∫ f+gx__________ (d+ex)3(cd2−bde−be2x−ce2x2)5∕2 dx

3.2230 \(\int \frac {f+g x}{(d+e x)^3 (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}} \, dx\)

Optimal. Leaf size=358 \[ \frac {256 c^3 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^7 \sqrt {d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac {32 c^2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x) (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x)^2 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}} \]

[Out]

32/63*c^2*(-3*b*e*g+2*c*d*g+4*c*e*f)*(2*c*x+b)/e/(-b*e+2*c*d)^5/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)-2/9*(-d

*g+e*f)/e^2/(-b*e+2*c*d)/(e*x+d)^3/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)-2/21*(-3*b*e*g+2*c*d*g+4*c*e*f)/e^2/

(-b*e+2*c*d)^2/(e*x+d)^2/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)-4/21*c*(-3*b*e*g+2*c*d*g+4*c*e*f)/e^2/(-b*e+2*

c*d)^3/(e*x+d)/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)+256/63*c^3*(-3*b*e*g+2*c*d*g+4*c*e*f)*(2*c*x+b)/e/(-b*e+

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

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Rubi [A] time = 0.51, antiderivative size = 358, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {792, 658, 614, 613} \[ \frac {256 c^3 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^7 \sqrt {d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac {32 c^2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x) (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x)^2 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}} \]

Antiderivative was successfully veriﬁed.

[In]

Int[(f + g*x)/((d + e*x)^3*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]

[Out]

(32*c^2*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x))/(63*e*(2*c*d - b*e)^5*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)

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

4*c*e*f + 2*c*d*g - 3*b*e*g))/(21*e^2*(2*c*d - b*e)^2*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))

- (4*c*(4*c*e*f + 2*c*d*g - 3*b*e*g))/(21*e^2*(2*c*d - b*e)^3*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)

^(3/2)) + (256*c^3*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x))/(63*e*(2*c*d - b*e)^7*Sqrt[d*(c*d - b*e) - b*e^2

*x - c*e^2*x^2])

Rule 613

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-3/2), x_Symbol] :> Simp[(-2*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a + b*x

+ c*x^2]), x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 614

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b + 2*c*x)*(a + b*x + c*x^2)^(p + 1))/((p +

1)*(b^2 - 4*a*c)), x] - Dist[(2*c*(2*p + 3))/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /;

FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2] && IntegerQ[4*p]

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}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx &=-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {(4 c e f+2 c d g-3 b e g) \int \frac {1}{(d+e x)^2 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx}{3 e (2 c d-b e)}\\ &=-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^2 (d+e x)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {(10 c (4 c e f+2 c d g-3 b e g)) \int \frac {1}{(d+e x) \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx}{21 e (2 c d-b e)^2}\\ &=-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^2 (d+e x)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^3 (d+e x) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {\left (16 c^2 (4 c e f+2 c d g-3 b e g)\right ) \int \frac {1}{\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx}{21 e (2 c d-b e)^3}\\ &=\frac {32 c^2 (4 c e f+2 c d g-3 b e g) (b+2 c x)}{63 e (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^2 (d+e x)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^3 (d+e x) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {\left (128 c^3 (4 c e f+2 c d g-3 b e g)\right ) \int \frac {1}{\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{3/2}} \, dx}{63 e (2 c d-b e)^5}\\ &=\frac {32 c^2 (4 c e f+2 c d g-3 b e g) (b+2 c x)}{63 e (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^2 (d+e x)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^3 (d+e x) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {256 c^3 (4 c e f+2 c d g-3 b e g) (b+2 c x)}{63 e (2 c d-b e)^7 \sqrt {d (c d-b e)-b e^2 x-c e^2 x^2}}\\ \end {align*}

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Mathematica [A] time = 0.36, size = 598, normalized size = 1.67 \[ \frac {2 (-b e+c d-c e x) (-g (c d-b e)-c e f)}{3 c e (d+e x)^2 (-e (c d-b e)-c d e) ((d+e x) (c (d-e x)-b e))^{5/2}}-\frac {2 (d+e x)^{5/2} (-b e+c d-c e x)^{5/2} \left (\frac {10 c e \left (\frac {8 c e \left (\frac {6 c e \left (\frac {4 c e \left (\frac {2}{\sqrt {d+e x} (-e (c d-b e)-c d e) \sqrt {-b e+c d-c e x}}-\frac {4 c e \sqrt {d+e x}}{(-e (c d-b e)-c d e) (e (c d-b e)+c d e) \sqrt {-b e+c d-c e x}}\right )}{3 (e (c d-b e)+c d e)}-\frac {2}{3 (d+e x)^{3/2} (e (c d-b e)+c d e) \sqrt {-b e+c d-c e x}}\right )}{5 (e (c d-b e)+c d e)}-\frac {2}{5 (d+e x)^{5/2} (e (c d-b e)+c d e) \sqrt {-b e+c d-c e x}}\right )}{7 (e (c d-b e)+c d e)}-\frac {2}{7 (d+e x)^{7/2} (e (c d-b e)+c d e) \sqrt {-b e+c d-c e x}}\right )}{9 (e (c d-b e)+c d e)}-\frac {2}{9 (d+e x)^{9/2} (e (c d-b e)+c d e) \sqrt {-b e+c d-c e x}}\right ) \left (6 c e^2 f-g \left (\frac {3 c d e}{2}-\frac {9}{2} e (c d-b e)\right )\right )}{3 c e (-e (c d-b e)-c d e) ((d+e x) (c (d-e x)-b e))^{5/2}} \]

Antiderivative was successfully veriﬁed.

[In]

Integrate[(f + g*x)/((d + e*x)^3*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]

[Out]

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

(b*e) + c*(d - e*x)))^(5/2)) - (2*(6*c*e^2*f - ((3*c*d*e)/2 - (9*e*(c*d - b*e))/2)*g)*(d + e*x)^(5/2)*(c*d - b

*e - c*e*x)^(5/2)*(-2/(9*(c*d*e + e*(c*d - b*e))*(d + e*x)^(9/2)*Sqrt[c*d - b*e - c*e*x]) + (10*c*e*(-2/(7*(c*

d*e + e*(c*d - b*e))*(d + e*x)^(7/2)*Sqrt[c*d - b*e - c*e*x]) + (8*c*e*(-2/(5*(c*d*e + e*(c*d - b*e))*(d + e*x

)^(5/2)*Sqrt[c*d - b*e - c*e*x]) + (6*c*e*(-2/(3*(c*d*e + e*(c*d - b*e))*(d + e*x)^(3/2)*Sqrt[c*d - b*e - c*e*

x]) + (4*c*e*(2/((-(c*d*e) - e*(c*d - b*e))*Sqrt[d + e*x]*Sqrt[c*d - b*e - c*e*x]) - (4*c*e*Sqrt[d + e*x])/((-

(c*d*e) - e*(c*d - b*e))*(c*d*e + e*(c*d - b*e))*Sqrt[c*d - b*e - c*e*x])))/(3*(c*d*e + e*(c*d - b*e)))))/(5*(

c*d*e + e*(c*d - b*e)))))/(7*(c*d*e + e*(c*d - b*e)))))/(9*(c*d*e + e*(c*d - b*e)))))/(3*c*e*(-(c*d*e) - e*(c*

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

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fricas [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((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm="fricas")

[Out]

Timed out

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Eval

uation time: 0.74Unable to transpose Error: Bad Argument Value

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maple [B] time = 0.06, size = 1036, normalized size = 2.89 \[ -\frac {2 \left (c e x +b e -c d \right ) \left (-768 b \,c^{5} e^{7} g \,x^{6}+512 c^{6} d \,e^{6} g \,x^{6}+1024 c^{6} e^{7} f \,x^{6}-1152 b^{2} c^{4} e^{7} g \,x^{5}-1536 b \,c^{5} d \,e^{6} g \,x^{5}+1536 b \,c^{5} e^{7} f \,x^{5}+1536 c^{6} d^{2} e^{5} g \,x^{5}+3072 c^{6} d \,e^{6} f \,x^{5}-288 b^{3} c^{3} e^{7} g \,x^{4}-4416 b^{2} c^{4} d \,e^{6} g \,x^{4}+384 b^{2} c^{4} e^{7} f \,x^{4}+1920 b \,c^{5} d^{2} e^{5} g \,x^{4}+6144 b \,c^{5} d \,e^{6} f \,x^{4}+768 c^{6} d^{3} e^{4} g \,x^{4}+1536 c^{6} d^{2} e^{5} f \,x^{4}+48 b^{4} c^{2} e^{7} g \,x^{3}-1472 b^{3} c^{3} d \,e^{6} g \,x^{3}-64 b^{3} c^{3} e^{7} f \,x^{3}-5376 b^{2} c^{4} d^{2} e^{5} g \,x^{3}+1920 b^{2} c^{4} d \,e^{6} f \,x^{3}+6912 b \,c^{5} d^{3} e^{4} g \,x^{3}+8448 b \,c^{5} d^{2} e^{5} f \,x^{3}-1792 c^{6} d^{4} e^{3} g \,x^{3}-3584 c^{6} d^{3} e^{4} f \,x^{3}-18 b^{5} c \,e^{7} g \,x^{2}+300 b^{4} c^{2} d \,e^{6} g \,x^{2}+24 b^{4} c^{2} e^{7} f \,x^{2}-3216 b^{3} c^{3} d^{2} e^{5} g \,x^{2}-384 b^{3} c^{3} d \,e^{6} f \,x^{2}-288 b^{2} c^{4} d^{3} e^{4} g \,x^{2}+4032 b^{2} c^{4} d^{2} e^{5} f \,x^{2}+4704 b \,c^{5} d^{4} e^{3} g \,x^{2}+3072 b \,c^{5} d^{3} e^{4} f \,x^{2}-2112 c^{6} d^{5} e^{2} g \,x^{2}-4224 c^{6} d^{4} e^{3} f \,x^{2}+9 b^{6} e^{7} g x -132 b^{5} c d \,e^{6} g x -12 b^{5} c \,e^{7} f x +876 b^{4} c^{2} d^{2} e^{5} g x +168 b^{4} c^{2} d \,e^{6} f x -4128 b^{3} c^{3} d^{3} e^{4} g x -1056 b^{3} c^{3} d^{2} e^{5} f x +4848 b^{2} c^{4} d^{4} e^{3} g x +4800 b^{2} c^{4} d^{3} e^{4} f x -1344 b \,c^{5} d^{5} e^{2} g x -3264 b \,c^{5} d^{4} e^{3} f x -192 c^{6} d^{6} e g x -384 c^{6} d^{5} e^{2} f x +2 b^{6} d \,e^{6} g +7 b^{6} e^{7} f -30 b^{5} c \,d^{2} e^{5} g -96 b^{5} c d \,e^{6} f +204 b^{4} c^{2} d^{3} e^{4} g +564 b^{4} c^{2} d^{2} e^{5} f -976 b^{3} c^{3} d^{4} e^{3} g -1856 b^{3} c^{3} d^{3} e^{4} f +1344 b^{2} c^{4} d^{5} e^{2} g +3984 b^{2} c^{4} d^{4} e^{3} f -480 b \,c^{5} d^{6} e g -3840 b \,c^{5} d^{5} e^{2} f -64 c^{6} d^{7} g +1216 c^{6} d^{6} e f \right )}{63 \left (e x +d \right )^{2} \left (b^{7} e^{7}-14 b^{6} c d \,e^{6}+84 b^{5} c^{2} d^{2} e^{5}-280 b^{4} c^{3} d^{3} e^{4}+560 b^{3} c^{4} d^{4} e^{3}-672 b^{2} c^{5} d^{5} e^{2}+448 b \,c^{6} d^{6} e -128 c^{7} d^{7}\right ) \left (-c \,e^{2} x^{2}-b \,e^{2} x -b d e +c \,d^{2}\right )^{\frac {5}{2}} e^{2}} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),x)

[Out]

-2/63*(c*e*x+b*e-c*d)*(-768*b*c^5*e^7*g*x^6+512*c^6*d*e^6*g*x^6+1024*c^6*e^7*f*x^6-1152*b^2*c^4*e^7*g*x^5-1536

*b*c^5*d*e^6*g*x^5+1536*b*c^5*e^7*f*x^5+1536*c^6*d^2*e^5*g*x^5+3072*c^6*d*e^6*f*x^5-288*b^3*c^3*e^7*g*x^4-4416

*b^2*c^4*d*e^6*g*x^4+384*b^2*c^4*e^7*f*x^4+1920*b*c^5*d^2*e^5*g*x^4+6144*b*c^5*d*e^6*f*x^4+768*c^6*d^3*e^4*g*x

^4+1536*c^6*d^2*e^5*f*x^4+48*b^4*c^2*e^7*g*x^3-1472*b^3*c^3*d*e^6*g*x^3-64*b^3*c^3*e^7*f*x^3-5376*b^2*c^4*d^2*

e^5*g*x^3+1920*b^2*c^4*d*e^6*f*x^3+6912*b*c^5*d^3*e^4*g*x^3+8448*b*c^5*d^2*e^5*f*x^3-1792*c^6*d^4*e^3*g*x^3-35

84*c^6*d^3*e^4*f*x^3-18*b^5*c*e^7*g*x^2+300*b^4*c^2*d*e^6*g*x^2+24*b^4*c^2*e^7*f*x^2-3216*b^3*c^3*d^2*e^5*g*x^

2-384*b^3*c^3*d*e^6*f*x^2-288*b^2*c^4*d^3*e^4*g*x^2+4032*b^2*c^4*d^2*e^5*f*x^2+4704*b*c^5*d^4*e^3*g*x^2+3072*b

*c^5*d^3*e^4*f*x^2-2112*c^6*d^5*e^2*g*x^2-4224*c^6*d^4*e^3*f*x^2+9*b^6*e^7*g*x-132*b^5*c*d*e^6*g*x-12*b^5*c*e^

7*f*x+876*b^4*c^2*d^2*e^5*g*x+168*b^4*c^2*d*e^6*f*x-4128*b^3*c^3*d^3*e^4*g*x-1056*b^3*c^3*d^2*e^5*f*x+4848*b^2

*c^4*d^4*e^3*g*x+4800*b^2*c^4*d^3*e^4*f*x-1344*b*c^5*d^5*e^2*g*x-3264*b*c^5*d^4*e^3*f*x-192*c^6*d^6*e*g*x-384*

c^6*d^5*e^2*f*x+2*b^6*d*e^6*g+7*b^6*e^7*f-30*b^5*c*d^2*e^5*g-96*b^5*c*d*e^6*f+204*b^4*c^2*d^3*e^4*g+564*b^4*c^

2*d^2*e^5*f-976*b^3*c^3*d^4*e^3*g-1856*b^3*c^3*d^3*e^4*f+1344*b^2*c^4*d^5*e^2*g+3984*b^2*c^4*d^4*e^3*f-480*b*c

^5*d^6*e*g-3840*b*c^5*d^5*e^2*f-64*c^6*d^7*g+1216*c^6*d^6*e*f)/(e*x+d)^2/(b^7*e^7-14*b^6*c*d*e^6+84*b^5*c^2*d^

2*e^5-280*b^4*c^3*d^3*e^4+560*b^3*c^4*d^4*e^3-672*b^2*c^5*d^5*e^2+448*b*c^6*d^6*e-128*c^7*d^7)/e^2/(-c*e^2*x^2

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

________________________________________________________________________________________

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)/(e*x+d)^3/(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2),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?

________________________________________________________________________________________

mupad [B] time = 22.91, size = 33819, normalized size = 94.47 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((f + g*x)/((d + e*x)^3*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(5/2)),x)

[Out]

((35968*c^9*d^6*g - 10062*b^5*c^4*e^6*f + 5714*b^6*c^3*e^6*g + 279680*c^9*d^5*e*f - 248960*b*c^8*d^5*e*g - 729

600*b*c^8*d^4*e^2*f + 98950*b^4*c^5*d*e^5*f - 57260*b^5*c^4*d*e^5*g + 755040*b^2*c^7*d^3*e^3*f - 387748*b^3*c^

6*d^2*e^4*f + 504032*b^2*c^7*d^4*e^2*g - 473132*b^3*c^6*d^3*e^3*g + 231104*b^4*c^5*d^2*e^4*g)/(945*e^2*(b*e -

2*c*d)^11) - x*((b*((b*((b*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*

e^4*g)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 4

1*b*c*d*e*g))/(945*(b*e - 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/(945*(b*e - 2*c*d)^11)))/c + (1608*b^2*c

^7*e^6*f - 912*b^3*c^6*e^6*g - 96*c^9*d^2*e^4*f + 224*c^9*d^3*e^3*g - 2528*b*c^8*d*e^5*f + 352*b*c^8*d^2*e^4*g

+ 1112*b^2*c^7*d*e^5*g)/(945*e^2*(b*e - 2*c*d)^11) + (((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e -

2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11))*(c*d^2 - b*d*e))/(c*e^2)))/c - (326*b^4*c^5*e^6*g - 137

2*b^3*c^6*e^6*f + 19840*c^9*d^3*e^3*f - 5248*c^9*d^4*e^2*g - 29904*b*c^8*d^2*e^4*f + 13056*b^2*c^7*d*e^5*f + 9

12*b*c^8*d^3*e^3*g - 3972*b^3*c^6*d*e^5*g + 7056*b^2*c^7*d^2*e^4*g)/(945*e^2*(b*e - 2*c*d)^11) + ((c*d^2 - b*d

*e)*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*

d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 41*b*c*d*e*g))/(945*(b*e

- 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/(945*(b*e - 2*c*d)^11)))/(c*e^2)))/c + (1670*b^4*c^5*e^6*f - 12

46*b^5*c^4*e^6*g + 60800*c^9*d^4*e^2*f + 2432*c^9*d^5*e*g - 101760*b*c^8*d^3*e^3*f - 16104*b^3*c^6*d*e^5*f - 4

1728*b*c^8*d^4*e^2*g + 11442*b^4*c^5*d*e^5*g + 61368*b^2*c^7*d^2*e^4*f + 67624*b^2*c^7*d^3*e^3*g - 41688*b^3*c

^6*d^2*e^4*g)/(945*e^2*(b*e - 2*c*d)^11) + ((c*d^2 - b*d*e)*((b*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f)

)/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^

2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 41*b*c*d*e*g))/(945*(b*e - 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/(94

5*(b*e - 2*c*d)^11)))/c + (1608*b^2*c^7*e^6*f - 912*b^3*c^6*e^6*g - 96*c^9*d^2*e^4*f + 224*c^9*d^3*e^3*g - 252

8*b*c^8*d*e^5*f + 352*b*c^8*d^2*e^4*g + 1112*b^2*c^7*d*e^5*g)/(945*e^2*(b*e - 2*c*d)^11) + (((32*c^8*e^3*(4*c*

d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11))*(c*d^2 - b*d*e))/(

c*e^2)))/(c*e^2)) + ((c*d^2 - b*d*e)*((b*((b*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d

)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f

- 82*c^2*d*e*f + 41*b*c*d*e*g))/(945*(b*e - 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/(945*(b*e - 2*c*d)^11)

))/c + (1608*b^2*c^7*e^6*f - 912*b^3*c^6*e^6*g - 96*c^9*d^2*e^4*f + 224*c^9*d^3*e^3*g - 2528*b*c^8*d*e^5*f + 3

52*b*c^8*d^2*e^4*g + 1112*b^2*c^7*d*e^5*g)/(945*e^2*(b*e - 2*c*d)^11) + (((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c

*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11))*(c*d^2 - b*d*e))/(c*e^2)))/c - (326*b

^4*c^5*e^6*g - 1372*b^3*c^6*e^6*f + 19840*c^9*d^3*e^3*f - 5248*c^9*d^4*e^2*g - 29904*b*c^8*d^2*e^4*f + 13056*b

^2*c^7*d*e^5*f + 912*b*c^8*d^3*e^3*g - 3972*b^3*c^6*d*e^5*g + 7056*b^2*c^7*d^2*e^4*g)/(945*e^2*(b*e - 2*c*d)^1

1) + ((c*d^2 - b*d*e)*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g

)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 41*b*c

*d*e*g))/(945*(b*e - 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/(945*(b*e - 2*c*d)^11)))/(c*e^2)))/(c*e^2))/(

c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2) - (((32*c^3*g*(4*b*e - 7*c*d))/(945*e^2*(b*e - 2*c*d)^7) - (32*c^4*

d*g)/(945*e^2*(b*e - 2*c*d)^7))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((d*((32*c^5*(c*

d*g - 4*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^9) + (32*c^6*d*g)/(945*(b*e - 2*c*d)^9)))/e + (208*b^2*c^4*e^2*g

- 512*c^6*d^2*g + 928*c^6*d*e*f - 592*b*c^5*e^2*f + 16*b*c^5*d*e*g)/(945*e*(b*e - 2*c*d)^9)))/e - (4*b*c^3*(19

*b^2*e^2*g - 64*c^2*d^2*g - 66*b*c*e^2*f + 116*c^2*d*e*f + 4*b*c*d*e*g))/(945*e*(b*e - 2*c*d)^9))*(c*d^2 - c*e

^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((d*((d*((16*c^5*(12*c*d*g - 13*b*e*g + 8*c*e*f))/(945*(b*e - 2*

c*d)^9) + (32*c^6*d*g)/(945*(b*e - 2*c*d)^9)))/e - (352*c^6*d^2*g - 488*b^2*c^4*e^2*g - 1568*c^6*d*e*f + 912*b

*c^5*e^2*f + 624*b*c^5*d*e*g)/(945*e*(b*e - 2*c*d)^9)))/e + (4*b*c^3*(44*c^2*d^2*g - 49*b^2*e^2*g + 106*b*c*e^

2*f - 196*c^2*d*e*f + 66*b*c*d*e*g))/(945*e*(b*e - 2*c*d)^9))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d

+ e*x) + (((4*b*c*g)/(63*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^4) - (8*c^2*d*g)/(63*e*(5*b*e^2 - 10*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)^3 - (((d*((d*((8*c^3*e*(3*b*e*g + c*d*g - 4

*c*e*f))/(63*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^6) - (8*c^4*d*e*g)/(63*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^6)))

/e - (26*b^2*c^2*e^2*g - 136*c^4*d^2*g + 168*c^4*d*e*f - 116*b*c^3*e^2*f + 60*b*c^3*d*e*g)/(63*(5*b*e^2 - 10*c

*d*e)*(b*e - 2*c*d)^6)))/e + (2*b*c*(4*b^2*e^2*g - 34*c^2*d^2*g - 25*b*c*e^2*f + 42*c^2*d*e*f + 14*b*c*d*e*g))

/(63*(5*b*e^2 - 10*c*d*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)^3 - (((824*

b^2*c^4*e^3*f - 1024*c^6*d^3*g - 252*b^3*c^3*e^3*g + 1856*c^6*d^2*e*f - 2512*b*c^5*d*e^2*f + 816*b*c^5*d^2*e*g

+ 312*b^2*c^4*d*e^2*g)/(945*e^2*(b*e - 2*c*d)^9) + (d*((d*((16*c^5*(8*c*d*g - 11*b*e*g + 8*c*e*f))/(945*(b*e

- 2*c*d)^9) + (32*c^6*d*g)/(945*(b*e - 2*c*d)^9)))/e - (784*b*c^5*e^3*f - 376*b^2*c^4*e^3*g - 1312*c^6*d*e^2*f

+ 416*c^6*d^2*e*g + 368*b*c^5*d*e^2*g)/(945*e^2*(b*e - 2*c*d)^9)))/e)*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(

1/2))/(d + e*x) + (((928*c^6*d^3*g + 704*b^2*c^4*e^3*f - 536*b^3*c^3*e^3*g + 736*c^6*d^2*e*f - 1712*b*c^5*d*e^

2*f - 1872*b*c^5*d^2*e*g + 1736*b^2*c^4*d*e^2*g)/(945*e^2*(b*e - 2*c*d)^9) + (d*((d*((32*c^5*(9*c*d*g - 8*b*e*

g + 4*c*e*f))/(945*(b*e - 2*c*d)^9) + (32*c^6*d*g)/(945*(b*e - 2*c*d)^9)))/e + (776*b^2*c^4*e^3*g - 1104*b*c^5

*e^3*f + 1952*c^6*d*e^2*f + 224*c^6*d^2*e*g - 1488*b*c^5*d*e^2*g)/(945*e^2*(b*e - 2*c*d)^9)))/e)*(c*d^2 - c*e^

2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) + (((d*((d*((2*c^2*e^3*(5*b*e*g + 4*c*d*g - 8*c*e*f))/(9*(b*e - 2*c*

d)^3*(7*b^3*e^6 - 56*c^3*d^3*e^3 + 84*b*c^2*d^2*e^4 - 42*b^2*c*d*e^5)) - (4*c^3*d*e^3*g)/(9*(b*e - 2*c*d)^3*(7

*b^3*e^6 - 56*c^3*d^3*e^3 + 84*b*c^2*d^2*e^4 - 42*b^2*c*d*e^5))))/e - (e*(8*b^2*c*e^3*g - 50*b*c^2*e^3*f + 68*

c^3*d*e^2*f - 64*c^3*d^2*e*g + 38*b*c^2*d*e^2*g))/(9*(b*e - 2*c*d)^3*(7*b^3*e^6 - 56*c^3*d^3*e^3 + 84*b*c^2*d^

2*e^4 - 42*b^2*c*d*e^5))))/e - (e*(20*c^3*d^3*g - 20*b^3*e^3*g + 52*b^2*c*e^3*f + 124*c^3*d^2*e*f - 158*b*c^2*

d*e^2*f - 60*b*c^2*d^2*e*g + 60*b^2*c*d*e^2*g))/(9*(b*e - 2*c*d)^3*(7*b^3*e^6 - 56*c^3*d^3*e^3 + 84*b*c^2*d^2*

e^4 - 42*b^2*c*d*e^5)))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^4 - (((4*c*g*(5*b*e - 8*c*d))/(

63*e*(5*b*e^2 - 10*c*d*e)*(b*e - 2*c*d)^4) - (8*c^2*d*g)/(63*e*(5*b*e^2 - 10*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)^3 + (((d*((d*((16*c^4*e*(5*c*d*g - 6*b*e*g + 4*c*e*f))/(315*(3*

b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7) + (16*c^5*d*e*g)/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7)))/e - (424*b*c^4*

e^3*f - 196*b^2*c^3*e^3*g - 720*c^5*d*e^2*f + 272*c^5*d^2*e*g + 168*b*c^4*d*e^2*g)/(315*e*(3*b*e^2 - 6*c*d*e)*

(b*e - 2*c*d)^7)))/e + (496*b^2*c^3*e^3*f - 816*c^5*d^3*g - 124*b^3*c^2*e^3*g + 1200*c^5*d^2*e*f - 1560*b*c^4*

d*e^2*f + 760*b*c^4*d^2*e*g + 52*b^2*c^3*d*e^2*g)/(315*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7))*(c*d^2 - c*e^2*

x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 - (((d*((d*((d*((d*((8*c^5*e^5*(c*d*g - 5*b*e*g + 4*c*e*f))/(63*(b*e

- 2*c*d)^6*(5*b^3*e^6 - 40*c^3*d^3*e^3 + 60*b*c^2*d^2*e^4 - 30*b^2*c*d*e^5)) + (8*c^6*d*e^5*g)/(63*(b*e - 2*c

*d)^6*(5*b^3*e^6 - 40*c^3*d^3*e^3 + 60*b*c^2*d^2*e^4 - 30*b^2*c*d*e^5))))/e + (e*(82*b^2*c^4*e^5*g - 144*c^6*d

^2*e^3*g - 180*b*c^5*e^5*f + 232*c^6*d*e^4*f + 12*b*c^5*d*e^4*g))/(63*(b*e - 2*c*d)^6*(5*b^3*e^6 - 40*c^3*d^3*

e^3 + 60*b*c^2*d^2*e^4 - 30*b^2*c*d*e^5))))/e + (e*(2*b^2*c^4*e^5*f + 8*b^3*c^3*e^5*g - 880*c^6*d^2*e^3*f + 23

2*c^6*d^3*e^2*g + 532*b*c^5*d*e^4*f + 308*b*c^5*d^2*e^3*g - 296*b^2*c^4*d*e^4*g))/(63*(b*e - 2*c*d)^6*(5*b^3*e

^6 - 40*c^3*d^3*e^3 + 60*b*c^2*d^2*e^4 - 30*b^2*c*d*e^5))))/e + (e*(660*b^3*c^3*e^5*f - 268*b^4*c^2*e^5*g - 43

44*c^6*d^3*e^2*f + 888*c^6*d^4*e*g + 7396*b*c^5*d^2*e^3*f - 3964*b^2*c^4*d*e^4*f + 164*b*c^5*d^3*e^2*g + 1468*

b^3*c^3*d*e^4*g - 2126*b^2*c^4*d^2*e^3*g))/(63*(b*e - 2*c*d)^6*(5*b^3*e^6 - 40*c^3*d^3*e^3 + 60*b*c^2*d^2*e^4

- 30*b^2*c*d*e^5))))/e - (e*(1504*c^6*d^5*g + 640*b^4*c^2*e^5*f - 336*b^5*c*e^5*g + 5280*c^6*d^4*e*f - 5956*b*

c^5*d^4*e*g - 12732*b*c^5*d^3*e^2*f - 4460*b^3*c^3*d*e^4*f + 2452*b^4*c^2*d*e^4*g + 11398*b^2*c^4*d^2*e^3*f +

9180*b^2*c^4*d^3*e^2*g - 6844*b^3*c^3*d^2*e^3*g))/(63*(b*e - 2*c*d)^6*(5*b^3*e^6 - 40*c^3*d^3*e^3 + 60*b*c^2*d

^2*e^4 - 30*b^2*c*d*e^5)))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^3 + (((2*e^2*f)/(9*b^3*e^6 -

72*c^3*d^3*e^3 + 108*b*c^2*d^2*e^4 - 54*b^2*c*d*e^5) - (2*d*e*g)/(9*b^3*e^6 - 72*c^3*d^3*e^3 + 108*b*c^2*d^2*

e^4 - 54*b^2*c*d*e^5))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^5 - (((3952*b^4*c^4*e^5*f - 7936

*c^8*d^5*g - 1640*b^5*c^3*e^5*g + 42240*c^8*d^4*e*f + 704*b*c^7*d^4*e*g - 96960*b*c^7*d^3*e^2*f - 29716*b^3*c^

5*d*e^4*f + 11624*b^4*c^4*d*e^4*g + 81512*b^2*c^6*d^2*e^3*f + 24984*b^2*c^6*d^3*e^2*g - 28344*b^3*c^5*d^2*e^3*

g)/(945*e^2*(b*e - 2*c*d)^11) - (d*((1900*b^3*c^5*e^5*f - 824*b^4*c^4*e^5*g - 24960*c^8*d^3*e^2*f + 3968*c^8*d

^4*e*g + 35168*b*c^7*d^2*e^3*f - 15272*b^2*c^6*d*e^4*f + 5792*b*c^7*d^3*e^2*g + 6588*b^3*c^5*d*e^4*g - 13600*b

^2*c^6*d^2*e^3*g)/(945*e^2*(b*e - 2*c*d)^11) + (d*((d*((d*((16*c^7*e^2*(12*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(

b*e - 2*c*d)^11) + (32*c^8*d*e^2*g)/(945*(b*e - 2*c*d)^11)))/e - (8*c^6*e*(16*c^2*d^2*g - 95*b^2*e^2*g + 130*b

*c*e^2*f - 196*c^2*d*e*f + 130*b*c*d*e*g))/(945*(b*e - 2*c*d)^11)))/e + (1936*b^2*c^6*e^5*f - 948*b^3*c^5*e^5*

g + 2272*c^8*d^2*e^3*f - 1248*c^8*d^3*e^2*g - 4624*b*c^7*d*e^4*f + 928*b*c^7*d^2*e^3*g + 1472*b^2*c^6*d*e^4*g)

/(945*e^2*(b*e - 2*c*d)^11)))/e))/e)*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x) - (((2*b*g)/(9*(7*

b*e^2 - 14*c*d*e)*(b*e - 2*c*d)^3) - (4*c*d*g)/(9*e*(7*b*e^2 - 14*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)^4 - (((16*c^3*d*g)/(315*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^5) - (16*c^2*g

*(2*b*e - 3*c*d))/(315*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^5))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d

+ e*x)^2 + (((16*c^3*d*g)/(315*e*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^5) + (16*c^2*g*(2*b*e - 5*c*d))/(315*e*(3*

b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^5))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d + e*x)^2 + (((d*((d*((8*c^4

*e^2*(7*b*g - 8*c*f))/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7) - (16*c^5*d*e*g)/(315*(3*b*e^2 - 6*c*d*e)*(b*e

- 2*c*d)^7)))/e - (76*b^2*c^3*e^2*g - 272*c^5*d^2*g + 400*c^5*d*e*f - 264*b*c^4*e^2*f + 72*b*c^4*d*e*g)/(315*

(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7)))/e + (2*b*c^2*(13*b^2*e^2*g - 68*c^2*d^2*g - 58*b*c*e^2*f + 100*c^2*d*e*

f + 18*b*c*d*e*g))/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^7))*(c*d^2 - c*e^2*x^2 - b*d*e - b*e^2*x)^(1/2))/(d

+ e*x)^2 - (((d*((d*((d*((d*((32*c^7*e^2*(3*c*d*g - 6*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*c^8*d*e^2

*g)/(945*(b*e - 2*c*d)^11)))/e - (16*c^6*e*(26*c^2*d^2*g - 31*b^2*e^2*g + 53*b*c*e^2*f - 74*c^2*d*e*f + 23*b*c

*d*e*g))/(945*(b*e - 2*c*d)^11)))/e - (8*c^5*e*(160*c^3*d^2*f + 42*b^3*e^2*g - 158*b*c^2*d^2*g - 95*b^2*c*e^2*

f + 62*b*c^2*d*e*f + 29*b^2*c*d*e*g))/(945*(b*e - 2*c*d)^11)))/e + (3968*c^8*d^4*g + 2452*b^3*c^5*e^4*f - 1022

*b^4*c^4*e^4*g - 21120*c^8*d^3*e*f + 2624*b*c^7*d^3*e*g + 32960*b*c^7*d^2*e^2*f - 16232*b^2*c^6*d*e^3*f + 6396

*b^3*c^5*d*e^3*g - 10840*b^2*c^6*d^2*e^2*g)/(945*e*(b*e - 2*c*d)^11)))/e - (1318*b^4*c^4*e^4*f - 544*b^5*c^3*e

^4*g + 1984*b*c^7*d^4*g - 10560*b*c^7*d^3*e*f - 8092*b^3*c^5*d*e^3*f + 1312*b^2*c^6*d^3*e*g + 3100*b^4*c^4*d*e

^3*g + 16160*b^2*c^6*d^2*e^2*f - 5156*b^3*c^5*d^2*e^2*g)/(945*e*(b*e - 2*c*d)^11))*(c*d^2 - c*e^2*x^2 - b*d*e

- b*e^2*x)^(1/2))/(d + e*x) + (((d*((d*((184*b^2*c^5*e^4*f - 66*b^3*c^4*e^4*g - 1232*c^7*d^2*e^2*f + 208*c^7*d

^3*e*g + 440*b*c^6*d*e^3*f + 688*b*c^6*d^2*e^2*g - 400*b^2*c^5*d*e^3*g)/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)

^9) + (d*((d*((8*c^6*e^3*(4*c*d*g - 11*b*e*g + 8*c*e*f))/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^9) + (16*c^7*d

*e^3*g)/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^9)))/e - (4*c^5*e^2*(64*c^2*d^2*g - 51*b^2*e^2*g + 98*b*c*e^2*f

- 132*c^2*d*e*f + 18*b*c*d*e*g))/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^9)))/e))/e + (1984*c^7*d^4*g + 1318*b

^3*c^4*e^4*f - 544*b^4*c^3*e^4*g - 9920*c^7*d^3*e*f + 784*b*c^6*d^3*e*g + 16112*b*c^6*d^2*e^2*f - 8276*b^2*c^5

*d*e^3*f + 3166*b^3*c^4*d*e^3*g - 4960*b^2*c^5*d^2*e^2*g)/(315*(3*b*e^2 - 6*c*d*e)*(b*e - 2*c*d)^9)))/e - (660

*b^4*c^3*e^4*f - 268*b^5*c^2*e^4*g + 992*b*c^6*d^4*g - 4960*b*c^6*d^3*e*f - 3962*b^3*c^4*d*e^3*f + 444*b^2*c^5

*d^3*e*g + 1476*b^4*c^3*d*e^3*g + 7748*b^2*c^5*d^2*e^2*f - 2340*b^3*c^4*d^2*e^2*g)/(315*(3*b*e^2 - 6*c*d*e)*(b

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

(b*e - c*d) + c*d*e)*((2*c^2*(348*b^4*c^5*e^7*f - 464*b^5*c^4*e^7*g + 30448*c^9*d^4*e^3*f + 1104*c^9*d^5*e^2*g

- 45032*b*c^8*d^3*e^4*f - 3978*b^3*c^6*d*e^6*f - 22160*b*c^8*d^4*e^3*g + 4316*b^4*c^5*d*e^6*g + 21708*b^2*c^7

*d^2*e^5*f + 33700*b^2*c^7*d^3*e^4*g - 18386*b^3*c^6*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2

- 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(4

4*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e -

2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^

9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b

*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^

2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)))

)/(c*e^2) + (d*(b*e - c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2

*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*

c^2*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*

b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c

^8*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c

^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b

*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b

*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2

*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^

5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4

*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(8*b^4*c^5*e^7*

g - 398*b^3*c^6*e^7*f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*

f + 376*b*c^8*d^3*e^4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) + (b*c*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*

g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c

*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e

^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*

e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e

^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) +

(8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (3

2*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e -

c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))

+ (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b

*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^7*

f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*

b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g -

99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4

*b*c^2*d*e))))/(c*e^2) + (b*c*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g

- 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2

*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(3248*b^6*c^3*e^7*g

- 5692*b^5*c^4*e^7*f + 149760*c^9*d^5*e^2*f + 15360*c^9*d^6*e*g - 404848*b*c^8*d^4*e^3*f + 56224*b^4*c^5*d*e^6

*f - 122064*b*c^8*d^5*e^2*g - 32356*b^5*c^4*d*e^6*g + 427364*b^2*c^7*d^3*e^4*f - 220918*b^3*c^6*d^2*e^5*f + 26

4872*b^2*c^7*d^4*e^3*g - 259042*b^3*c^6*d^3*e^4*g + 129352*b^4*c^5*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d

^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^

4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^

2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b

*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c

*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*

c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*

e))))/(c*e^2) + (d*(b*e - c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e

^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) -

(2*c^2*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f +

424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4

*b*c^8*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*

(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 1

30*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((

e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e

^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b

*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^

9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d

*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(8*b^4*c^5*

e^7*g - 398*b^3*c^6*e^7*f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*

e^6*f + 376*b*c^8*d^3*e^4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^

2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (b*c*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*

e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b

^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (b*c*(348*b^4*c^5*e^7*f - 464*b^5*c^4*e^7*g + 30448*c^9*d^4*e^3*f + 1104*

c^9*d^5*e^2*g - 45032*b*c^8*d^3*e^4*f - 3978*b^3*c^6*d*e^6*f - 22160*b*c^8*d^4*e^3*g + 4316*b^4*c^5*d*e^6*g +

21708*b^2*c^7*d^2*e^5*f + 33700*b^2*c^7*d^3*e^4*g - 18386*b^3*c^6*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^

2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((2*c^2*(348*b^4*c^5*e^7*f - 464*b^5*c^4*e^7*g + 3044

8*c^9*d^4*e^3*f + 1104*c^9*d^5*e^2*g - 45032*b*c^8*d^3*e^4*f - 3978*b^3*c^6*d*e^6*f - 22160*b*c^8*d^4*e^3*g +

4316*b^4*c^5*d*e^6*g + 21708*b^2*c^7*d^2*e^5*f + 33700*b^2*c^7*d^3*e^4*g - 18386*b^3*c^6*d^2*e^5*g))/(945*e*(b

*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*(((e

*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g)

)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*

g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e

- c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2

*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(

b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*

c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(

945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e

- 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c

*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d

^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2

+ b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b

*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((8*c^9*e^4*

(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2

+ b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e

- 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d

)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4

*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*

e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)

)))/(c*e^2) + (2*c^2*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b

*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/

(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (b*c*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g -

112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*

e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*

((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9

*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f

))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*

(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b

^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*

d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4

*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2

+ b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))

/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*

d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*

d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e -

2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (b*c*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*f + 10576

*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^4*g - 207

4*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(

c*e^2) + (2*c^2*(57088*c^9*d^7*g + 5000*b^6*c^3*e^7*f - 3096*b^7*c^2*e^7*g + 149760*c^9*d^6*e*f - 282368*b*c^8

*d^6*e*g - 524160*b*c^8*d^5*e^2*f - 54308*b^5*c^4*d*e^6*f + 35096*b^6*c^3*d*e^6*g + 756412*b^2*c^7*d^4*e^3*f -

575502*b^3*c^6*d^3*e^4*f + 243428*b^4*c^5*d^2*e^5*f + 585108*b^2*c^7*d^5*e^2*g - 657804*b^3*c^6*d^4*e^3*g + 4

33220*b^4*c^5*d^3*e^4*g - 167244*b^5*c^4*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d

*e)) - (b*c*(3248*b^6*c^3*e^7*g - 5692*b^5*c^4*e^7*f + 149760*c^9*d^5*e^2*f + 15360*c^9*d^6*e*g - 404848*b*c^8

*d^4*e^3*f + 56224*b^4*c^5*d*e^6*f - 122064*b*c^8*d^5*e^2*g - 32356*b^5*c^4*d*e^6*g + 427364*b^2*c^7*d^3*e^4*f

- 220918*b^3*c^6*d^2*e^5*f + 264872*b^2*c^7*d^4*e^3*g - 259042*b^3*c^6*d^3*e^4*g + 129352*b^4*c^5*d^2*e^5*g))

/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*((2

*c^2*(348*b^4*c^5*e^7*f - 464*b^5*c^4*e^7*g + 30448*c^9*d^4*e^3*f + 1104*c^9*d^5*e^2*g - 45032*b*c^8*d^3*e^4*f

- 3978*b^3*c^6*d*e^6*f - 22160*b*c^8*d^4*e^3*g + 4316*b^4*c^5*d*e^6*g + 21708*b^2*c^7*d^2*e^5*f + 33700*b^2*c

^7*d^3*e^4*g - 18386*b^3*c^6*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(

b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2

*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)

) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b

^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2

- 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (

8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*

c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*

d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) +

(32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c

^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^7*f

- 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^

2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g - 9

9*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b

*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f

+ 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*

c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^1

0*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*

g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g +

8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*

e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*f +

10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^4*g

- 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)

) + (b*c*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f +

424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(

c*e^2) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 1

64*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) +

c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e

)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16

*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g -

15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*

d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((16*c^10*e^5*(8*c*

d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*

e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e -

2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g -

112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e

*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*

e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) +

(b*c*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f

+ 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2

*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(3248*b^6*c^3*e^7*g - 5692*b^5*c^4*e^7*f + 1

49760*c^9*d^5*e^2*f + 15360*c^9*d^6*e*g - 404848*b*c^8*d^4*e^3*f + 56224*b^4*c^5*d*e^6*f - 122064*b*c^8*d^5*e^

2*g - 32356*b^5*c^4*d*e^6*g + 427364*b^2*c^7*d^3*e^4*f - 220918*b^3*c^6*d^2*e^5*f + 264872*b^2*c^7*d^4*e^3*g -

259042*b^3*c^6*d^3*e^4*g + 129352*b^4*c^5*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2

*d*e)) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2

*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*

d*e)) - ((e*(b*e - c*d) + c*d*e)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2

+ b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c

*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2)

+ (8*b*c^9*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) +

(32*c^10*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e

- c*d)*((16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e

)) + (32*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16

*b*c^10*e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(1032*b^2*c^7*e^

7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6*f + 424*b*c^8*d^2*e^5*g + 60

0*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (4*b*c^8*e^4*(44*c^2*d^2*g

- 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((8*c^9*e^4*(44*c^2*d^2*g - 99*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d

*e*f + 86*b*c*d*e*g))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*(

(16*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32

*c^10*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^10*

e^6*g)/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (8*b*c^9*e^5*(8*c*d*g - 15*b*e*

g + 8*c*e*f))/(945*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (32*c^10*d*e^4*g*(b*e - c*d))/(945

*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(8*b^4*c^5*e^7*g - 398*b^3*c^6*e^7*

f + 10576*c^9*d^3*e^4*f - 2784*c^9*d^4*e^3*g - 16088*b*c^8*d^2*e^5*f + 6516*b^2*c^7*d*e^6*f + 376*b*c^8*d^3*e^

4*g - 2074*b^3*c^6*d*e^6*g + 4164*b^2*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*

d*e)) + (b*c*(1032*b^2*c^7*e^7*f - 602*b^3*c^6*e^7*g - 112*c^9*d^2*e^5*f + 48*c^9*d^3*e^4*g - 1528*b*c^8*d*e^6

*f + 424*b*c^8*d^2*e^5*g + 600*b^2*c^7*d*e^6*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))

))/(c*e^2) - (b*c*(348*b^4*c^5*e^7*f - 464*b^5*c^4*e^7*g + 30448*c^9*d^4*e^3*f + 1104*c^9*d^5*e^2*g - 45032*b*

c^8*d^3*e^4*f - 3978*b^3*c^6*d*e^6*f - 22160*b*c^8*d^4*e^3*g + 4316*b^4*c^5*d*e^6*g + 21708*b^2*c^7*d^2*e^5*f

+ 33700*b^2*c^7*d^3*e^4*g - 18386*b^3*c^6*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*

d*e))))/(c*e^2) + (b*c*(57088*c^9*d^7*g + 5000*b^6*c^3*e^7*f - 3096*b^7*c^2*e^7*g + 149760*c^9*d^6*e*f - 28236

8*b*c^8*d^6*e*g - 524160*b*c^8*d^5*e^2*f - 54308*b^5*c^4*d*e^6*f + 35096*b^6*c^3*d*e^6*g + 756412*b^2*c^7*d^4*

e^3*f - 575502*b^3*c^6*d^3*e^4*f + 243428*b^4*c^5*d^2*e^5*f + 585108*b^2*c^7*d^5*e^2*g - 657804*b^3*c^6*d^4*e^

3*g + 433220*b^4*c^5*d^3*e^4*g - 167244*b^5*c^4*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^9*(4*c^3*d^2 + b^2*c*e^2 - 4*

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

c*d)*((2*c^2*(3696*b^4*c^6*e^7*f - 3096*b^5*c^5*e^7*g + 121024*c^10*d^4*e^3*f + 6208*c^10*d^5*e^2*g - 194336*

b*c^9*d^3*e^4*f - 28872*b^3*c^7*d*e^6*f - 88896*b*c^9*d^4*e^3*g + 23856*b^4*c^6*d*e^6*g + 110832*b^2*c^8*d^2*e

^5*f + 140240*b^2*c^8*d^3*e^4*g - 84648*b^3*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4

*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((32*c^10*e^4*(28*

c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e

- 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*

d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2

- 4*b*c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*

c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^

3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2

+ b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))

/(c*e^2) - (2*c^2*(4384*b^2*c^8*e^7*f - 2824*b^3*c^7*e^7*g + 576*c^10*d^2*e^5*f + 1216*c^10*d^3*e^4*g - 7136*b

*c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^8*d*e^6*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4

*b*c^2*d*e)) - (16*b*c^9*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(

945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((32*c^10*e^4*(28*c^2*d

^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*

c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c

*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11

*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b

*c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c

*e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d

*e))))/(c*e^2) + (2*c^2*(232*b^3*c^7*e^7*f - 1136*b^4*c^6*e^7*g + 31808*c^10*d^3*e^4*f - 8576*c^10*d^4*e^3*g -

46560*b*c^9*d^2*e^5*f + 16144*b^2*c^8*d*e^6*f + 3680*b*c^9*d^3*e^4*g - 2440*b^3*c^7*d*e^6*g + 7888*b^2*c^8*d^

2*e^5*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (b*c*(4384*b^2*c^8*e^7*f - 2824*b^3

*c^7*e^7*g + 576*c^10*d^2*e^5*f + 1216*c^10*d^3*e^4*g - 7136*b*c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^

8*d*e^6*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*(((e*(b*

e - c*d) + c*d*e)*((32*c^10*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g)

)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d

*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b

*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e

- 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))

/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c

*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8

*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e

))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c

^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(4384*b^2*c^8*e^7*f - 2824*b^3*c^7*e^7*g + 576*c^10*d^2*

e^5*f + 1216*c^10*d^3*e^4*g - 7136*b*c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^8*d*e^6*g))/(945*e*(b*e -

2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^9*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f

- 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (b

*c*(232*b^3*c^7*e^7*f - 1136*b^4*c^6*e^7*g + 31808*c^10*d^3*e^4*f - 8576*c^10*d^4*e^3*g - 46560*b*c^9*d^2*e^5*

f + 16144*b^2*c^8*d*e^6*f + 3680*b*c^9*d^3*e^4*g - 2440*b^3*c^7*d*e^6*g + 7888*b^2*c^8*d^2*e^5*g))/(945*e*(b*e

- 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - ((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*

d*e)*((2*c^2*(3696*b^4*c^6*e^7*f - 3096*b^5*c^5*e^7*g + 121024*c^10*d^4*e^3*f + 6208*c^10*d^5*e^2*g - 194336*b

*c^9*d^3*e^4*f - 28872*b^3*c^7*d*e^6*f - 88896*b*c^9*d^4*e^3*g + 23856*b^4*c^6*d*e^6*g + 110832*b^2*c^8*d^2*e^

5*f + 140240*b^2*c^8*d^3*e^4*g - 84648*b^3*c^7*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*

b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((32*c^10*e^4*(28*c

^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e -

2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d

)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 -

4*b*c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b

^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c

^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3

*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 +

b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/

(c*e^2) - (2*c^2*(4384*b^2*c^8*e^7*f - 2824*b^3*c^7*e^7*g + 576*c^10*d^2*e^5*f + 1216*c^10*d^3*e^4*g - 7136*b*

c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^8*d*e^6*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*

b*c^2*d*e)) - (16*b*c^9*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(9

45*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (d*(b*e - c*d)*((32*c^10*e^4*(28*c^2*d^

2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c

*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*

d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11*

(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*

c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*

e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*

e))))/(c*e^2) + (2*c^2*(232*b^3*c^7*e^7*f - 1136*b^4*c^6*e^7*g + 31808*c^10*d^3*e^4*f - 8576*c^10*d^4*e^3*g -

46560*b*c^9*d^2*e^5*f + 16144*b^2*c^8*d*e^6*f + 3680*b*c^9*d^3*e^4*g - 2440*b^3*c^7*d*e^6*g + 7888*b^2*c^8*d^2

*e^5*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (b*c*(4384*b^2*c^8*e^7*f - 2824*b^3*

c^7*e^7*g + 576*c^10*d^2*e^5*f + 1216*c^10*d^3*e^4*g - 7136*b*c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^8

*d*e^6*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*(((e*(b*e

- c*d) + c*d*e)*((32*c^10*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f - 164*c^2*d*e*f + 102*b*c*d*e*g))

/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - ((e*(b*e - c*d) + c*d*e)*((64*c^11*e^5*(8*c*d*

g - 15*b*e*g + 8*c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*

e - c*d) + c*d*e))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e

- 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (32*b*c^10*e^5*(8*c*d*g - 15*b*e*g + 8*c*e*f))/

(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*d*e^4*g*(b*e - c*d))/(945*(b*e - 2*c*

d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (d*(b*e - c*d)*((64*c^11*e^5*(8*c*d*g - 15*b*e*g + 8*

c*e*f))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) + (128*c^11*e^4*g*(e*(b*e - c*d) + c*d*e)

)/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (64*b*c^11*e^6*g)/(945*(b*e - 2*c*d)^11*(4*c^

3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) - (2*c^2*(4384*b^2*c^8*e^7*f - 2824*b^3*c^7*e^7*g + 576*c^10*d^2*e

^5*f + 1216*c^10*d^3*e^4*g - 7136*b*c^9*d*e^6*f - 992*b*c^9*d^2*e^5*g + 4320*b^2*c^8*d*e^6*g))/(945*e*(b*e - 2

*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e)) - (16*b*c^9*e^4*(28*c^2*d^2*g - 103*b^2*e^2*g + 130*b*c*e^2*f

- 164*c^2*d*e*f + 102*b*c*d*e*g))/(945*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (b*

c*(232*b^3*c^7*e^7*f - 1136*b^4*c^6*e^7*g + 31808*c^10*d^3*e^4*f - 8576*c^10*d^4*e^3*g - 46560*b*c^9*d^2*e^5*f

+ 16144*b^2*c^8*d*e^6*f + 3680*b*c^9*d^3*e^4*g - 2440*b^3*c^7*d*e^6*g + 7888*b^2*c^8*d^2*e^5*g))/(945*e*(b*e

- 2*c*d)^11*(4*c^3*d^2 + b^2*c*e^2 - 4*b*c^2*d*e))))/(c*e^2) + (2*c^2*(11720*b^6*c^4*e^7*g - 18872*b^5*c^5*e^7

*f + 440320*c^10*d^5*e^2*f + 103424*c^10*d^6*e*g - 1221824*b*c^9*d^4*e^3*f + 181328*b^4*c^6*d*e^6*f - 536640*b

*c^9*d^5*e^2*g - 115576*b^5*c^5*d*e^6*g + 1318992*b^2*c^8*d^3*e^4*f - 696440*b^3*c^7*d^2*e^5*f + 1020704*b^2*c

^8*d^4*e^3*g - 947048*b^3*c^7*d^3*e^4*g + 463360*b^4*c^6*d^2*e^5*g))/(945*e*(b*e - 2*c*d)^11*(4*c^3*d^2 + b^2*

c*e^2 - 4*b*c^2*d*e)) + (d*(b*e - c*d)*(((e*(b*e - c*d) + c*d*e)*(((e*(b*e - c*d) + c*d*e)*((32*c^10*e^4*(28*c