∫ (f+gx)(cd2−bde−be2x−ce2x2)5∕2 __________________________________________________

3.20.76 $\int \frac {(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{(d+e x)^9} \, dx$

Optimal. Leaf size=210 \[ -\frac {4 c \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-11 b e g+18 c d g+4 c e f)}{693 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac {2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-11 b e g+18 c d g+4 c e f)}{99 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac {2 (e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{11 e^2 (d+e x)^9 (2 c d-b e)} \]

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Rubi [A] time = 0.33, antiderivative size = 210, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 44, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.068, Rules used = {792, 658, 650} \begin {gather*} -\frac {4 c \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-11 b e g+18 c d g+4 c e f)}{693 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac {2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-11 b e g+18 c d g+4 c e f)}{99 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac {2 (e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{11 e^2 (d+e x)^9 (2 c d-b e)} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^9,x]

[Out]

(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(11*e^2*(2*c*d - b*e)*(d + e*x)^9) - (2*(4*c*e*f

+ 18*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(99*e^2*(2*c*d - b*e)^2*(d + e*x)^8) - (4*

c*(4*c*e*f + 18*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(693*e^2*(2*c*d - b*e)^3*(d + e

*x)^7)

Rule 650

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[(e*(d + e*x)^m*(a +

b*x + c*x^2)^(p + 1))/((p + 1)*(2*c*d - b*e)), x] /; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c, 0] &&

EqQ[c*d^2 - b*d*e + a*e^2, 0] && !IntegerQ[p] && EqQ[m + 2*p + 2, 0]

Rule 658

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> -Simp[(e*(d + e*x)^m*(a +

b*x + c*x^2)^(p + 1))/((m + p + 1)*(2*c*d - b*e)), x] + Dist[(c*Simplify[m + 2*p + 2])/((m + p + 1)*(2*c*d -

b*e)), Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c

, 0] && EqQ[c*d^2 - b*d*e + a*e^2, 0] && !IntegerQ[p] && ILtQ[Simplify[m + 2*p + 2], 0]

Rule 792

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp

[((d*g - e*f)*(d + e*x)^m*(a + b*x + c*x^2)^(p + 1))/((2*c*d - b*e)*(m + p + 1)), x] + Dist[(m*(g*(c*d - b*e)

+ c*e*f) + e*(p + 1)*(2*c*f - b*g))/(e*(2*c*d - b*e)*(m + p + 1)), Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p,

x], x] /; FreeQ[{a, b, c, d, e, f, g, m, p}, x] && NeQ[b^2 - 4*a*c, 0] && EqQ[c*d^2 - b*d*e + a*e^2, 0] && ((L

tQ[m, -1] && !IGtQ[m + p + 1, 0]) || (LtQ[m, 0] && LtQ[p, -1]) || EqQ[m + 2*p + 2, 0]) && NeQ[m + p + 1, 0]

Rubi steps

\begin {align*} \int \frac {(f+g x) \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^9} \, dx &=-\frac {2 (e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{11 e^2 (2 c d-b e) (d+e x)^9}+\frac {(4 c e f+18 c d g-11 b e g) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^8} \, dx}{11 e (2 c d-b e)}\\ &=-\frac {2 (e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{11 e^2 (2 c d-b e) (d+e x)^9}-\frac {2 (4 c e f+18 c d g-11 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{99 e^2 (2 c d-b e)^2 (d+e x)^8}+\frac {(2 c (4 c e f+18 c d g-11 b e g)) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^7} \, dx}{99 e (2 c d-b e)^2}\\ &=-\frac {2 (e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{11 e^2 (2 c d-b e) (d+e x)^9}-\frac {2 (4 c e f+18 c d g-11 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{99 e^2 (2 c d-b e)^2 (d+e x)^8}-\frac {4 c (4 c e f+18 c d g-11 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{693 e^2 (2 c d-b e)^3 (d+e x)^7}\\ \end {align*}

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Mathematica [A] time = 0.15, size = 169, normalized size = 0.80 \begin {gather*} -\frac {2 (b e-c d+c e x)^3 \sqrt {(d+e x) (c (d-e x)-b e)} \left (7 b^2 e^2 (2 d g+9 e f+11 e g x)-2 b c e \left (25 d^2 g+2 d e (70 f+81 g x)+e^2 x (14 f+11 g x)\right )+4 c^2 \left (9 d^3 g+d^2 e (79 f+81 g x)+9 d e^2 x (2 f+g x)+2 e^3 f x^2\right )\right )}{693 e^2 (d+e x)^6 (b e-2 c d)^3} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^9,x]

[Out]

(-2*(-(c*d) + b*e + c*e*x)^3*Sqrt[(d + e*x)*(-(b*e) + c*(d - e*x))]*(7*b^2*e^2*(9*e*f + 2*d*g + 11*e*g*x) - 2*

b*c*e*(25*d^2*g + e^2*x*(14*f + 11*g*x) + 2*d*e*(70*f + 81*g*x)) + 4*c^2*(9*d^3*g + 2*e^3*f*x^2 + 9*d*e^2*x*(2

*f + g*x) + d^2*e*(79*f + 81*g*x))))/(693*e^2*(-2*c*d + b*e)^3*(d + e*x)^6)

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IntegrateAlgebraic [F] time = 180.07, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

IntegrateAlgebraic[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^9,x]

[Out]

$Aborted

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^9,x, algorithm="fricas")

[Out]

Timed out

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^9,x, algorithm="giac")

[Out]

Timed out

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maple [A] time = 0.05, size = 236, normalized size = 1.12 \begin {gather*} -\frac {2 \left (c e x +b e -c d \right ) \left (-22 b c \,e^{3} g \,x^{2}+36 c^{2} d \,e^{2} g \,x^{2}+8 c^{2} e^{3} f \,x^{2}+77 b^{2} e^{3} g x -324 b c d \,e^{2} g x -28 b c \,e^{3} f x +324 c^{2} d^{2} e g x +72 c^{2} d \,e^{2} f x +14 b^{2} d \,e^{2} g +63 b^{2} e^{3} f -50 b c \,d^{2} e g -280 b c d \,e^{2} f +36 c^{2} d^{3} g +316 c^{2} d^{2} e f \right ) \left (-c \,e^{2} x^{2}-b \,e^{2} x -b d e +c \,d^{2}\right )^{\frac {5}{2}}}{693 \left (e x +d \right )^{8} \left (b^{3} e^{3}-6 b^{2} c d \,e^{2}+12 b \,c^{2} d^{2} e -8 c^{3} d^{3}\right ) e^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^9,x)

[Out]

-2/693*(c*e*x+b*e-c*d)*(-22*b*c*e^3*g*x^2+36*c^2*d*e^2*g*x^2+8*c^2*e^3*f*x^2+77*b^2*e^3*g*x-324*b*c*d*e^2*g*x-

28*b*c*e^3*f*x+324*c^2*d^2*e*g*x+72*c^2*d*e^2*f*x+14*b^2*d*e^2*g+63*b^2*e^3*f-50*b*c*d^2*e*g-280*b*c*d*e^2*f+3

6*c^2*d^3*g+316*c^2*d^2*e*f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^8/(b^3*e^3-6*b^2*c*d*e^2+12*b*c^2*

d^2*e-8*c^3*d^3)/e^2

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^9,x, algorithm="maxima")

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a

ssume' command before evaluation *may* help (example of legal syntax is 'assume(b*e-2*c*d>0)', see `assume?` f

or more details)Is b*e-2*c*d zero or nonzero?

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mupad [B] time = 53.40, size = 25236, normalized size = 120.17

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((f + g*x)*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(5/2))/(d + e*x)^9,x)

[Out]

(((d*((1632*b^2*c^6*e^3*f - 16704*c^8*d^3*g + 2784*b^3*c^5*e^3*g + 4672*c^8*d^2*e*f - 5504*b*c^7*d*e^2*f + 273

92*b*c^7*d^2*e*g - 15072*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(51*b^2*e^2*g + 146*c^2*d^2*

g + 16*b*c*e^2*f - 26*c^2*d*e*f - 172*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(8*b*e*g - 13*c*d*g

+ c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (696*b^3*c^5*e^3*f +

1044*b^4*c^4*e^3*g - 8352*b*c^7*d^3*g + 2336*b*c^7*d^2*e*f - 2544*b^2*c^6*d*e^2*f + 12528*b^2*c^6*d^2*e*g - 62

64*b^3*c^5*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*(

(1952*b^2*c^6*e^3*f - 20928*c^8*d^3*g + 3456*b^3*c^5*e^3*g + 5696*c^8*d^2*e*f - 6656*b*c^7*d*e^2*f + 34240*b*c

^7*d^2*e*g - 18784*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(61*b^2*e^2*g + 178*c^2*d^2*g + 18

*b*c*e^2*f - 30*c^2*d*e*f - 208*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(9*b*e*g - 15*c*d*g + c*e*

f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (840*b^3*c^5*e^3*f + 1308*b

^4*c^4*e^3*g - 10464*b*c^7*d^3*g + 2848*b*c^7*d^2*e*f - 3088*b^2*c^6*d*e^2*f + 15696*b^2*c^6*d^2*e*g - 7848*b^

3*c^5*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((2272

*b^2*c^6*e^3*f - 25152*c^8*d^3*g + 4128*b^3*c^5*e^3*g + 6720*c^8*d^2*e*f - 7808*b*c^7*d*e^2*f + 41088*b*c^7*d^

2*e*g - 22496*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(71*b^2*e^2*g + 210*c^2*d^2*g + 20*b*c*

e^2*f - 34*c^2*d*e*f - 244*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(10*b*e*g - 17*c*d*g + c*e*f))/

(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (984*b^3*c^5*e^3*f + 1572*b^4*c

^4*e^3*g - 12576*b*c^7*d^3*g + 3360*b*c^7*d^2*e*f - 3632*b^2*c^6*d*e^2*f + 18864*b^2*c^6*d^2*e*g - 9432*b^3*c^

5*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((2592*b^2

*c^6*e^3*f - 29376*c^8*d^3*g + 4800*b^3*c^5*e^3*g + 7744*c^8*d^2*e*f - 8960*b*c^7*d*e^2*f + 47936*b*c^7*d^2*e*

g - 26208*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(81*b^2*e^2*g + 242*c^2*d^2*g + 22*b*c*e^2*

f - 38*c^2*d*e*f - 280*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(11*b*e*g - 19*c*d*g + c*e*f))/(103

95*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (1128*b^3*c^5*e^3*f + 1836*b^4*c^4*

e^3*g - 14688*b*c^7*d^3*g + 3872*b*c^7*d^2*e*f - 4176*b^2*c^6*d*e^2*f + 22032*b^2*c^6*d^2*e*g - 11016*b^3*c^5*

d*e^2*g)/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((d*((d*((4*

c^4*e^2*(17*b*e*g - 28*c*d*g + 2*c*e*f))/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2) - (8*c^5*d*e^2*g)/(99*(7*b*

e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e - (4*c^3*e*(44*b^2*e^2*g + 114*c^2*d^2*g + 17*b*c*e^2*f - 28*c^2*d*e*f -

142*b*c*d*e*g))/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e + (176*b^2*c^3*e^4*f + 200*b^3*c^2*e^4*g + 456*c

^5*d^2*e^2*f - 1024*c^5*d^3*e*g - 568*b*c^4*d*e^3*f + 1764*b*c^4*d^2*e^2*g - 1024*b^2*c^3*d*e^3*g)/(99*e*(7*b*

e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e - (800*c^5*d^4*g + 132*b^3*c^2*e^4*f + 84*b^4*c*e^4*g - 480*c^5*d^3*e*f -

1872*b*c^4*d^3*e*g + 948*b*c^4*d^2*e^2*f - 616*b^2*c^3*d*e^3*f - 604*b^3*c^2*d*e^3*g + 1608*b^2*c^3*d^2*e^2*g

)/(99*e*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^4 - (((d

*((832*b^2*c^6*e^3*f - 6144*c^8*d^3*g + 1104*b^3*c^5*e^3*g + 2112*c^8*d^2*e*f - 2624*b*c^7*d*e^2*f + 10272*b*c

^7*d^2*e*g - 5792*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(26*b^2*e^2*g + 66*c^2*d^2*g + 11*b

*c*e^2*f - 16*c^2*d*e*f - 82*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(11*b*e*g - 16*c*d*g + 2*c*e*

f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (16*b*c^4*(24*b^3*e^3*g - 1

92*c^3*d^3*g + 21*b^2*c*e^3*f + 66*c^3*d^2*e*f - 74*b*c^2*d*e^2*f + 288*b*c^2*d^2*e*g - 144*b^2*c*d*e^2*g))/(1

0395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((3312*b^2*c^6*e^3*f -

49408*c^8*d^3*g + 7656*b^3*c^5*e^3*g + 10496*c^8*d^2*e*f - 11776*b*c^7*d*e^2*f + 79360*b*c^7*d^2*e*g - 42624*b

^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((16*c^6*(207*b^2*e^2*g + 656*c^2*d^2*g + 46*b*c*e^2*f - 80*c^2

*d*e*f - 736*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(23*b*e*g - 40*c*d*g + 2*c*e*f))/(10395*(b*e

- 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(386*b^3*e^3*g - 3088*c^3*d^3*g +

185*b^2*c*e^3*f + 656*c^3*d^2*e*f - 696*b*c^2*d*e^2*f + 4632*b*c^2*d^2*e*g - 2316*b^2*c*d*e^2*g))/(10395*e*(b*

e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((3792*b^2*c^6*e^3*f - 58752*c^8*

d^3*g + 9048*b^3*c^5*e^3*g + 12160*c^8*d^2*e*f - 13568*b*c^7*d*e^2*f + 94208*b*c^7*d^2*e*g - 50496*b^2*c^6*d*e

^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((16*c^6*(237*b^2*e^2*g + 760*c^2*d^2*g + 50*b*c*e^2*f - 88*c^2*d*e*f - 8

48*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(25*b*e*g - 44*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6

) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(459*b^3*e^3*g - 3672*c^3*d^3*g + 213*b^2*c*

e^3*f + 760*c^3*d^2*e*f - 804*b*c^2*d*e^2*f + 5508*b*c^2*d^2*e*g - 2754*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)

^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((4272*b^2*c^6*e^3*f - 68096*c^8*d^3*g + 10

440*b^3*c^5*e^3*g + 13824*c^8*d^2*e*f - 15360*b*c^7*d*e^2*f + 109056*b*c^7*d^2*e*g - 58368*b^2*c^6*d*e^2*g)/(1

0395*e*(b*e - 2*c*d)^6) - (d*((16*c^6*(89*b^2*e^2*g + 288*c^2*d^2*g + 18*b*c*e^2*f - 32*c^2*d*e*f - 320*b*c*d*

e*g))/(3465*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(27*b*e*g - 48*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^

8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(532*b^3*e^3*g - 4256*c^3*d^3*g + 241*b^2*c*e^3*f + 86

4*c^3*d^2*e*f - 912*b*c^2*d*e^2*f + 6384*b*c^2*d^2*e*g - 3192*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^

2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((4400*b^2*c^6*e^3*f - 72192*c^8*d^3*g + 11016*b^3*c^

5*e^3*g + 14336*c^8*d^2*e*f - 15872*b*c^7*d*e^2*f + 115456*b*c^7*d^2*e*g - 61696*b^2*c^6*d*e^2*g)/(10395*e*(b*

e - 2*c*d)^6) - (d*((16*c^6*(275*b^2*e^2*g + 896*c^2*d^2*g + 54*b*c*e^2*f - 96*c^2*d*e*f - 992*b*c*d*e*g))/(10

395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(27*b*e*g - 48*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)

/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(564*b^3*e^3*g - 4512*c^3*d^3*g + 249*b^2*c*e^3*f + 896*c^3*d^

2*e*f - 944*b*c^2*d*e^2*f + 6768*b*c^2*d^2*e*g - 3384*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^

2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((4944*b^2*c^6*e^3*f - 83584*c^8*d^3*g + 12696*b^3*c^5*e^3*g

+ 16256*c^8*d^2*e*f - 17920*b*c^7*d*e^2*f + 133504*b*c^7*d^2*e*g - 71232*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*

d)^6) - (d*((16*c^6*(309*b^2*e^2*g + 1016*c^2*d^2*g + 58*b*c*e^2*f - 104*c^2*d*e*f - 1120*b*c*d*e*g))/(10395*(

b*e - 2*c*d)^6) - (d*((32*c^7*e*(29*b*e*g - 52*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(103

95*(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(653*b^3*e^3*g - 5224*c^3*d^3*g + 281*b^2*c*e^3*f + 1016*c^3*d^2*e*

f - 1068*b*c^2*d*e^2*f + 7836*b*c^2*d^2*e*g - 3918*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x

^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((5616*b^2*c^6*e^3*f - 99072*c^8*d^3*g + 14952*b^3*c^5*e^3*g + 1

8688*c^8*d^2*e*f - 20480*b*c^7*d*e^2*f + 157952*b*c^7*d^2*e*g - 84096*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^

6) - (d*((16*c^6*(351*b^2*e^2*g + 1168*c^2*d^2*g + 62*b*c*e^2*f - 112*c^2*d*e*f - 1280*b*c*d*e*g))/(10395*(b*e

- 2*c*d)^6) - (d*((32*c^7*e*(31*b*e*g - 56*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*

(b*e - 2*c*d)^6)))/e))/e))/e - (8*b*c^4*(774*b^3*e^3*g - 6192*c^3*d^3*g + 321*b^2*c*e^3*f + 1168*c^3*d^2*e*f -

1224*b*c^2*d*e^2*f + 9288*b*c^2*d^2*e*g - 4644*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2

- b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((6480*b^2*c^6*e^3*f - 143872*c^8*d^3*g + 20976*b^3*c^5*e^3*g + 220

16*c^8*d^2*e*f - 23872*b*c^7*d*e^2*f + 226816*b*c^7*d^2*e*g - 119376*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6

) - (d*((16*c^6*(405*b^2*e^2*g + 1376*c^2*d^2*g + 64*b*c*e^2*f - 116*c^2*d*e*f - 1492*b*c*d*e*g))/(10395*(b*e

- 2*c*d)^6) - (d*((64*c^7*e*(16*b*e*g - 29*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*

e - 2*c*d)^6)))/e))/e))/e - (16*b*c^4*(562*b^3*e^3*g - 4496*c^3*d^3*g + 187*b^2*c*e^3*f + 688*c^3*d^2*e*f - 71

7*b*c^2*d*e^2*f + 6744*b*c^2*d^2*e*g - 3372*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*

d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((7184*b^2*c^6*e^3*f - 164864*c^8*d^3*g + 23936*b^3*c^5*e^3*g + 24576*c

^8*d^2*e*f - 26560*b*c^7*d*e^2*f + 259584*b*c^7*d^2*e*g - 136432*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) -

(d*((16*c^6*(449*b^2*e^2*g + 1536*c^2*d^2*g + 68*b*c*e^2*f - 124*c^2*d*e*f - 1660*b*c*d*e*g))/(10395*(b*e - 2*

c*d)^6) - (d*((64*c^7*e*(17*b*e*g - 31*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e -

2*c*d)^6)))/e))/e))/e - (16*b*c^4*(644*b^3*e^3*g - 5152*c^3*d^3*g + 208*b^2*c*e^3*f + 768*c^3*d^2*e*f - 799*b*

c^2*d*e^2*f + 7728*b*c^2*d^2*e*g - 3864*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e

- b*e^2*x)^(1/2))/(d + e*x) + (((d*((8016*b^2*c^6*e^3*f - 192512*c^8*d^3*g + 27792*b^3*c^5*e^3*g + 27648*c^8*d

^2*e*f - 29760*b*c^7*d*e^2*f + 302592*b*c^7*d^2*e*g - 158736*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*(

(16*c^6*(167*b^2*e^2*g + 576*c^2*d^2*g + 24*b*c*e^2*f - 44*c^2*d*e*f - 620*b*c*d*e*g))/(3465*(b*e - 2*c*d)^6)

- (d*((64*c^7*e*(18*b*e*g - 33*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6

)))/e))/e))/e - (16*b*c^4*(752*b^3*e^3*g - 6016*c^3*d^3*g + 233*b^2*c*e^3*f + 864*c^3*d^2*e*f - 897*b*c^2*d*e^

2*f + 9024*b*c^2*d^2*e*g - 4512*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*

x)^(1/2))/(d + e*x) + (((d*((8976*b^2*c^6*e^3*f - 229888*c^8*d^3*g + 32928*b^3*c^5*e^3*g + 31232*c^8*d^2*e*f -

33472*b*c^7*d*e^2*f + 360448*b*c^7*d^2*e*g - 188592*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((16*c^6*

(561*b^2*e^2*g + 1952*c^2*d^2*g + 76*b*c*e^2*f - 140*c^2*d*e*f - 2092*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d

*((64*c^7*e*(19*b*e*g - 35*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/

e))/e))/e - (16*b*c^4*(898*b^3*e^3*g - 7184*c^3*d^3*g + 262*b^2*c*e^3*f + 976*c^3*d^2*e*f - 1011*b*c^2*d*e^2*f

+ 10776*b*c^2*d^2*e*g - 5388*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)

^(1/2))/(d + e*x) - (((d*((11936*b^2*c^6*e^3*f - 386048*c^8*d^3*g + 53888*b^3*c^5*e^3*g + 42432*c^8*d^2*e*f -

44992*b*c^7*d*e^2*f + 600288*b*c^7*d^2*e*g - 311392*b^2*c^6*d*e^2*g)/(10395*e*(b*e - 2*c*d)^6) - (d*((32*c^6*(

373*b^2*e^2*g + 1326*c^2*d^2*g + 43*b*c*e^2*f - 80*c^2*d*e*f - 1406*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*(

(32*c^7*e*(43*b*e*g - 80*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/

e))/e))/e - (32*b*c^4*(754*b^3*e^3*g - 6032*c^3*d^3*g + 176*b^2*c*e^3*f + 663*c^3*d^2*e*f - 683*b*c^2*d*e^2*f

+ 9048*b*c^2*d^2*e*g - 4524*b^2*c*d*e^2*g))/(10395*e*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(

1/2))/(d + e*x) + (((d*((484*b^2*c^4*e^3*f - 3776*c^6*d^3*g + 676*b^3*c^3*e^3*g + 1344*c^6*d^2*e*f - 1616*b*c^

5*d*e^2*f + 6336*b*c^5*d^2*e*g - 3572*b^2*c^4*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) + (d*((d*((1

6*c^5*e^2*(10*b*e*g - 17*c*d*g + c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5

*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (484*b^2*c^4*e^3*g + 160*b*c^5*e^3*f - 272*c^6*d*e^2*f + 1344*c^6*d^

2*e*g - 1616*b*c^5*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e))/e - (204*b^3*c^3*e^3*f + 236*b^4*

c^2*e^3*g - 1888*b*c^5*d^3*g + 672*b*c^5*d^2*e*f - 740*b^2*c^4*d*e^2*f + 2832*b^2*c^4*d^2*e*g - 1416*b^3*c^3*d

*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 +

(((d*((1312*b^2*c^6*e^4*f + 2112*b^3*c^5*e^4*g + 3648*c^8*d^2*e^2*f - 12480*c^8*d^3*e*g - 4352*b*c^7*d*e^3*f

+ 20544*b*c^7*d^2*e^2*g - 11360*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((32*c^6*(41*b^2*e^2*g + 114

*c^2*d^2*g + 14*b*c*e^2*f - 22*c^2*d*e*f - 136*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(7*b*e*g -

11*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (12288*c^8*d

^4*g + 1080*b^3*c^5*e^4*f + 1284*b^4*c^4*e^4*g - 4224*c^8*d^3*e*f - 28704*b*c^7*d^3*e*g + 8160*b*c^7*d^2*e^2*f

- 5168*b^2*c^6*d*e^3*f - 9240*b^3*c^5*d*e^3*g + 24624*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2

- c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((2352*b^2*c^6*e^4*f + 4872*b^3*c^5*e^4*g + 7168*c^8*d^

2*e^2*f - 30720*c^8*d^3*e*g - 8192*b*c^7*d*e^3*f + 49664*b*c^7*d^2*e^2*g - 26880*b^2*c^6*d*e^3*g)/(10395*e^2*(

b*e - 2*c*d)^6) - (d*((16*c^6*(147*b^2*e^2*g + 448*c^2*d^2*g + 38*b*c*e^2*f - 64*c^2*d*e*f - 512*b*c*d*e*g))/(

10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(19*b*e*g - 32*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*

g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (21312*c^8*d^4*g + 1600*b^3*c^5*e^4*f + 2968*b^4*c^4*e^4*g - 4544*c^8

*d^3*e*f - 55712*b*c^7*d^3*e*g + 10400*b*c^7*d^2*e^2*f - 7248*b^2*c^6*d*e^3*f - 20472*b^3*c^5*d*e^3*g + 51600*

b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*

((2768*b^2*c^6*e^4*f + 5976*b^3*c^5*e^4*g + 8576*c^8*d^2*e^2*f - 38016*c^8*d^3*e*g - 9728*b*c^7*d*e^3*f + 6131

2*b*c^7*d^2*e^2*g - 33088*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(173*b^2*e^2*g + 536*c^2*

d^2*g + 42*b*c*e^2*f - 72*c^2*d*e*f - 608*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(21*b*e*g - 36*c

*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (41856*c^8*d^4

*g + 2648*b^3*c^5*e^4*f + 4280*b^4*c^4*e^4*g - 11392*c^8*d^3*e*f - 97024*b*c^7*d^3*e*g + 21376*b*c^7*d^2*e^2*f

- 13120*b^2*c^6*d*e^3*f - 30912*b^3*c^5*d*e^3*g + 82752*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^

2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((3184*b^2*c^6*e^4*f + 7080*b^3*c^5*e^4*g + 9984*c^8*

d^2*e^2*f - 45312*c^8*d^3*e*g - 11264*b*c^7*d*e^3*f + 72960*b*c^7*d^2*e^2*g - 39296*b^2*c^6*d*e^3*g)/(10395*e^

2*(b*e - 2*c*d)^6) - (d*((16*c^6*(199*b^2*e^2*g + 624*c^2*d^2*g + 46*b*c*e^2*f - 80*c^2*d*e*f - 704*b*c*d*e*g)

)/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(23*b*e*g - 40*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d

*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (50304*c^8*d^4*g + 3096*b^3*c^5*e^4*f + 5136*b^4*c^4*e^4*g - 13440

*c^8*d^3*e*f - 116544*b*c^7*d^3*e*g + 25152*b*c^7*d^2*e^2*f - 15392*b^2*c^6*d*e^3*f - 37104*b^3*c^5*d*e^3*g +

99360*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) -

(((d*((3600*b^2*c^6*e^4*f + 8184*b^3*c^5*e^4*g + 11392*c^8*d^2*e^2*f - 52608*c^8*d^3*e*g - 12800*b*c^7*d*e^3*

f + 84608*b*c^7*d^2*e^2*g - 45504*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(225*b^2*e^2*g +

712*c^2*d^2*g + 50*b*c*e^2*f - 88*c^2*d*e*f - 800*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(25*b*e*

g - 44*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (58752

*c^8*d^4*g + 3544*b^3*c^5*e^4*f + 5992*b^4*c^4*e^4*g - 15488*c^8*d^3*e*f - 136064*b*c^7*d^3*e*g + 28928*b*c^7*

d^2*e^2*f - 17664*b^2*c^6*d*e^3*f - 43296*b^3*c^5*d*e^3*g + 115968*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)

^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((4368*b^2*c^6*e^4*f + 12096*b^3*c^5*e^4*g

+ 14336*c^8*d^2*e^2*f - 80896*c^8*d^3*e*g - 15808*b*c^7*d*e^3*f + 128512*b*c^7*d^2*e^2*g - 68208*b^2*c^6*d*e^3

*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(273*b^2*e^2*g + 896*c^2*d^2*g + 52*b*c*e^2*f - 92*c^2*d*e*f - 9

88*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(13*b*e*g - 23*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6)

- (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (72576*c^8*d^4*g + 3984*b^3*c^5*e^4*f + 8592*b^4*c^4*e^

4*g - 16000*c^8*d^3*e*f - 177600*b*c^7*d^3*e*g + 31168*b*c^7*d^2*e^2*f - 19536*b^2*c^6*d*e^3*f - 60624*b^3*c^5

*d*e^3*g + 157536*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))

/(d + e*x) + (((d*((4944*b^2*c^6*e^4*f + 14160*b^3*c^5*e^4*g + 16384*c^8*d^2*e^2*f - 95232*c^8*d^3*e*g - 17984

*b*c^7*d*e^3*f + 151040*b*c^7*d^2*e^2*g - 80016*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(30

9*b^2*e^2*g + 1024*c^2*d^2*g + 56*b*c*e^2*f - 100*c^2*d*e*f - 1124*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((

64*c^7*e*(14*b*e*g - 25*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))

/e))/e - (62208*c^8*d^4*g + 3184*b^3*c^5*e^4*f + 9376*b^4*c^4*e^4*g - 7424*c^8*d^3*e*f - 168320*b*c^7*d^3*e*g

+ 19328*b*c^7*d^2*e^2*f - 14160*b^2*c^6*d*e^3*f - 64032*b^3*c^5*d*e^3*g + 159168*b^2*c^6*d^2*e^2*g)/(10395*e^2

*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((5520*b^2*c^6*e^4*f + 16224*

b^3*c^5*e^4*g + 18432*c^8*d^2*e^2*f - 109568*c^8*d^3*e*g - 20160*b*c^7*d*e^3*f + 173568*b*c^7*d^2*e^2*g - 9182

4*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(115*b^2*e^2*g + 384*c^2*d^2*g + 20*b*c*e^2*f - 3

6*c^2*d*e*f - 420*b*c*d*e*g))/(3465*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(15*b*e*g - 27*c*d*g + c*e*f))/(10395*(b*

e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (71296*c^8*d^4*g + 3536*b^3*c^5*e^4*f + 1

0800*b^4*c^4*e^4*g - 8064*c^8*d^3*e*f - 193344*b*c^7*d^3*e*g + 21312*b*c^7*d^2*e^2*f - 15696*b^2*c^6*d*e^3*f -

73712*b^3*c^5*d*e^3*g + 183072*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b

*e^2*x)^(1/2))/(d + e*x) + (((d*((5648*b^2*c^6*e^4*f + 16992*b^3*c^5*e^4*g + 18944*c^8*d^2*e^2*f - 115200*c^8*

d^3*e*g - 20672*b*c^7*d*e^3*f + 182272*b*c^7*d^2*e^2*g - 96304*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) -

(d*((16*c^6*(353*b^2*e^2*g + 1184*c^2*d^2*g + 60*b*c*e^2*f - 108*c^2*d*e*f - 1292*b*c*d*e*g))/(10395*(b*e - 2*

c*d)^6) - (d*((64*c^7*e*(15*b*e*g - 27*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e -

2*c*d)^6)))/e))/e))/e - (144384*c^8*d^4*g + 6176*b^3*c^5*e^4*f + 14432*b^4*c^4*e^4*g - 28672*c^8*d^3*e*f - 332

032*b*c^7*d^3*e*g + 52480*b*c^7*d^2*e^2*f - 31408*b^2*c^6*d*e^3*f - 104640*b^3*c^5*d*e^3*g + 281472*b^2*c^6*d^

2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((6288*b^2

*c^6*e^4*f + 19440*b^3*c^5*e^4*g + 21248*c^8*d^2*e^2*f - 132352*c^8*d^3*e*g - 23104*b*c^7*d*e^3*f + 209152*b*c

^7*d^2*e^2*g - 110352*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(393*b^2*e^2*g + 1328*c^2*d^2

*g + 64*b*c*e^2*f - 116*c^2*d*e*f - 1444*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(16*b*e*g - 29*c*

d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (167168*c^8*d^4*g

+ 6960*b^3*c^5*e^4*f + 16688*b^4*c^4*e^4*g - 32512*c^8*d^3*e*f - 384256*b*c^7*d^3*e*g + 59392*b*c^7*d^2*e^2*f

- 35472*b^2*c^6*d*e^3*f - 121024*b^3*c^5*d*e^3*g + 325632*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*

d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((7056*b^2*c^6*e^4*f + 22656*b^3*c^5*e^4*g + 24064*

c^8*d^2*e^2*f - 155136*c^8*d^3*e*g - 26048*b*c^7*d*e^3*f + 244736*b*c^7*d^2*e^2*g - 128880*b^2*c^6*d*e^3*g)/(1

0395*e^2*(b*e - 2*c*d)^6) - (d*((16*c^6*(441*b^2*e^2*g + 1504*c^2*d^2*g + 68*b*c*e^2*f - 124*c^2*d*e*f - 1628*

b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(17*b*e*g - 31*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (

64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (198144*c^8*d^4*g + 7936*b^3*c^5*e^4*f + 19744*b^4*c^4*e^4

*g - 37376*c^8*d^3*e*f - 455168*b*c^7*d^3*e*g + 68096*b*c^7*d^2*e^2*f - 40560*b^2*c^6*d*e^3*f - 143232*b^3*c^5

*d*e^3*g + 385536*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))

/(d + e*x) - (((d*((7968*b^2*c^6*e^4*f + 29952*b^3*c^5*e^4*g + 27584*c^8*d^2*e^2*f - 209920*c^8*d^3*e*g - 2963

2*b*c^7*d*e^3*f + 328672*b*c^7*d^2*e^2*g - 171744*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((32*c^6*(

249*b^2*e^2*g + 862*c^2*d^2*g + 35*b*c*e^2*f - 64*c^2*d*e*f - 926*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((3

2*c^7*e*(35*b*e*g - 64*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e)

)/e))/e - (178176*c^8*d^4*g + 6144*b^3*c^5*e^4*f + 23040*b^4*c^4*e^4*g - 19456*c^8*d^3*e*f - 451584*b*c^7*d^3*

e*g + 42976*b*c^7*d^2*e^2*f - 28896*b^2*c^6*d*e^3*f - 160512*b^3*c^5*d*e^3*g + 410112*b^2*c^6*d^2*e^2*g)/(1039

5*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((9696*b^2*c^6*e^4*f + 3

8976*b^3*c^5*e^4*g + 33984*c^8*d^2*e^2*f - 275456*c^8*d^3*e*g - 36288*b*c^7*d*e^3*f + 430176*b*c^7*d^2*e^2*g -

224160*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((32*c^6*(101*b^2*e^2*g + 354*c^2*d^2*g + 13*b*c*e^2

*f - 24*c^2*d*e*f - 378*b*c*d*e*g))/(3465*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(39*b*e*g - 72*c*d*g + 2*c*e*f))/(1

0395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (143872*c^8*d^4*g + 5120*b^3*c^5*

e^4*f + 25920*b^4*c^4*e^4*g - 4608*c^8*d^3*e*f - 423168*b*c^7*d^3*e*g + 23904*b*c^7*d^2*e^2*f - 21024*b^2*c^6*

d*e^3*f - 173504*b^3*c^5*d*e^3*g + 418944*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 -

b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((8768*b^2*c^6*e^4*f + 33920*b^3*c^5*e^4*g + 30528*c^8*d^2*e^2*f - 2

38592*c^8*d^3*e*g - 32704*b*c^7*d*e^3*f + 373152*b*c^7*d^2*e^2*g - 194752*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2

*c*d)^6) - (d*((32*c^6*(274*b^2*e^2*g + 954*c^2*d^2*g + 37*b*c*e^2*f - 68*c^2*d*e*f - 1022*b*c*d*e*g))/(10395*

(b*e - 2*c*d)^6) - (d*((32*c^7*e*(37*b*e*g - 68*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10

395*(b*e - 2*c*d)^6)))/e))/e))/e - (248576*c^8*d^4*g + 10144*b^3*c^5*e^4*f + 27424*b^4*c^4*e^4*g - 48384*c^8*d

^3*e*f - 592256*b*c^7*d^3*e*g + 87840*b*c^7*d^2*e^2*f - 52096*b^2*c^6*d*e^3*f - 195616*b^3*c^5*d*e^3*g + 51552

0*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((

d*((10752*b^2*c^6*e^4*f + 45504*b^3*c^5*e^4*g + 37952*c^8*d^2*e^2*f - 323584*c^8*d^3*e*g - 40384*b*c^7*d*e^3*f

+ 504352*b*c^7*d^2*e^2*g - 262272*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((32*c^6*(336*b^2*e^2*g +

1186*c^2*d^2*g + 41*b*c*e^2*f - 76*c^2*d*e*f - 1262*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((32*c^7*e*(41*b

*e*g - 76*c*d*g + 2*c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (45

9776*c^8*d^4*g + 12864*b^3*c^5*e^4*f + 45056*b^4*c^4*e^4*g - 62464*c^8*d^3*e*f - 1050112*b*c^7*d^3*e*g + 11267

2*b*c^7*d^2*e^2*f - 66432*b^2*c^6*d*e^3*f - 327808*b^3*c^5*d*e^3*g + 885504*b^2*c^6*d^2*e^2*g)/(10395*e^2*(b*e

- 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((2*b^4*e^3*g - 16*b*c^3*d^3*g + 6*b^3

*c*e^3*f + 14*b*c^3*d^2*e*f - 12*b^3*c*d*e^2*g - 18*b^2*c^2*d*e^2*f + 24*b^2*c^2*d^2*e*g)/(11*(9*b*e^2 - 18*c*

d*e)*(b*e - 2*c*d)) - (d*((18*b^2*c^2*e^3*f - 32*c^4*d^3*g + 10*b^3*c*e^3*g + 28*c^4*d^2*e*f - 44*b*c^3*d*e^2*

f + 62*b*c^3*d^2*e*g - 42*b^2*c^2*d*e^2*g)/(11*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d)) + (d*((d*((2*c^3*e^2*(7*b*e

*g - 8*c*d*g + 2*c*e*f))/(11*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d)) - (4*c^4*d*e^2*g)/(11*(9*b*e^2 - 18*c*d*e)*(b

*e - 2*c*d))))/e - (18*b^2*c^2*e^3*g + 14*b*c^3*e^3*f - 16*c^4*d*e^2*f + 28*c^4*d^2*e*g - 44*b*c^3*d*e^2*g)/(1

1*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d))))/e))/e)*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^5 - (((d

*((1168*b^2*c^4*e^3*f - 15872*c^6*d^3*g + 2512*b^3*c^3*e^3*g + 3792*c^6*d^2*e*f - 4208*b*c^5*d*e^2*f + 25704*b

*c^5*d^2*e*g - 13904*b^2*c^4*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) + (d*((d*((8*c^5*e^2*(29*b*e*

g - 52*c*d*g + 2*c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*

e)*(b*e - 2*c*d)^3)))/e - (1168*b^2*c^4*e^3*g + 232*b*c^5*e^3*f - 416*c^6*d*e^2*f + 3792*c^6*d^2*e*g - 4208*b*

c^5*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e))/e - (8*b*c^2*(124*b^3*e^3*g - 992*c^3*d^3*g + 66

*b^2*c*e^3*f + 237*c^3*d^2*e*f - 250*b*c^2*d*e^2*f + 1488*b*c^2*d^2*e*g - 744*b^2*c*d*e^2*g))/(693*(5*b*e^2 -

10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 + (((d*((1992*b^2*c^5*e^3

*f - 28928*c^7*d^3*g + 4512*b^3*c^4*e^3*g + 6400*c^7*d^2*e*f - 7136*b*c^6*d*e^2*f + 46592*b*c^6*d^2*e*g - 2508

0*b^2*c^5*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((32*c^6*e^2*(13*b*e*g - 23*c*d*g + c*e

*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))

)/e - (1992*b^2*c^5*e^3*g + 416*b*c^6*e^3*f - 736*c^7*d*e^2*f + 6400*c^7*d^2*e*g - 7136*b*c^6*d*e^2*g)/(3465*(

3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e))/e - (8*b*c^3*(226*b^3*e^3*g - 1808*c^3*d^3*g + 112*b^2*c*e^3*f + 400

*c^3*d^2*e*f - 423*b*c^2*d*e^2*f + 2712*b*c^2*d^2*e*g - 1356*b^2*c*d*e^2*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e -

2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*((2248*b^2*c^5*e^3*f - 33664*c^7*d^

3*g + 5224*b^3*c^4*e^3*g + 7296*c^7*d^2*e*f - 8096*b*c^6*d*e^2*f + 54144*b*c^6*d^2*e*g - 29096*b^2*c^5*d*e^2*g

)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((32*c^6*e^2*(14*b*e*g - 25*c*d*g + c*e*f))/(3465*(3*b*e

^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (2248*b^2*c

^5*e^3*g + 448*b*c^6*e^3*f - 800*c^7*d*e^2*f + 7296*c^7*d^2*e*g - 8096*b*c^6*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e

)*(b*e - 2*c*d)^4)))/e))/e - (8*b*c^3*(263*b^3*e^3*g - 2104*c^3*d^3*g + 127*b^2*c*e^3*f + 456*c^3*d^2*e*f - 48

1*b*c^2*d*e^2*f + 3156*b*c^2*d^2*e*g - 1578*b^2*c*d*e^2*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2

- c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*((d*((d*((8*c^4*e^2*(14*b*e*g - 25*c*d*g + c*e*f))/(

99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2) - (8*c^5*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e - (8*

c^3*e*(66*b^2*e^2*g + 211*c^2*d^2*g + 14*b*c*e^2*f - 25*c^2*d*e*f - 236*b*c*d*e*g))/(99*(7*b*e^2 - 14*c*d*e)*(

b*e - 2*c*d)^2)))/e + (528*b^2*c^3*e^4*f + 992*b^3*c^2*e^4*g + 1688*c^5*d^2*e^2*f - 6040*c^5*d^3*e*g - 1888*b*

c^4*d*e^3*f + 9904*b*c^4*d^2*e^2*g - 5424*b^2*c^3*d*e^3*g)/(99*e*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e - (

8*c*(b*e - c*d)*(71*b^3*e^3*g - 568*c^3*d^3*g + 53*b^2*c*e^3*f + 187*c^3*d^2*e*f - 199*b*c^2*d*e^2*f + 852*b*c

^2*d^2*e*g - 426*b^2*c*d*e^2*g))/(99*e*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e

^2*x)^(1/2))/(d + e*x)^4 + (((d*((d*((d*((16*c^5*e^2*(8*b*e*g - 13*c*d*g + c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(

b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (4*c^4*e*(89*b^2*e^2*g + 2

40*c^2*d^2*g + 32*b*c*e^2*f - 52*c^2*d*e*f - 292*b*c*d*e*g))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e +

(356*b^2*c^4*e^4*f + 476*b^3*c^3*e^4*g + 960*c^6*d^2*e^2*f - 2624*c^6*d^3*e*g - 1168*b*c^5*d*e^3*f + 4416*b*c^

5*d^2*e^2*g - 2500*b^2*c^4*d*e^3*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (2432*c^6*d^4*g + 292*b

^3*c^3*e^4*f + 244*b^4*c^2*e^4*g - 1152*c^6*d^3*e*f - 5600*b*c^5*d^3*e*g + 2208*b*c^5*d^2*e^2*f - 1396*b^2*c^4

*d*e^3*f - 1768*b^3*c^3*d*e^3*g + 4752*b^2*c^4*d^2*e^2*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2

- c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 - (((d*((d*((d*((16*c^6*e^2*(15*b*e*g - 24*c*d*g + 2*c*e*f)

)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e

- (8*c^5*e*(29*b^2*e^2*g + 80*c^2*d^2*g + 10*b*c*e^2*f - 16*c^2*d*e*f - 96*b*c*d*e*g))/(1155*(3*b*e^2 - 6*c*d

*e)*(b*e - 2*c*d)^4)))/e + (696*b^2*c^5*e^4*f + 1044*b^3*c^4*e^4*g + 1920*c^7*d^2*e^2*f - 6016*c^7*d^3*e*g - 2

304*b*c^6*d*e^3*f + 9984*b*c^6*d^2*e^2*g - 5568*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))

)/e - (6048*c^7*d^4*g + 592*b^3*c^4*e^4*f + 604*b^4*c^3*e^4*g - 2400*c^7*d^3*e*f - 13904*b*c^6*d^3*e*g + 4560*

b*c^6*d^2*e^2*f - 2856*b^2*c^5*d*e^3*f - 4380*b^3*c^4*d*e^3*g + 11784*b^2*c^5*d^2*e^2*g)/(3465*e*(3*b*e^2 - 6*

c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((d*((d*((8*c^5*e^2*(

25*b*e*g - 44*c*d*g + 2*c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5*b*e^2 -

10*c*d*e)*(b*e - 2*c*d)^3)))/e - (8*c^4*e*(112*b^2*e^2*g + 354*c^2*d^2*g + 25*b*c*e^2*f - 44*c^2*d*e*f - 398*b

*c*d*e*g))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e + (896*b^2*c^4*e^4*f + 1808*b^3*c^3*e^4*g + 2832*c^6

*d^2*e^2*f - 11264*c^6*d^3*e*g - 3184*b*c^5*d*e^3*f + 18312*b*c^5*d^2*e^2*g - 9952*b^2*c^4*d*e^3*g)/(693*e*(5*

b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (8000*c^6*d^4*g + 616*b^3*c^3*e^4*f + 1096*b^4*c^2*e^4*g - 1728*c^6*d

^3*e*f - 20768*b*c^5*d^3*e*g + 4008*b*c^5*d^2*e^2*f - 2800*b^2*c^4*d*e^3*f - 7576*b^3*c^3*d*e^3*g + 19152*b^2*

c^4*d^2*e^2*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d +

e*x)^3 - (((d*((d*((d*((8*c^5*e^2*(27*b*e*g - 48*c*d*g + 2*c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)

- (16*c^6*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (8*c^4*e*(127*b^2*e^2*g + 406*c^2*d^2*g +

27*b*c*e^2*f - 48*c^2*d*e*f - 454*b*c*d*e*g))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e + (1016*b^2*c^4*

e^4*f + 2104*b^3*c^3*e^4*g + 3248*c^6*d^2*e^2*f - 13184*c^6*d^3*e*g - 3632*b*c^5*d*e^3*f + 21400*b*c^5*d^2*e^2

*g - 11608*b^2*c^4*d*e^3*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (15104*c^6*d^4*g + 1128*b^3*c^3

*e^4*f + 1432*b^4*c^2*e^4*g - 5376*c^6*d^3*e*f - 34112*b*c^5*d^3*e*g + 9688*b*c^5*d^2*e^2*f - 5752*b^2*c^4*d*e

^3*f - 10480*b^3*c^3*d*e^3*g + 28512*b^2*c^4*d^2*e^2*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 -

c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 + (((d*((d*((d*((32*c^6*e^2*(11*b*e*g - 19*c*d*g + c*e*f))/(3

465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (

8*c^5*e*(185*b^2*e^2*g + 576*c^2*d^2*g + 44*b*c*e^2*f - 76*c^2*d*e*f - 652*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*

e)*(b*e - 2*c*d)^4)))/e + (1480*b^2*c^5*e^4*f + 3088*b^3*c^4*e^4*g + 4608*c^7*d^2*e^2*f - 19456*c^7*d^3*e*g -

5216*b*c^6*d*e^3*f + 31488*b*c^6*d^2*e^2*g - 17048*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^

4)))/e - (13120*c^7*d^4*g + 968*b^3*c^4*e^4*f + 1880*b^4*c^3*e^4*g - 2496*c^7*d^3*e*f - 34720*b*c^6*d^3*e*g +

6048*b*c^6*d^2*e^2*f - 4328*b^2*c^5*d*e^3*f - 12920*b^3*c^4*d*e^3*g + 32400*b^2*c^5*d^2*e^2*g)/(3465*e*(3*b*e^

2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*((d*((d*((32*c^

6*e^2*(12*b*e*g - 21*c*d*g + c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*

e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*c^5*e*(71*b^2*e^2*g + 224*c^2*d^2*g + 16*b*c*e^2*f - 28*c^2*d*e*f - 2

52*b*c*d*e*g))/(1155*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e + (1704*b^2*c^5*e^4*f + 3672*b^3*c^4*e^4*g + 537

6*c^7*d^2*e^2*f - 23296*c^7*d^3*e*g - 6048*b*c^6*d*e^3*f + 37632*b*c^6*d^2*e^2*g - 20328*b^2*c^5*d*e^3*g)/(346

5*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (27648*c^7*d^4*g + 1816*b^3*c^4*e^4*f + 2656*b^4*c^3*e^4*g - 84

48*c^7*d^3*e*f - 62720*b*c^6*d^3*e*g + 15360*b*c^6*d^2*e^2*f - 9192*b^2*c^5*d*e^3*f - 19392*b^3*c^4*d*e^3*g +

52608*b^2*c^5*d^2*e^2*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(

1/2))/(d + e*x)^2 + (((d*((d*((d*((32*c^6*e^2*(13*b*e*g - 23*c*d*g + c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e -

2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*c^5*e*(241*b^2*e^2*g + 768*c^

2*d^2*g + 52*b*c*e^2*f - 92*c^2*d*e*f - 860*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e + (1928

*b^2*c^5*e^4*f + 4256*b^3*c^4*e^4*g + 6144*c^7*d^2*e^2*f - 27136*c^7*d^3*e*g - 6880*b*c^6*d*e^3*f + 43776*b*c^

6*d^2*e^2*g - 23608*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (32448*c^7*d^4*g + 208

8*b^3*c^4*e^4*f + 3112*b^4*c^3*e^4*g - 9792*c^7*d^3*e*f - 73568*b*c^6*d^3*e*g + 17760*b*c^6*d^2*e^2*f - 10600*

b^2*c^5*d*e^3*f - 22728*b^3*c^4*d*e^3*g + 61680*b^2*c^5*d^2*e^2*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4

))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((d*((d*((16*c^6*e^2*(33*b*e*g - 60*c*d*g +

2*c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*

d)^4)))/e - (16*c^5*e*(208*b^2*e^2*g + 706*c^2*d^2*g + 33*b*c*e^2*f - 60*c^2*d*e*f - 766*b*c*d*e*g))/(3465*(3*

b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e + (3328*b^2*c^5*e^4*f + 10304*b^3*c^4*e^4*g + 11296*c^7*d^2*e^2*f - 7014

4*c^7*d^3*e*g - 12256*b*c^6*d*e^3*f + 110864*b*c^6*d^2*e^2*g - 58496*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d

*e)*(b*e - 2*c*d)^4)))/e - (40576*c^7*d^4*g + 1584*b^3*c^4*e^4*f + 6896*b^4*c^3*e^4*g - 384*c^7*d^3*e*f - 1160

32*b*c^6*d^3*e*g + 6224*b*c^6*d^2*e^2*f - 6176*b^2*c^5*d*e^3*f - 46448*b^3*c^4*d*e^3*g + 113184*b^2*c^5*d^2*e^

2*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 -

(((d*((d*((d*((16*c^6*e^2*(31*b*e*g - 56*c*d*g + 2*c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^

7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (16*c^5*e*(187*b^2*e^2*g + 630*c^2*d^2*g + 31*b*c*

e^2*f - 56*c^2*d*e*f - 686*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e + (2992*b^2*c^5*e^4*f +

8992*b^3*c^4*e^4*g + 10080*c^7*d^2*e^2*f - 60928*c^7*d^3*e*g - 10976*b*c^6*d*e^3*f + 96432*b*c^6*d^2*e^2*g - 5

0960*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (54784*c^7*d^4*g + 2912*b^3*c^4*e^4*f

+ 6464*b^4*c^3*e^4*g - 12288*c^7*d^3*e*f - 133888*b*c^6*d^3*e*g + 23472*b*c^6*d^2*e^2*f - 14480*b^2*c^5*d*e^3

*f - 45632*b^3*c^4*d*e^3*g + 118656*b^2*c^5*d^2*e^2*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 -

c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((d*((d*((16*c^6*e^2*(35*b*e*g - 64*c*d*g + 2*c*e*f))/(

3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e -

(16*c^5*e*(233*b^2*e^2*g + 798*c^2*d^2*g + 35*b*c*e^2*f - 64*c^2*d*e*f - 862*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*

d*e)*(b*e - 2*c*d)^4)))/e + (3728*b^2*c^5*e^4*f + 12032*b^3*c^4*e^4*g + 12768*c^7*d^2*e^2*f - 82432*c^7*d^3*e*

g - 13792*b*c^6*d*e^3*f + 130032*b*c^6*d^2*e^2*g - 68464*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2

*c*d)^4)))/e - (120576*c^7*d^4*g + 4896*b^3*c^4*e^4*f + 11104*b^4*c^3*e^4*g - 25344*c^7*d^3*e*f - 269696*b*c^6

*d^3*e*g + 44400*b*c^6*d^2*e^2*f - 25648*b^2*c^5*d*e^3*f - 81696*b^3*c^4*d*e^3*g + 223680*b^2*c^5*d^2*e^2*g)/(

3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*(

(13952*b^2*c^6*e^4*f + 70784*b^3*c^5*e^4*g + 50112*c^8*d^2*e^2*f - 513344*c^8*d^3*e*g - 52864*b*c^7*d*e^3*f +

795072*b*c^7*d^2*e^2*g - 410752*b^2*c^6*d*e^3*g)/(10395*e^2*(b*e - 2*c*d)^6) - (d*((64*c^6*(218*b^2*e^2*g + 78

3*c^2*d^2*g + 23*b*c*e^2*f - 43*c^2*d*e*f - 826*b*c*d*e*g))/(10395*(b*e - 2*c*d)^6) - (d*((64*c^7*e*(23*b*e*g

- 43*c*d*g + c*e*f))/(10395*(b*e - 2*c*d)^6) - (64*c^8*d*e*g)/(10395*(b*e - 2*c*d)^6)))/e))/e))/e - (64*c^4*(b

*e - c*d)*(910*b^3*e^3*g - 7280*c^3*d^3*g + 196*b^2*c*e^3*f + 741*c^3*d^2*e*f - 762*b*c^2*d*e^2*f + 10920*b*c^

2*d^2*e*g - 5460*b^2*c*d*e^2*g))/(10395*e^2*(b*e - 2*c*d)^6))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d

+ e*x) + (((d*((d*((d*((4*c^3*e^2*(9*b*e*g - 15*c*d*g + c*e*f))/(11*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d)) - (4*c

^4*d*e^2*g)/(11*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d))))/e - (12*c^2*e*(7*b^2*e^2*g + 17*c^2*d^2*g + 3*b*c*e^2*f

- 5*c^2*d*e*f - 22*b*c*d*e*g))/(11*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d))))/e + (84*b^2*c^2*e^4*f + 204*c^4*d^2*e

^2*f + 76*b^3*c*e^4*g - 340*c^4*d^3*e*g - 264*b*c^3*d*e^3*f + 612*b*c^3*d^2*e^2*g - 372*b^2*c^2*d*e^3*g)/(11*e

*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d))))/e - (4*(b*e - c*d)*(6*b^3*e^3*g - 48*c^3*d^3*g + 13*b^2*c*e^3*f + 37*c^

3*d^2*e*f - 44*b*c^2*d*e^2*f + 72*b*c^2*d^2*e*g - 36*b^2*c*d*e^2*g))/(11*e*(9*b*e^2 - 18*c*d*e)*(b*e - 2*c*d))

)*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^5 - (((d*((132*b^2*c^4*e^3*f - 608*c^6*d^3*g + 126*b^

3*c^3*e^3*g + 288*c^6*d^2*e*f - 384*b*c^5*d*e^2*f + 1056*b*c^5*d^2*e*g - 624*b^2*c^4*d*e^2*g)/(693*(5*b*e^2 -

10*c*d*e)*(b*e - 2*c*d)^3) + (d*((d*((8*c^5*e^2*(9*b*e*g - 12*c*d*g + 2*c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e

- 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (4*c^4*e*(11*b^2*e^2*g + 24*c

^2*d^2*g + 6*b*c*e^2*f - 8*c^2*d*e*f - 32*b*c*d*e*g))/(231*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e))/e - (50

*b^3*c^3*e^3*f + 38*b^4*c^2*e^3*g - 304*b*c^5*d^3*g + 144*b*c^5*d^2*e*f - 168*b^2*c^4*d*e^2*f + 456*b^2*c^4*d^

2*e*g - 228*b^3*c^3*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)

^(1/2))/(d + e*x)^3 + (((d*((420*b^2*c^4*e^3*f - 3200*c^6*d^3*g + 576*b^3*c^3*e^3*g + 1152*c^6*d^2*e*f - 1392*

b*c^5*d*e^2*f + 5376*b*c^5*d^2*e*g - 3036*b^2*c^4*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) + (d*((d

*((16*c^5*e^2*(9*b*e*g - 15*c*d*g + c*e*f))/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693

*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e - (4*c^4*e*(35*b^2*e^2*g + 96*c^2*d^2*g + 12*b*c*e^2*f - 20*c^2*d*e

*f - 116*b*c*d*e*g))/(231*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e))/e - (176*b^3*c^3*e^3*f + 200*b^4*c^2*e^3

*g - 1600*b*c^5*d^3*g + 576*b*c^5*d^2*e*f - 636*b^2*c^4*d*e^2*f + 2400*b^2*c^4*d^2*e*g - 1200*b^3*c^3*d*e^2*g)

/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 + (((d*(

(336*b^2*c^5*e^3*f - 2016*c^7*d^3*g + 384*b^3*c^4*e^3*g + 800*c^7*d^2*e*f - 1024*b*c^6*d*e^2*f + 3424*b*c^6*d^

2*e*g - 1968*b^2*c^5*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((32*c^6*e^2*(5*b*e*g - 7*c*

d*g + c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2

*c*d)^4)))/e - (16*c^5*e*(21*b^2*e^2*g + 50*c^2*d^2*g + 10*b*c*e^2*f - 14*c^2*d*e*f - 64*b*c*d*e*g))/(3465*(3*

b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e))/e - (132*b^3*c^4*e^3*f + 126*b^4*c^3*e^3*g - 1008*b*c^6*d^3*g + 400*b*

c^6*d^2*e*f - 456*b^2*c^5*d*e^2*f + 1512*b^2*c^5*d^2*e*g - 756*b^3*c^4*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e

- 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((840*b^2*c^5*e^3*f - 7616*c^7*d

^3*g + 1308*b^3*c^4*e^3*g + 2368*c^7*d^2*e*f - 2816*b*c^6*d*e^2*f + 12608*b*c^6*d^2*e*g - 7008*b^2*c^5*d*e^2*g

)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((16*c^6*e^2*(17*b*e*g - 28*c*d*g + 2*c*e*f))/(3465*(3*b

*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*c^5*e*

(105*b^2*e^2*g + 296*c^2*d^2*g + 34*b*c*e^2*f - 56*c^2*d*e*f - 352*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e

- 2*c*d)^4)))/e))/e - (356*b^3*c^4*e^3*f + 476*b^4*c^3*e^3*g - 3808*b*c^6*d^3*g + 1184*b*c^6*d^2*e*f - 1296*b^

2*c^5*d*e^2*f + 5712*b^2*c^5*d^2*e*g - 2856*b^3*c^4*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^

2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((984*b^2*c^5*e^3*f - 9216*c^7*d^3*g + 1572*b^3*c^4

*e^3*g + 2816*c^7*d^2*e*f - 3328*b*c^6*d*e^2*f + 15232*b*c^6*d^2*e*g - 8448*b^2*c^5*d*e^2*g)/(3465*(3*b*e^2 -

6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((16*c^6*e^2*(19*b*e*g - 32*c*d*g + 2*c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*

e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*c^5*e*(123*b^2*e^2*g + 35

2*c^2*d^2*g + 38*b*c*e^2*f - 64*c^2*d*e*f - 416*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e))/e

- (420*b^3*c^4*e^3*f + 576*b^4*c^3*e^3*g - 4608*b*c^6*d^3*g + 1408*b*c^6*d^2*e*f - 1536*b^2*c^5*d*e^2*f + 691

2*b^2*c^5*d^2*e*g - 3456*b^3*c^4*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d

*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((1128*b^2*c^5*e^3*f - 10816*c^7*d^3*g + 1836*b^3*c^4*e^3*g + 3264*c^7

*d^2*e*f - 3840*b*c^6*d*e^2*f + 17856*b*c^6*d^2*e*g - 9888*b^2*c^5*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2

*c*d)^4) + (d*((d*((16*c^6*e^2*(21*b*e*g - 36*c*d*g + 2*c*e*f))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (

32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*c^5*e*(47*b^2*e^2*g + 136*c^2*d^2*g + 14*b

*c*e^2*f - 24*c^2*d*e*f - 160*b*c*d*e*g))/(1155*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e))/e - (484*b^3*c^4*e^

3*f + 676*b^4*c^3*e^3*g - 5408*b*c^6*d^3*g + 1632*b*c^6*d^2*e*f - 1776*b^2*c^5*d*e^2*f + 8112*b^2*c^5*d^2*e*g

- 4056*b^3*c^4*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2

))/(d + e*x)^2 - (((2*f*(b*e - c*d)^3)/(11*b*e^2 - 22*c*d*e) - (d*((2*(b*e - c*d)^2*(b*e*g - c*d*g + 3*c*e*f))

/(11*b*e^2 - 22*c*d*e) + (d*((d*((2*c^2*e^2*(3*b*e*g - 3*c*d*g + c*e*f))/(11*b*e^2 - 22*c*d*e) - (2*c^3*d*e^2*

g)/(11*b*e^2 - 22*c*d*e)))/e - (6*c*e*(b*e - c*d)*(b*e*g - c*d*g + c*e*f))/(11*b*e^2 - 22*c*d*e)))/e))/e)*(c*d

^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^6 + (((d*((d*((d*((16*c^5*e^2*(18*b*e*g - 33*c*d*g + c*e*f)

)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3) - (16*c^6*d*e^2*g)/(693*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3)))/e

- (16*c^4*e*(122*b^2*e^2*g + 419*c^2*d^2*g + 18*b*c*e^2*f - 33*c^2*d*e*f - 452*b*c*d*e*g))/(693*(5*b*e^2 - 10

*c*d*e)*(b*e - 2*c*d)^3)))/e + (1952*b^2*c^4*e^4*f + 6208*b^3*c^3*e^4*g + 6704*c^6*d^2*e^2*f - 42416*c^6*d^3*e

*g - 7232*b*c^5*d*e^3*f + 66976*b*c^5*d^2*e^2*g - 35296*b^2*c^4*d*e^3*g)/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*

c*d)^3)))/e - (16*c^2*(b*e - c*d)*(283*b^3*e^3*g - 2264*c^3*d^3*g + 105*b^2*c*e^3*f + 387*c^3*d^2*e*f - 403*b*

c^2*d*e^2*f + 3396*b*c^2*d^2*e*g - 1698*b^2*c*d*e^2*g))/(693*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^3))*(c*d^2 -

c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 + (((d*((d*((d*((32*c^6*e^2*(21*b*e*g - 39*c*d*g + c*e*f))/(3

465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (

32*c^5*e*(176*b^2*e^2*g + 623*c^2*d^2*g + 21*b*c*e^2*f - 39*c^2*d*e*f - 662*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d

*e)*(b*e - 2*c*d)^4)))/e + (5632*b^2*c^5*e^4*f + 24128*b^3*c^4*e^4*g + 19936*c^7*d^2*e^2*f - 171808*c^7*d^3*e*

g - 21184*b*c^6*d*e^3*f + 267680*b*c^6*d^2*e^2*g - 139136*b^2*c^5*d*e^3*g)/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e -

2*c*d)^4)))/e - (32*c^3*(b*e - c*d)*(598*b^3*e^3*g - 4784*c^3*d^3*g + 156*b^2*c*e^3*f + 585*c^3*d^2*e*f - 604*

b*c^2*d*e^2*f + 7176*b*c^2*d^2*e*g - 3588*b^2*c*d*e^2*g))/(3465*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2

- c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*((50*b^2*c^3*e^3*f - 160*c^5*d^3*g + 38*b^3*c^2*e^3*

g + 96*c^5*d^2*e*f - 136*b*c^4*d*e^2*f + 288*b*c^4*d^2*e*g - 178*b^2*c^3*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*

e - 2*c*d)^2) + (d*((d*((8*c^4*e^2*(4*b*e*g - 5*c*d*g + c*e*f))/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2) - (8

*c^5*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e - (50*b^2*c^3*e^3*g + 32*b*c^4*e^3*f - 40*c^5*d*e^

2*f + 96*c^5*d^2*e*g - 136*b*c^4*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e))/e - (18*b^3*c^2*e^3*

f - 80*b*c^4*d^3*g + 10*b^4*c*e^3*g + 48*b*c^4*d^2*e*f - 58*b^2*c^3*d*e^2*f + 120*b^2*c^3*d^2*e*g - 60*b^3*c^2

*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^4

- (((d*((204*b^2*c^3*e^3*f - 1216*c^5*d^3*g + 236*b^3*c^2*e^3*g + 536*c^5*d^2*e*f - 664*b*c^4*d*e^2*f + 2092*b

*c^4*d^2*e*g - 1212*b^2*c^3*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2) + (d*((d*((4*c^4*e^2*(19*b*e*g

- 32*c*d*g + 2*c*e*f))/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2) - (8*c^5*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)*(b

*e - 2*c*d)^2)))/e - (204*b^2*c^3*e^3*g + 76*b*c^4*e^3*f - 128*c^5*d*e^2*f + 536*c^5*d^2*e*g - 664*b*c^4*d*e^2

*g)/(99*(7*b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^2)))/e))/e - (84*b^3*c^2*e^3*f - 608*b*c^4*d^3*g + 76*b^4*c*e^3*g +

268*b*c^4*d^2*e*f - 300*b^2*c^3*d*e^2*f + 912*b^2*c^3*d^2*e*g - 456*b^3*c^2*d*e^2*g)/(99*(7*b*e^2 - 14*c*d*e)

*(b*e - 2*c*d)^2))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^4 + (((d*((2568*b^2*c^5*e^3*f - 4019

2*c^7*d^3*g + 6192*b^3*c^4*e^3*g + 8448*c^7*d^2*e*f - 9312*b*c^6*d*e^2*f + 64512*b*c^6*d^2*e*g - 34584*b^2*c^5

*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((32*c^6*e^2*(15*b*e*g - 27*c*d*g + c*e*f))/(346

5*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (8*

c^5*e*(107*b^2*e^2*g + 352*c^2*d^2*g + 20*b*c*e^2*f - 36*c^2*d*e*f - 388*b*c*d*e*g))/(1155*(3*b*e^2 - 6*c*d*e)

*(b*e - 2*c*d)^4)))/e))/e - (8*b*c^3*(314*b^3*e^3*g - 2512*c^3*d^3*g + 146*b^2*c*e^3*f + 528*c^3*d^2*e*f - 555

*b*c^2*d*e^2*f + 3768*b*c^2*d^2*e*g - 1884*b^2*c*d*e^2*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2

- c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((4192*b^2*c^5*e^3*f - 99328*c^7*d^3*g + 14368*b^3*c^

4*e^3*g + 14496*c^7*d^2*e*f - 15584*b*c^6*d*e^2*f + 156240*b*c^6*d^2*e*g - 82016*b^2*c^5*d*e^2*g)/(3465*(3*b*e

^2 - 6*c*d*e)*(b*e - 2*c*d)^4) + (d*((d*((16*c^6*e^2*(37*b*e*g - 68*c*d*g + 2*c*e*f))/(3465*(3*b*e^2 - 6*c*d*e

)*(b*e - 2*c*d)^4) - (32*c^7*d*e^2*g)/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))/e - (16*c^5*e*(262*b^2*e^2*

g + 906*c^2*d^2*g + 37*b*c*e^2*f - 68*c^2*d*e*f - 974*b*c*d*e*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4)))

/e))/e - (16*b*c^3*(388*b^3*e^3*g - 3104*c^3*d^3*g + 122*b^2*c*e^3*f + 453*c^3*d^2*e*f - 470*b*c^2*d*e^2*f + 4

656*b*c^2*d^2*e*g - 2328*b^2*c*d*e^2*g))/(3465*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^4))*(c*d^2 - c*e^2*x^2 - b*d*

e - b*e^2*x)^(1/2))/(d + e*x)^2

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**9,x)

[Out]

Timed out

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3.20.76 \(\int \frac {(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{(d+e x)^9} \, dx\)