3.815 \(\int \frac {(d^2-e^2 x^2)^{7/2}}{(d+e x)^{13}} \, dx\)
Optimal. Leaf size=166 \[ -\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{109395 d^5 e (d+e x)^9}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{12155 d^4 e (d+e x)^{10}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{1105 d^3 e (d+e x)^{11}} \]
[Out]
-1/17*(-e^2*x^2+d^2)^(9/2)/d/e/(e*x+d)^13-4/255*(-e^2*x^2+d^2)^(9/2)/d^2/e/(e*x+d)^12-4/1105*(-e^2*x^2+d^2)^(9
/2)/d^3/e/(e*x+d)^11-8/12155*(-e^2*x^2+d^2)^(9/2)/d^4/e/(e*x+d)^10-8/109395*(-e^2*x^2+d^2)^(9/2)/d^5/e/(e*x+d)
^9
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Rubi [A] time = 0.08, antiderivative size = 166, normalized size of antiderivative = 1.00,
number of steps used = 5, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used =
{659, 651} \[ -\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{109395 d^5 e (d+e x)^9}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{12155 d^4 e (d+e x)^{10}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{1105 d^3 e (d+e x)^{11}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}} \]
Antiderivative was successfully verified.
[In]
Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^13,x]
[Out]
-(d^2 - e^2*x^2)^(9/2)/(17*d*e*(d + e*x)^13) - (4*(d^2 - e^2*x^2)^(9/2))/(255*d^2*e*(d + e*x)^12) - (4*(d^2 -
e^2*x^2)^(9/2))/(1105*d^3*e*(d + e*x)^11) - (8*(d^2 - e^2*x^2)^(9/2))/(12155*d^4*e*(d + e*x)^10) - (8*(d^2 - e
^2*x^2)^(9/2))/(109395*d^5*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)^{13}} \, dx &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}+\frac {4 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{12}} \, dx}{17 d}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}+\frac {4 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{11}} \, dx}{85 d^2}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{1105 d^3 e (d+e x)^{11}}+\frac {8 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^{10}} \, dx}{1105 d^3}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{1105 d^3 e (d+e x)^{11}}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{12155 d^4 e (d+e x)^{10}}+\frac {8 \int \frac {\left (d^2-e^2 x^2\right )^{7/2}}{(d+e x)^9} \, dx}{12155 d^4}\\ &=-\frac {\left (d^2-e^2 x^2\right )^{9/2}}{17 d e (d+e x)^{13}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac {4 \left (d^2-e^2 x^2\right )^{9/2}}{1105 d^3 e (d+e x)^{11}}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{12155 d^4 e (d+e x)^{10}}-\frac {8 \left (d^2-e^2 x^2\right )^{9/2}}{109395 d^5 e (d+e x)^9}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 82, normalized size = 0.49 \[ -\frac {(d-e x)^4 \sqrt {d^2-e^2 x^2} \left (8627 d^4+2756 d^3 e x+660 d^2 e^2 x^2+104 d e^3 x^3+8 e^4 x^4\right )}{109395 d^5 e (d+e x)^9} \]
Antiderivative was successfully verified.
[In]
Integrate[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^13,x]
[Out]
-1/109395*((d - e*x)^4*Sqrt[d^2 - e^2*x^2]*(8627*d^4 + 2756*d^3*e*x + 660*d^2*e^2*x^2 + 104*d*e^3*x^3 + 8*e^4*
x^4))/(d^5*e*(d + e*x)^9)
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fricas [B] time = 2.42, size = 302, normalized size = 1.82 \[ -\frac {8627 \, e^{9} x^{9} + 77643 \, d e^{8} x^{8} + 310572 \, d^{2} e^{7} x^{7} + 724668 \, d^{3} e^{6} x^{6} + 1087002 \, d^{4} e^{5} x^{5} + 1087002 \, d^{5} e^{4} x^{4} + 724668 \, d^{6} e^{3} x^{3} + 310572 \, d^{7} e^{2} x^{2} + 77643 \, d^{8} e x + 8627 \, d^{9} + {\left (8 \, e^{8} x^{8} + 72 \, d e^{7} x^{7} + 292 \, d^{2} e^{6} x^{6} + 708 \, d^{3} e^{5} x^{5} + 1155 \, d^{4} e^{4} x^{4} - 20508 \, d^{5} e^{3} x^{3} + 41398 \, d^{6} e^{2} x^{2} - 31752 \, d^{7} e x + 8627 \, d^{8}\right )} \sqrt {-e^{2} x^{2} + d^{2}}}{109395 \, {\left (d^{5} e^{10} x^{9} + 9 \, d^{6} e^{9} x^{8} + 36 \, d^{7} e^{8} x^{7} + 84 \, d^{8} e^{7} x^{6} + 126 \, d^{9} e^{6} x^{5} + 126 \, d^{10} e^{5} x^{4} + 84 \, d^{11} e^{4} x^{3} + 36 \, d^{12} e^{3} x^{2} + 9 \, d^{13} e^{2} x + d^{14} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^13,x, algorithm="fricas")
[Out]
-1/109395*(8627*e^9*x^9 + 77643*d*e^8*x^8 + 310572*d^2*e^7*x^7 + 724668*d^3*e^6*x^6 + 1087002*d^4*e^5*x^5 + 10
87002*d^5*e^4*x^4 + 724668*d^6*e^3*x^3 + 310572*d^7*e^2*x^2 + 77643*d^8*e*x + 8627*d^9 + (8*e^8*x^8 + 72*d*e^7
*x^7 + 292*d^2*e^6*x^6 + 708*d^3*e^5*x^5 + 1155*d^4*e^4*x^4 - 20508*d^5*e^3*x^3 + 41398*d^6*e^2*x^2 - 31752*d^
7*e*x + 8627*d^8)*sqrt(-e^2*x^2 + d^2))/(d^5*e^10*x^9 + 9*d^6*e^9*x^8 + 36*d^7*e^8*x^7 + 84*d^8*e^7*x^6 + 126*
d^9*e^6*x^5 + 126*d^10*e^5*x^4 + 84*d^11*e^4*x^3 + 36*d^12*e^3*x^2 + 9*d^13*e^2*x + d^14*e)
________________________________________________________________________________________
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)^13,x, algorithm="giac")
[Out]
Exception raised: NotImplementedError >> Unable to parse Giac output: (3633315840*(-1/2*(-2*d*exp(1)-2*sqrt(d^
2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^60*exp(2)^2+9991618560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^14*exp(1)^58*exp(2)^3+16652697600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^1
5*exp(1)^56*exp(2)^4+18734284800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^54*exp(
2)^5+14987427840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^52*exp(2)^6+8742666240*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^50*exp(2)^7+3746856960*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^48*exp(2)^8+1170892800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^20*exp(1)^46*exp(2)^9+260198400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/
exp(2))^21*exp(1)^44*exp(2)^10+39029760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^
42*exp(2)^11+3548160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^40*exp(2)^12+237817
0368*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^60*exp(2)^2+14269022208*(-1/2*(-2*d
*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^58*exp(2)^3+39239811072*(-1/2*(-2*d*exp(1)-2*sqrt(d
^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^56*exp(2)^4+65399685120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^15*exp(1)^54*exp(2)^5+73574645760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^16*exp(1)^52*exp(2)^6+58859716608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^50*ex
p(2)^7+34334834688*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^48*exp(2)^8+147149291
52*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^46*exp(2)^9+4598415360*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^44*exp(2)^10+1021870080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-
x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^42*exp(2)^11+156119040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^22*exp(1)^40*exp(2)^12+14192640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*ex
p(1)^38*exp(2)^13+3633315840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^60*exp(2)^2
+18612486144*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^58*exp(2)^3+41733586944*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^56*exp(2)^4+52319748096*(-1/2*(-2*d*exp(1)-
2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^54*exp(2)^5+37241487360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^15*exp(1)^52*exp(2)^6+10048389120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^16*exp(1)^50*exp(2)^7-7698087936*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1
)^48*exp(2)^8-10423074816*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^46*exp(2)^9-61
39736064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^44*exp(2)^10-2281466880*(-1/2*(
-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^42*exp(2)^11-554695680*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^40*exp(2)^12-78059520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^22*exp(1)^38*exp(2)^13-7096320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2
3*exp(1)^36*exp(2)^14+14269022208*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^58*exp
(2)^3+61669376000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^56*exp(2)^4+9533757849
6*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^54*exp(2)^5+16929521664*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^52*exp(2)^6-167983185920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^50*exp(2)^7-314057981952*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^16*exp(1)^48*exp(2)^8-313049088000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))
^17*exp(1)^46*exp(2)^9-205834911744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^44*e
xp(2)^10-94784126976*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^42*exp(2)^11-310109
18400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^40*exp(2)^12-7082127360*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^38*exp(2)^13-1092833280*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^36*exp(2)^14-99348480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^23*exp(1)^34*exp(2)^15+9991618560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
10*exp(1)^58*exp(2)^3+41733586944*(-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)^4+56838160384*(-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)^5-2520927436
8*(-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)^6-208981082112*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^50*exp(2)^7-375097507840*(-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)^8-405739800576*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^16*exp(1)^46*exp(2)^9-305830305792*(-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)^10-168604068864*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^42
*exp(2)^11-68999648256*(-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)^12-2066
4483840*(-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)^13-4496701440*(-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)^14-741565440*(-1/2*(-2*d*exp(1)-2*sqrt
(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^34*exp(2)^15-67415040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^23*exp(1)^32*exp(2)^16+39239811072*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2)
)^10*exp(1)^56*exp(2)^4+95337578496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^54*e
xp(2)^5-64430014464*(-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)^6-50508673
8432*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^50*exp(2)^7-759051583488*(-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)^8-427598020608*(-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)^9+184408621056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^16*exp(1)^44*exp(2)^10+518029737984*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^17*exp(1)^42*exp(2)^11+451412054016*(-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)^12+237763620864*(-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)^13
+84063006720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^36*exp(2)^14+20016353280*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^34*exp(2)^15+3122380800*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^32*exp(2)^16+283852800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^23*exp(1)^30*exp(2)^17+16652697600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/
x/exp(2))^9*exp(1)^56*exp(2)^4+52319748096*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(
1)^54*exp(2)^5-25209274368*(-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)^6-3
61201188864*(-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)^7-704339558400*(-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)^8-531226460160*(-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)^9+196595367936*(-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)^10+872819076096*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^16*exp(1)^42*exp(2)^11+1001742584832*(-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)^12+692720523264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^38*e
xp(2)^13+326400915456*(-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)^14+10734
2484480*(-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)^15+24760243200*(-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)^16+4059095040*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^30*exp(2)^17+369008640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^23*exp(1)^28*exp(2)^18+65399685120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^9*exp(1)^54*exp(2)^5+16929521664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^52
*exp(2)^6-505086738432*(-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)^7-89238
4968704*(-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)^8-40948727808*(-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)^9+1490656493568*(-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)^10+1992671166464*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^15*exp(1)^42*exp(2)^11+1138841358336*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1)
)/x/exp(2))^16*exp(1)^40*exp(2)^12+98531389440*(-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)^13-314748284928*(-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)^14-254982131712*(-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)^15-10792083
4560*(-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)^16-27798650880*(-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)^17-4371333120*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^28*exp(2)^18-397393920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^23*exp(1)^26*exp(2)^19+18734284800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2)
)^8*exp(1)^54*exp(2)^5+37241487360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^52*exp
(2)^6-208981082112*(-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)^7-704339558
400*(-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)^8-421015711744*(-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)^9+1208840871936*(-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)^10+2620233775104*(-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)^11+2064517801984*(-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)^12+203609032704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*ex
p(1)^38*exp(2)^13-1070521030656*(-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
)^14-1130175771648*(-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)^15-63529875
7632*(-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)^16-229467490560*(-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)^17-55823792640*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^28*exp(2)^18-9319685760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^22*exp(1)^26*exp(2)^19-845792640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^23*exp(1)^24*exp(2)^20+73574645760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^52*
exp(2)^6-167983185920*(-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)^7-7590515
83488*(-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)^8-40948727808*(-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)^9+2227965165568*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^44*exp(2)^10+2944095485952*(-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)^11+641259429888*(-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)^12-1951491874816*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*e
xp(1)^38*exp(2)^13-2381984022528*(-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)^14-1330047848448*(-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)^15-3802861
11744*(-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)^16-7201345536*(-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)^17+39577950720*(-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)^18+14224573440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2)
)*exp(1))/x/exp(2))^21*exp(1)^26*exp(2)^19+2165264640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(
2))^22*exp(1)^24*exp(2)^20+197809920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^22*
exp(2)^21+14987427840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^52*exp(2)^6+1004838
9120*(-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)^7-375097507840*(-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)^8-529409802240*(-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)^9+1163424423936*(-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)^10+2767599859712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^12*exp(1)^42*exp(2)^11-458699667456*(-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)^12-7444893333504*(-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)^1
3-11230681155584*(-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)^14-8901935716
608*(-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)^15-4195292884992*(-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)^16-1026059451648*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^30*exp(2)^17+44636030208*(-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)^18+129406828320*(-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)^19+48542450880*(-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)^20+10051105680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^22*exp(2)^2
1+1007178480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^20*exp(2)^22+58859716608*(-
1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^50*exp(2)^7-314057981952*(-1/2*(-2*d*exp(1)
-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^48*exp(2)^8-427598020608*(-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)^9+1491110658048*(-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)^10+2919116439552*(-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)^11-291794620416*(-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)^12-5580818153472*(-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)^13-722965
5595008*(-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)^14-4845058639872*(-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)^15-1950845301504*(-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)^16-440589118464*(-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)^17-12483432192*(-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)^18+14084243712*(-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)^19-1619845920*(-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
)^20+1055947200*(-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)^21+1233151920*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^20*exp(2)^22+157283280*(-1/2*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^18*exp(2)^23+8742666240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2
*exp(2))*exp(1))/x/exp(2))^6*exp(1)^50*exp(2)^7-7698087936*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^7*exp(1)^48*exp(2)^8-405512718336*(-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)^9+199017578496*(-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)^10+2
419947239424*(-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)^11-1611369117696*
(-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)^12-20394493680384*(-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)^13-47009805421056*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^36*exp(2)^14-64693756854144*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^14*exp(1)^34*exp(2)^15-64361042858112*(-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)^16-49319747067888*(-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)^17-29401482432960*(-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)^18-13493361017136*(-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)^19-4
677949395504*(-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)^20-1186377004890*
(-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)^21-210244589940*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^20*exp(2)^22-24443166825*(-1/2*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^18*exp(2)^23-1503335295*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp
(1))/x/exp(2))^23*exp(1)^16*exp(2)^24+34334834688*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
6*exp(1)^48*exp(2)^8-313049088000*(-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)^9+183954456576*(-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)^10+1994639212
544*(-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)^11+530159443968*(-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)^12-6120649408512*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^38*exp(2)^13-13026315630592*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^12*exp(1)^36*exp(2)^14-17400920672256*(-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)^15-20485439698944*(-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)^16-21234005467136*(-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)^17-17570909169792*(-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)^18-1
1064357824256*(-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)^19-5205933976320
*(-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)^20-1783723233600*(-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)^21-434180411280*(-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)^22-75880007280*(-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)^23-9429734160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2
))^22*exp(1)^16*exp(2)^24-617324400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^14*e
xp(2)^25+3746856960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^48*exp(2)^8-104230748
16*(-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)^9-305648640000*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^44*exp(2)^10+871638248448*(-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)^11+1683897690112*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*
exp(1))/x/exp(2))^9*exp(1)^40*exp(2)^12-12304353921024*(-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)^13-59479387961856*(-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)^14-143593018481792*(-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
)^15-237166603158144*(-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)^16-286346
882190336*(-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)^17-257675282795392*(
-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)^18-174746407249656*(-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)^19-89907648331248*(-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)^20-35015057689920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^18*exp(1)^22*exp(2)^21-10170718214580*(-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)^22-2137994601435*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2
0*exp(1)^18*exp(2)^23-306624175935*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^16*ex
p(2)^24-26272821960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^14*exp(2)^25-9497703
60*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^12*exp(2)^26+14714929152*(-1/2*(-2*d*
exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^46*exp(2)^9-205986299904*(-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)^10+517938905088*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^7*exp(1)^42*exp(2)^11+1145449451520*(-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)^12-2187585495040*(-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)^13-9427840063488*(-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)^14-22
312397285376*(-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)^15-47217734952960
*(-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)^16-77845733763072*(-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)^17-92532900100608*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^28*exp(2)^18-79715941544448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^15*exp(1)^26*exp(2)^19-50769328151520*(-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)^20-24177974958720*(-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)^21-8635298345520*(-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)^22-2309573463120*(-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)^23-45
0855100080*(-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)^24-57446133360*(-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)^25-3462338880*(-1/2*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^12*exp(2)^26-2439360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2
))*exp(1))/x/exp(2))^23*exp(1)^10*exp(2)^27+1170892800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp
(2))^4*exp(1)^46*exp(2)^9-6139736064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^44*e
xp(2)^10-168649485312*(-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)^11+100087
9672320*(-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)^12-242213900544*(-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)^13-21581784621056*(-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)^14-105104778286464*(-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)^15-297359872639104*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^11*exp(1)^32*exp(2)^16-554851757306880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^12*exp(1)^30*exp(2)^17-719949139396608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*ex
p(1)^28*exp(2)^18-676712915426592*(-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)^19-474916346835744*(-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)^20-2536
95557302110*(-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)^21-104235049677528
*(-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)^22-33113255533743*(-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)^23-8138326753557*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^16*exp(2)^24-1528173135720*(-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)^25-210116426520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x
/exp(2))^21*exp(1)^12*exp(2)^26-19095005160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp
(1)^10*exp(2)^27-865390680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^8*exp(2)^28+4
598415360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^44*exp(2)^10-94849007616*(-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)^11+453155450880*(-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)^12+100679749632*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*ex
p(2))*exp(1))/x/exp(2))^7*exp(1)^38*exp(2)^13-2697801689088*(-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)^14-9371338893312*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*ex
p(1)^34*exp(2)^15-35414693935104*(-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)^16-97466150234112*(-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)^17-172215
437982720*(-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)^18-206014197717504*(
-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)^19-176155173950976*(-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)^20-111609047742720*(-1/2*(-2*d*exp(1)-2*sq
rt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^22*exp(2)^21-53602292121840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^16*exp(1)^20*exp(2)^22-19833217777296*(-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)^23-5709483820656*(-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)^24-1276732561104*(-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)^25-222192653760*(-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)^26-3114
4639680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^10*exp(2)^27-3398250240*(-1/2*(-
2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^8*exp(2)^28-199584000*(-1/2*(-2*d*exp(1)-2*sqrt(
d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^6*exp(2)^29+260198400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^3*exp(1)^44*exp(2)^10-2238888960*(-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)^11-69079938048*(-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
)^12+694101805056*(-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)^13-1456643054
592*(-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)^14-22641864600960*(-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)^15-134519714862720*(-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)^16-437798084798976*(-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)^17-869257179360768*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^11*exp(1)^28*exp(2)^18-1157668056997056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^12*exp(1)^26*exp(2)^19-1102376948995872*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*e
xp(1)^24*exp(2)^20-781279704773568*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^22*ex
p(2)^21-422388448371120*(-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)^22-176
855460677973*(-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)^23-57767208761493
*(-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)^24-14655466708344*(-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)^25-2831351785416*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^12*exp(2)^26-404769186360*(-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)^27-41983538520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^21*exp(1)^8*exp(2)^28-3117945600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(1)^
6*exp(2)^29-139265280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^23*exp(1)^4*exp(2)^30+102187
0080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^42*exp(2)^11-30931845120*(-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)^12+238397829120*(-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)^13-322967513088*(-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)^14-1585892284416*(-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)^15-7846229140992*(-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)^16-45807352076288*(-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)^17-
138169690103808*(-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)^18-24565292664
4224*(-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)^19-290380698712896*(-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)^20-244918778442624*(-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)^21-153820118412576*(-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)^22-73957287206880*(-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)^23-27708477538896*(-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)^24-8138473591248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*ex
p(1)^14*exp(2)^25-1864452891840*(-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
)^26-328384203840*(-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)^27-417591820
80*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^8*exp(2)^28-2962417920*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^6*exp(2)^29-7096320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*
exp(2))*exp(1))/x/exp(2))^22*exp(1)^4*exp(2)^30+7096320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^23*exp(2)^32+39029760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^42*exp(2)^11-
545233920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^40*exp(2)^12-21041729280*(-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)^13+327531815424*(-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)^14-1379396768640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^6*exp(1)^34*exp(2)^15-16522516796544*(-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)^16-130395759794784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
8*exp(1)^30*exp(2)^17-469991643886336*(-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)^18-964853486099712*(-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)^19-1
298674924284672*(-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)^20-12379519330
06404*(-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)^21-873465310578168*(-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)^22-468320769401562*(-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)^23-193539750955782*(-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)^24-61786176611544*(-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)^25-15090138162792*(-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)^26-2777634856920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*e
xp(1)^10*exp(2)^27-380972619720*(-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)
^28-37767502080*(-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)^29-2296546560*(
-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)^30-42577920*(-1/2*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^22*exp(2)^32+150441984*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1
))/x/exp(2))^2*exp(1)^40*exp(2)^12-7057616896*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*ex
p(1)^38*exp(2)^13+83295860736*(-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)^1
4-257408735232*(-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)^15-509393426432*
(-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)^16-5795647266816*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^30*exp(2)^17-44598615747840*(-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)^18-139002975682560*(-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)^19-245733478442496*(-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)^20-286429039357824*(-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)^21-237940665140640*(-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)^22-147304999483488*(-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)^23-6
9753946645152*(-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)^24-2553196856918
4*(-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)^25-7180606762560*(-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)^26-1514111860800*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^10*exp(2)^27-224381794560*(-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)^28-19027895040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^19*exp(1)^6*exp(2)^29-219985920*(-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)^30+63866880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(2)^32-95090688*(-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)^13-4559717888*(-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)^14+108898044288*(-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)^15-749147372160*(-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)^16-8867289823744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^3
0*exp(2)^17-96562894361472*(-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)^18-3
76204584579120*(-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)^19-7918250108313
60*(-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)^20-1071332855496288*(-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)^21-1013669963609688*(-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)^22-702642515859438*(-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)^23-366219245310534*(-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)^24-145053972390096*(-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)^25-43566910985136*(-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)^26-9834460823880*(-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)^27-1651457835720*(-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)^28-1999006
73280*(-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)^29-15242008320*(-1/2*(-2*
d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^4*exp(2)^30-468357120*(-1/2*(-2*d*exp(1)-2*sqrt(d^
2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(2)^32-1060177920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^2*exp(1)^36*exp(2)^14+19805964288*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^3
4*exp(2)^15-104468103168*(-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)^16-706
77116928*(-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)^17-3502013560320*(-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)^18-32345167523328*(-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)^19-103044212365248*(-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)^20-181369264868352*(-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)^21-208717708247136*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^10*exp(1)^20*exp(2)^22-170218195586208*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*ex
p(1)^18*exp(2)^23-102664292534496*(-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)^24-46691318896992*(-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)^25-15989
027015808*(-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)^26-4022912826240*(-1
/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^10*exp(2)^27-699110818560*(-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)^28-70745875200*(-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)^29-1714944000*(-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)^30+295680*exp(1)^38*exp(2)^13+248371200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))/x/exp(2))^19*exp(2)^32-598424448*(-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)^15+24930973056*(-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)^16-26
8391646336*(-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)^17-3573415524096*(-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)^18-54398624580960*(-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)^19-228647571055200*(-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)^20-494458628877180*(-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)^21-670221322267200*(-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)^22-624014594721342*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*e
xp(1)^18*exp(2)^23-419143396142394*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^16*ex
p(2)^24-208074182157072*(-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)^25-768
58367992560*(-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)^26-21059380354320*
(-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)^27-4249031389680*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^8*exp(2)^28-614370113280*(-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)^29-56854828800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^17*exp(1)^4*exp(2)^30+1161216*exp(1)^36*exp(2)^14-2341785600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2
*exp(2))*exp(1))/x/exp(2))^18*exp(2)^32+3077511168*(-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)^16-26976536576*(-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)^17+7977463296*(-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)^18-1588233546
240*(-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)^19-17623886080768*(-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)^20-57779181351936*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^21-101839352405472*(-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)^22-115761371819808*(-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)^23-91989868446432*(-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)^24-53073485875872*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^1
4*exp(2)^25-22430709780864*(-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)^26-
6812391535488*(-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)^27-1405116421632
*(-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)^28-170400975360*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^6*exp(2)^29-6706022400*(-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)^30-669312*exp(1)^34*exp(2)^15+532224000*(-1/2*(-2*d*exp(1)-2*s
qrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(2)^32+3533837568*(-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)^17-64091822080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*ex
p(1)^28*exp(2)^18-1074761175840*(-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)
^19-23068109650080*(-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)^20-106877560
130000*(-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)^21-238881587190048*(-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)^22-323207677946538*(-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)^23-293517486250362*(-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)^24-188228652082416*(-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)^25-87053446584720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^11*exp(1)^12*exp(2)^26-29192634199344*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*ex
p(1)^10*exp(2)^27-7087591559664*(-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)
^28-1221578620416*(-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)^29-1357543756
80*(-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)^30-8208128*exp(1)^32*exp(2)^
16-7025356800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(2)^32-4503412992*(-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)^18+7190208256*(-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)^19-518408712096*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))/x/exp(2))^4*exp(1)^24*exp(2)^20-7257587422272*(-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)^21-24857634297232*(-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)^22-44232819087600*(-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)^23-49
584685528224*(-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)^24-37925955071136*
(-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)^25-20396972458368*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^12*exp(2)^26-7654129515648*(-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)^27-1909800313344*(-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)^28-280441244160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^13*exp(1)^6*exp(2)^29-15966720000*(-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)^30-5045296*exp(1)^30*exp(2)^17+638668800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^
15*exp(2)^32-9467792592*(-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)^19-2356
58721232*(-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)^20-7238676342018*(-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)^21-38604613212660*(-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)^22-89810507879213*(-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)^23-121020527994795*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^7*exp(1)^16*exp(2)^24-106229274638256*(-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)^25-63862926469584*(-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)^26-26836219278000*(-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)^2
7-7954821406224*(-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)^28-164965915699
2*(-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)^29-220739904000*(-1/2*(-2*d*e
xp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^4*exp(2)^30+23857536*exp(1)^28*exp(2)^18-14050713600*
(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(2)^32+2004697344*(-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)^20-121714469184*(-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)^21-2232864858576*(-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)^22-8234475855408*(-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)^23-14967626262864*(-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)^24-
16477258712112*(-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)^25-1190112618816
0*(-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)^26-5735798428800*(-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)^27-1782649262592*(-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)^28-322802726400*(-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)^29-25135165440*(-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)^30+28990440*exp(1)^26*exp(2)^19+298045440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))/x/exp(2))^13*exp(2)^32-36118030944*(-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)^21-1630129911828*(-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)^22-106
88804936007*(-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)^23-26219286798507*(
-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)^24-35237824942056*(-1/2*(-2*d*ex
p(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^25-29514297866328*(-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)^26-16239679750800*(-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)^27-6045926465040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/ex
p(2))^9*exp(1)^8*exp(2)^28-1538965080576*(-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)^29-251364072960*(-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)^30-34
700896*exp(1)^24*exp(2)^20-19670999040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(2)^3
2-19811414640*(-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)^22-494089953808*(
-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)^23-2096074738032*(-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)^24-3946414848816*(-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)^25-4224740886080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*e
xp(1))/x/exp(2))^6*exp(1)^12*exp(2)^26-2790725699520*(-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)^27-1131659527680*(-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)^28-260487575040*(-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)^29-271221
35040*(-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)^30-72482438*exp(1)^22*exp
(2)^21-298045440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^32-248978762403*(-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)^23-2209593363329*(-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)^24-5906045579016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^25-7931175043704*(-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)^26-6200952013960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*e
xp(1)^10*exp(2)^27-3046398256440*(-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)
^28-984513277440*(-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)^29-201462750720
*(-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)^30+17372624*exp(1)^20*exp(2)^22
-19670999040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^32-74101692336*(-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)^24-406444309392*(-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)^25-801184705728*(-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)^26-819302616000*(-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)^27-469602650880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*e
xp(2)^28-144698400000*(-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)^29-2022451
2000*(-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)^30-95443697*exp(1)^18*exp(2
)^23-638668800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^32-322694527512*(-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)^25-1015416527400*(-1/2*(-2*d*exp(1)-2*sqr
t(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^26-1350008445720*(-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)^27-960167993400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^5*exp(1)^8*exp(2)^28-417042743040*(-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)^29-111753734400*(-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)^30-7116
1872*exp(1)^16*exp(2)^24-14050713600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^32-5
7477672384*(-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)^26-121790315328*(-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)^27-116165820672*(-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)^28-52786863360*(-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)^29-10254182400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^6*exp(1)^4*exp(2)^30-1031350776*exp(1)^14*exp(2)^25-532224000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))/x/exp(2))^7*exp(2)^32-129545864184*(-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)^27-166294872744*(-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)^28-
107973524736*(-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)^29-40960846080*(-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)^30-313172288*exp(1)^12*exp(2)^26-702
5356800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^32-13563880704*(-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)^28-11400533760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*e
xp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^29-3370752000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/e
xp(2))^4*exp(1)^4*exp(2)^30-1274966440*exp(1)^10*exp(2)^27-248371200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))
*exp(1))/x/exp(2))^5*exp(2)^32-14183592192*(-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)^29-8944024320*(-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)^30-2165
98272*exp(1)^8*exp(2)^28-2341785600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^32-64
5765120*(-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)^30-505080576*exp(1)^6*ex
p(2)^29-63866880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^32-54405120*exp(1)^4*exp
(2)^30-468357120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^32-42577920*exp(2)^32+60
5552640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^62*exp(2)+3548160*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^32/x/exp(2)+441302400*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^
4*exp(2)^30/x/exp(2)+553069440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^29/x/exp(2)+5628271
572*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^28/x/exp(2)+2597959584*(-2*d*exp(1)-2*sqrt(d^2
-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^27/x/exp(2)+14824712100*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(
1)^12*exp(2)^26/x/exp(2)+3449405256*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^25/x/exp(2)+2
3249083329/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^24/x/exp(2)+932584104*(-2*d*exp(1)-2
*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^23/x/exp(2)+1648913604*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))*exp(1)^20*exp(2)^22/x/exp(2)-109566528*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^21/x/e
xp(2)+446892936*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^20/x/exp(2)+217713792*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^26*exp(2)^19/x/exp(2)-163380960*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*ex
p(1))*exp(1)^28*exp(2)^18/x/exp(2)-144364032*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^30*exp(2)^17/x
/exp(2)+26836032*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^32*exp(2)^16/x/exp(2)+48823296*(-2*d*exp(1
)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^34*exp(2)^15/x/exp(2)+4483584*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(
1))*exp(1)^36*exp(2)^14/x/exp(2)-6838272*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^38*exp(2)^13/x/exp
(2)-1774080*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^40*exp(2)^12/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sq
rt(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))^12/(177408
0*d^5*exp(1)^41-3548160*d^5*exp(1)^37*exp(2)^2-49674240*d^5*exp(1)^35*exp(2)^3-33707520*d^5*exp(1)^33*exp(2)^4
+141926400*d^5*exp(1)^31*exp(2)^5+184504320*d^5*exp(1)^29*exp(2)^6-198696960*d^5*exp(1)^27*exp(2)^7-422231040*
d^5*exp(1)^25*exp(2)^8+99348480*d^5*exp(1)^23*exp(2)^9+546416640*d^5*exp(1)^21*exp(2)^10+99348480*d^5*exp(1)^1
9*exp(2)^11-422231040*d^5*exp(1)^17*exp(2)^12-198696960*d^5*exp(1)^15*exp(2)^13+184504320*d^5*exp(1)^13*exp(2)
^14+141926400*d^5*exp(1)^11*exp(2)^15-33707520*d^5*exp(1)^9*exp(2)^16-49674240*d^5*exp(1)^7*exp(2)^17-3548160*
d^5*exp(1)^5*exp(2)^18+7096320*d^5*exp(1)^39*exp(2)+8870400*d^5*exp(1)*exp(2)^20)+1/2*(-384*exp(1)^24*exp(2)^9
-256*exp(1)^22*exp(2)^10-24720*exp(1)^20*exp(2)^11-11952*exp(1)^18*exp(2)^12-190151*exp(1)^16*exp(2)^13-63472*
exp(1)^14*exp(2)^14-380600*exp(1)^12*exp(2)^15-82624*exp(1)^10*exp(2)^16-230296*exp(1)^8*exp(2)^17-28928*exp(1
)^6*exp(2)^18-38144*exp(1)^4*exp(2)^19-3072*exp(2)^21)*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)/(256*d^5*exp(1)^41-512*d^5*exp(1)^37*exp(2)^2-716
8*d^5*exp(1)^35*exp(2)^3-4864*d^5*exp(1)^33*exp(2)^4+20480*d^5*exp(1)^31*exp(2)^5+26624*d^5*exp(1)^29*exp(2)^6
-28672*d^5*exp(1)^27*exp(2)^7-60928*d^5*exp(1)^25*exp(2)^8+14336*d^5*exp(1)^23*exp(2)^9+78848*d^5*exp(1)^21*ex
p(2)^10+14336*d^5*exp(1)^19*exp(2)^11-60928*d^5*exp(1)^17*exp(2)^12-28672*d^5*exp(1)^15*exp(2)^13+26624*d^5*ex
p(1)^13*exp(2)^14+20480*d^5*exp(1)^11*exp(2)^15-4864*d^5*exp(1)^9*exp(2)^16-7168*d^5*exp(1)^7*exp(2)^17-512*d^
5*exp(1)^5*exp(2)^18+1024*d^5*exp(1)^39*exp(2)+1280*d^5*exp(1)*exp(2)^20)
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maple [A] time = 0.05, size = 77, normalized size = 0.46 \[ -\frac {\left (-e x +d \right ) \left (8 e^{4} x^{4}+104 e^{3} x^{3} d +660 e^{2} x^{2} d^{2}+2756 x \,d^{3} e +8627 d^{4}\right ) \left (-e^{2} x^{2}+d^{2}\right )^{\frac {7}{2}}}{109395 \left (e x +d \right )^{12} d^{5} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^13,x)
[Out]
-1/109395*(-e*x+d)*(8*e^4*x^4+104*d*e^3*x^3+660*d^2*e^2*x^2+2756*d^3*e*x+8627*d^4)*(-e^2*x^2+d^2)^(7/2)/(e*x+d
)^12/d^5/e
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maxima [B] time = 1.65, size = 1085, normalized size = 6.54 \[ -\frac {{\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {7}{2}}}{5 \, {\left (e^{13} x^{12} + 12 \, d e^{12} x^{11} + 66 \, d^{2} e^{11} x^{10} + 220 \, d^{3} e^{10} x^{9} + 495 \, d^{4} e^{9} x^{8} + 792 \, d^{5} e^{8} x^{7} + 924 \, d^{6} e^{7} x^{6} + 792 \, d^{7} e^{6} x^{5} + 495 \, d^{8} e^{5} x^{4} + 220 \, d^{9} e^{4} x^{3} + 66 \, d^{10} e^{3} x^{2} + 12 \, d^{11} e^{2} x + d^{12} e\right )}} + \frac {7 \, {\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {5}{2}} d}{30 \, {\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 {{\left (-e^{2} x^{2} + d^{2}\right )}^{\frac {3}{2}} d^{2}}{6 \, {\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 {\sqrt {-e^{2} x^{2} + d^{2}} d^{3}}{17 \, {\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 {\sqrt {-e^{2} x^{2} + d^{2}} d^{2}}{510 \, {\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}{6630 \, {\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}}}{12155 \, {\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}}}{21879 \, {\left (d e^{6} x^{5} + 5 \, d^{2} e^{5} x^{4} + 10 \, d^{3} e^{4} x^{3} + 10 \, d^{4} e^{3} x^{2} + 5 \, d^{5} e^{2} x + d^{6} e\right )}} - \frac {4 \, \sqrt {-e^{2} x^{2} + d^{2}}}{21879 \, {\left (d^{2} e^{5} x^{4} + 4 \, d^{3} e^{4} x^{3} + 6 \, d^{4} e^{3} x^{2} + 4 \, d^{5} e^{2} x + d^{6} e\right )}} - \frac {4 \, \sqrt {-e^{2} x^{2} + d^{2}}}{36465 \, {\left (d^{3} e^{4} x^{3} + 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x + d^{6} e\right )}} - \frac {8 \, \sqrt {-e^{2} x^{2} + d^{2}}}{109395 \, {\left (d^{4} e^{3} x^{2} + 2 \, d^{5} e^{2} x + d^{6} e\right )}} - \frac {8 \, \sqrt {-e^{2} x^{2} + d^{2}}}{109395 \, {\left (d^{5} e^{2} x + d^{6} 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)^13,x, algorithm="maxima")
[Out]
-1/5*(-e^2*x^2 + d^2)^(7/2)/(e^13*x^12 + 12*d*e^12*x^11 + 66*d^2*e^11*x^10 + 220*d^3*e^10*x^9 + 495*d^4*e^9*x^
8 + 792*d^5*e^8*x^7 + 924*d^6*e^7*x^6 + 792*d^7*e^6*x^5 + 495*d^8*e^5*x^4 + 220*d^9*e^4*x^3 + 66*d^10*e^3*x^2
+ 12*d^11*e^2*x + d^12*e) + 7/30*(-e^2*x^2 + d^2)^(5/2)*d/(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) - 1/6*(-e^2*x^2 + d^2)^(3/2)*d^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) + 1/17*sqrt(-e^2*x^2 + d^2)*d^3/(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) - 1/510*sqrt(
-e^2*x^2 + d^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) - 7/6630*sqrt(-e^2*x^2 + d^2)*d/(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) - 7/12155*sqrt(-e^2*x^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) - 7/21879*sqrt(
-e^2*x^2 + d^2)/(d*e^6*x^5 + 5*d^2*e^5*x^4 + 10*d^3*e^4*x^3 + 10*d^4*e^3*x^2 + 5*d^5*e^2*x + d^6*e) - 4/21879*
sqrt(-e^2*x^2 + d^2)/(d^2*e^5*x^4 + 4*d^3*e^4*x^3 + 6*d^4*e^3*x^2 + 4*d^5*e^2*x + d^6*e) - 4/36465*sqrt(-e^2*x
^2 + d^2)/(d^3*e^4*x^3 + 3*d^4*e^3*x^2 + 3*d^5*e^2*x + d^6*e) - 8/109395*sqrt(-e^2*x^2 + d^2)/(d^4*e^3*x^2 + 2
*d^5*e^2*x + d^6*e) - 8/109395*sqrt(-e^2*x^2 + d^2)/(d^5*e^2*x + d^6*e)
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mupad [B] time = 3.55, size = 257, normalized size = 1.55 \[ \frac {2424\,\sqrt {d^2-e^2\,x^2}}{12155\,e\,{\left (d+e\,x\right )}^6}-\frac {3208\,d\,\sqrt {d^2-e^2\,x^2}}{3315\,e\,{\left (d+e\,x\right )}^7}-\frac {7\,\sqrt {d^2-e^2\,x^2}}{21879\,d\,e\,{\left (d+e\,x\right )}^5}-\frac {4\,\sqrt {d^2-e^2\,x^2}}{21879\,d^2\,e\,{\left (d+e\,x\right )}^4}-\frac {4\,\sqrt {d^2-e^2\,x^2}}{36465\,d^3\,e\,{\left (d+e\,x\right )}^3}-\frac {8\,\sqrt {d^2-e^2\,x^2}}{109395\,d^4\,e\,{\left (d+e\,x\right )}^2}-\frac {8\,\sqrt {d^2-e^2\,x^2}}{109395\,d^5\,e\,\left (d+e\,x\right )}+\frac {416\,d^2\,\sqrt {d^2-e^2\,x^2}}{255\,e\,{\left (d+e\,x\right )}^8}-\frac {16\,d^3\,\sqrt {d^2-e^2\,x^2}}{17\,e\,{\left (d+e\,x\right )}^9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^13,x)
[Out]
(2424*(d^2 - e^2*x^2)^(1/2))/(12155*e*(d + e*x)^6) - (3208*d*(d^2 - e^2*x^2)^(1/2))/(3315*e*(d + e*x)^7) - (7*
(d^2 - e^2*x^2)^(1/2))/(21879*d*e*(d + e*x)^5) - (4*(d^2 - e^2*x^2)^(1/2))/(21879*d^2*e*(d + e*x)^4) - (4*(d^2
- e^2*x^2)^(1/2))/(36465*d^3*e*(d + e*x)^3) - (8*(d^2 - e^2*x^2)^(1/2))/(109395*d^4*e*(d + e*x)^2) - (8*(d^2
- e^2*x^2)^(1/2))/(109395*d^5*e*(d + e*x)) + (416*d^2*(d^2 - e^2*x^2)^(1/2))/(255*e*(d + e*x)^8) - (16*d^3*(d^
2 - e^2*x^2)^(1/2))/(17*e*(d + e*x)^9)
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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)**13,x)
[Out]
Timed out
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