640*(-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)^22+1738410240*(-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)^23+174585600*(-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)^24+7257600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^16*exp(2)^26+13936640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^28*e
xp(2)^12-128029440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^26*exp(2)^13+517811520
*(-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)^14+13026980544*(-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)^15+52302367680*(-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)^16+102041876160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^7*exp(1)^18*exp(2)^17+120149885520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8
*exp(1)^16*exp(2)^18+94033280880*(-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
)^19+50876119728*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^12*exp(2)^20+1897081704
0*(-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)^21+4651879680*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^8*exp(2)^22+647082240*(-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)^23+24729600*(-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)^24-8064*exp(1)^30*exp(2)^11-3225600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^15*exp(2)^26+11471680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^26*ex
p(2)^13-90493920*(-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)^14+10401732360
*(-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)^15+76918626504*(-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)^16+203376842880*(-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)^17+295411003440*(-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)^18+271007541210*(-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)^19+165831454530*(-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)^20+69454965636*(-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)^21+20254057
740*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^8*exp(2)^22+4085679360*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^6*exp(2)^23+516337920*(-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)^24-31360*exp(1)^28*exp(2)^12+29030400*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(2)^26-26490560*(-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)^14+184770240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^2
2*exp(2)^15+5513823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^16+25493
550912*(-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)^17+51721682400*(-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)^18+60273363360*(-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)^19+44878066800*(-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)^20+21879955440*(-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)^21+6761591424*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*ex
p(2)^22+1180448640*(-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)^23+73758720*
(-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)^24+3088*exp(1)^26*exp(2)^13-451
5840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(2)^26-14112520*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^22*exp(2)^15+3103252200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^16+30052895160*(-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)^17+86099072352*(-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)^18+126610305060*(-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)^19+11115
7085340*(-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)^20+62345645460*(-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)^21+23324927220*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^22+5904517248*(-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)^23+935786880*(-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)^24+159808*exp(1)^24*exp(2)^14+67737600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^12*exp(2)^26+42150720*(-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)^1
6+1591686720*(-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)^17+9211270560*(-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)^18+19524015840*(-1/2*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^19+22238250720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^20+15162930720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^7*exp(1)^10*exp(2)^21+6188434560*(-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)^22+1393580160*(-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)^23+128701
440*(-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)^24+144200*exp(1)^22*exp(2)^
15-2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^26+597529920*(-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)^17+8373516720*(-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)^18+27284576580*(-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)^19+40282077636*(-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)^20+32887950120*(-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)^21
[phone]*(-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)^22+5416494720*(-1/2
*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^23+1096341120*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^24-301200*exp(1)^20*exp(2)^16+101606400*(-1/2*(-2*d*exp
(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^26+297686440*(-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)^18+2453117880*(-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)^19+5481548640*(-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)^20+5973274080*(-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)^21+3501492480*
(-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)^22+1068936960*(-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)^23+140743680*(-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)^24-340206*exp(1)^18*exp(2)^17+2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x
^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^26+1580153255*(-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)^19+6442776045*(-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)^20+9327311880*(-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)^21+6931281000
*(-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)^22+3110795520*(-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)^23+838414080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^24+335800*exp(1)^16*exp(2)^18+101606400*(-1/2*(-2*d*exp(1)-2*sqrt(d^
2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^26+457911560*(-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)^20+1122424920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*e
xp(2)^21+1130292480*(-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)^22+515477760
*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^23+97843200*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^24+3874823*exp(1)^14*exp(2)^19+4515840*(-1/2*(-2*d*
exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^26+1093846150*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^21+1514988930*(-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)^22+1043723520*(-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)^23+406022400*(-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)^24+1823528*exp(
1)^12*exp(2)^20+67737600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^26+164998080*(-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)^22+142336320*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^23+41932800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^24+9127486*exp(1)^10*exp(2)^21+3225600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^5*exp(2)^26+169579200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*e
xp(1)^6*exp(2)^23+113440320*(-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)^24+2
591424*exp(1)^8*exp(2)^22+29030400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^26+100
53120*(-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)^24+6541248*exp(1)^6*exp(2)
^23+1128960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^26+1021440*exp(1)^4*exp(2)^24
+7257600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^26+806400*exp(2)^26-4128768*(-1/
2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^50*exp(2)-80640*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))*exp(2)^26/x/exp(2)-6985440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^24/x/ex
p(2)-8611680*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^23/x/exp(2)-60386655*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^22/x/exp(2)-25973460*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*e
xp(1)^10*exp(2)^21/x/exp(2)-179921675/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^20/x/exp(
2)-16918580*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^19/x/exp(2)-34297910*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^18/x/exp(2)-2531440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*e
xp(1)^18*exp(2)^17/x/exp(2)+841740*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^16/x/exp(2)+15
60480*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^15/x/exp(2)-635600*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^14/x/exp(2)-791680*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^26*
exp(2)^13/x/exp(2)-30880*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^28*exp(2)^12/x/exp(2)+152320*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^30*exp(2)^11/x/exp(2)+40320*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))*exp(1)^32*exp(2)^10/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))^10/(-40320*d^3*exp(1)^33+806400*d^3*exp(1)^27*exp(2)^3+806
400*d^3*exp(1)^25*exp(2)^4-1451520*d^3*exp(1)^23*exp(2)^5-2580480*d^3*exp(1)^21*exp(2)^6+806400*d^3*exp(1)^19*
exp(2)^7+3628800*d^3*exp(1)^17*exp(2)^8+806400*d^3*exp(1)^15*exp(2)^9-2580480*d^3*exp(1)^13*exp(2)^10-1451520*
d^3*exp(1)^11*exp(2)^11+806400*d^3*exp(1)^9*exp(2)^12+806400*d^3*exp(1)^7*exp(2)^13-161280*d^3*exp(1)^31*exp(2
)-201600*d^3*exp(1)*exp(2)^16)+1/2*(-128*exp(1)^20*exp(2)^7-128*exp(1)^18*exp(2)^8-5216*exp(1)^16*exp(2)^9-324
0*exp(1)^14*exp(2)^10-24727*exp(1)^12*exp(2)^11-8840*exp(1)^10*exp(2)^12-26790*exp(1)^8*exp(2)^13-5056*exp(1)^
6*exp(2)^14-6848*exp(1)^4*exp(2)^15-768*exp(2)^17)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+ex
p(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(64*d^3*exp(1)^33-1280*d^3*exp(1)^27*exp(2)^3-1280*d^
3*exp(1)^25*exp(2)^4+2304*d^3*exp(1)^23*exp(2)^5+4096*d^3*exp(1)^21*exp(2)^6-1280*d^3*exp(1)^19*exp(2)^7-5760*
d^3*exp(1)^17*exp(2)^8-1280*d^3*exp(1)^15*exp(2)^9+4096*d^3*exp(1)^13*exp(2)^10+2304*d^3*exp(1)^11*exp(2)^11-1
280*d^3*exp(1)^9*exp(2)^12-1280*d^3*exp(1)^7*exp(2)^13+256*d^3*exp(1)^31*exp(2)+320*d^3*exp(1)*exp(2)^16)

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maple [A]  time = 0.04, size = 55, normalized size = 0.55 \[ -\frac {\left (-e x +d \right ) \left (2 e^{2} x^{2}+22 d e x +119 d^{2}\right ) \left (-e^{2} x^{2}+d^{2}\right )^{\frac {7}{2}}}{1287 \left (e x +d \right )^{10} d^{3} e} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x)

[Out]

-1/1287*(-e*x+d)*(2*e^2*x^2+22*d*e*x+119*d^2)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^10/d^3/e

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maxima [B]  time = 1.63, size = 790, normalized size = 7.90 \[ -\frac {{\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {7}{2}}}{3 \, {\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 {5}{2}} d}{12 \, {\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 \, {\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {3}{2}} d^{2}}{12 \, {\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^{3}}{26 \, {\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^{2}}{572 \, {\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 {35 \, \sqrt {-e^{2} x^{2} + d^{2}} d}{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 {5 \, \sqrt {-e^{2} x^{2} + d^{2}}}{1287 \, {\left (e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right )}} - \frac {\sqrt {-e^{2} x^{2} + d^{2}}}{429 \, {\left (d e^{4} x^{3} + 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x + d^{4} e\right )}} - \frac {2 \, \sqrt {-e^{2} x^{2} + d^{2}}}{1287 \, {\left (d^{2} e^{3} x^{2} + 2 \, d^{3} e^{2} x + d^{4} e\right )}} - \frac {2 \, \sqrt {-e^{2} x^{2} + d^{2}}}{1287 \, {\left (d^{3} e^{2} x + d^{4} e\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x, algorithm="maxima")

[Out]

-1/3*(-e^2*x^2 + d^2)^(7/2)/(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) + 7/12*(-e^2*x^2
+ d^2)^(5/2)*d/(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) - 7/12*(-e^2*x^2 + d^2)^(3/2)*d^2/(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
) + 7/26*sqrt(-e^2*x^2 + d^2)*d^3/(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) - 7/572*sqrt(-e^2*x^2 + d^2)*d^2/(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) - 35/5148*sqrt(-e^2*x^2 + d^2)*d/(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) - 5/1287*sqrt(-e^2*x^2 + d^2)/(e^5*x^4 + 4*d*e^4*
x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e) - 1/429*sqrt(-e^2*x^2 + d^2)/(d*e^4*x^3 + 3*d^2*e^3*x^2 + 3*d^3*e^2
*x + d^4*e) - 2/1287*sqrt(-e^2*x^2 + d^2)/(d^2*e^3*x^2 + 2*d^3*e^2*x + d^4*e) - 2/1287*sqrt(-e^2*x^2 + d^2)/(d
^3*e^2*x + d^4*e)

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mupad [B]  time = 2.53, size = 199, normalized size = 1.99 \[ \frac {424\,\sqrt {d^2-e^2\,x^2}}{1287\,e\,{\left (d+e\,x\right )}^4}-\frac {1832\,d\,\sqrt {d^2-e^2\,x^2}}{1287\,e\,{\left (d+e\,x\right )}^5}-\frac {\sqrt {d^2-e^2\,x^2}}{429\,d\,e\,{\left (d+e\,x\right )}^3}-\frac {2\,\sqrt {d^2-e^2\,x^2}}{1287\,d^2\,e\,{\left (d+e\,x\right )}^2}-\frac {2\,\sqrt {d^2-e^2\,x^2}}{1287\,d^3\,e\,\left (d+e\,x\right )}+\frac {320\,d^2\,\sqrt {d^2-e^2\,x^2}}{143\,e\,{\left (d+e\,x\right )}^6}-\frac {16\,d^3\,\sqrt {d^2-e^2\,x^2}}{13\,e\,{\left (d+e\,x\right )}^7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^11,x)

[Out]

(424*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^4) - (1832*d*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^5) - (d^2
- e^2*x^2)^(1/2)/(429*d*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(1/2))/(1287*d^2*e*(d + e*x)^2) - (2*(d^2 - e^2*x^
2)^(1/2))/(1287*d^3*e*(d + e*x)) + (320*d^2*(d^2 - e^2*x^2)^(1/2))/(143*e*(d + e*x)^6) - (16*d^3*(d^2 - e^2*x^
2)^(1/2))/(13*e*(d + e*x)^7)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**11,x)

[Out]

Timed out

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