3.1395 \(\int \frac{(5-x) (2+3 x^2)^{5/2}}{(3+2 x)^{10}} \, dx\)

Optimal. Leaf size=180 \[ -\frac{4741 \left (3 x^2+2\right )^{7/2}}{1800750 (2 x+3)^7}-\frac{27 \left (3 x^2+2\right )^{7/2}}{2450 (2 x+3)^8}-\frac{13 \left (3 x^2+2\right )^{7/2}}{315 (2 x+3)^9}-\frac{949 (4-9 x) \left (3 x^2+2\right )^{5/2}}{3001250 (2 x+3)^6}-\frac{2847 (4-9 x) \left (3 x^2+2\right )^{3/2}}{42017500 (2 x+3)^4}-\frac{25623 (4-9 x) \sqrt{3 x^2+2}}{1470612500 (2 x+3)^2}-\frac{76869 \tanh ^{-1}\left (\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right )}{735306250 \sqrt{35}} \]

[Out]

(-25623*(4 - 9*x)*Sqrt[2 + 3*x^2])/(1470612500*(3 + 2*x)^2) - (2847*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(42017500*(3
+ 2*x)^4) - (949*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(3001250*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(315*(3 + 2*x)^9)
- (27*(2 + 3*x^2)^(7/2))/(2450*(3 + 2*x)^8) - (4741*(2 + 3*x^2)^(7/2))/(1800750*(3 + 2*x)^7) - (76869*ArcTanh
[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(735306250*Sqrt[35])

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Rubi [A]  time = 0.10851, antiderivative size = 180, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208, Rules used = {835, 807, 721, 725, 206} \[ -\frac{4741 \left (3 x^2+2\right )^{7/2}}{1800750 (2 x+3)^7}-\frac{27 \left (3 x^2+2\right )^{7/2}}{2450 (2 x+3)^8}-\frac{13 \left (3 x^2+2\right )^{7/2}}{315 (2 x+3)^9}-\frac{949 (4-9 x) \left (3 x^2+2\right )^{5/2}}{3001250 (2 x+3)^6}-\frac{2847 (4-9 x) \left (3 x^2+2\right )^{3/2}}{42017500 (2 x+3)^4}-\frac{25623 (4-9 x) \sqrt{3 x^2+2}}{1470612500 (2 x+3)^2}-\frac{76869 \tanh ^{-1}\left (\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right )}{735306250 \sqrt{35}} \]

Antiderivative was successfully verified.

[In]

Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^10,x]

[Out]

(-25623*(4 - 9*x)*Sqrt[2 + 3*x^2])/(1470612500*(3 + 2*x)^2) - (2847*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(42017500*(3
+ 2*x)^4) - (949*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(3001250*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(315*(3 + 2*x)^9)
- (27*(2 + 3*x^2)^(7/2))/(2450*(3 + 2*x)^8) - (4741*(2 + 3*x^2)^(7/2))/(1800750*(3 + 2*x)^7) - (76869*ArcTanh
[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(735306250*Sqrt[35])

Rule 835

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[((e*f - d*g)
*(d + e*x)^(m + 1)*(a + c*x^2)^(p + 1))/((m + 1)*(c*d^2 + a*e^2)), x] + Dist[1/((m + 1)*(c*d^2 + a*e^2)), Int[
(d + e*x)^(m + 1)*(a + c*x^2)^p*Simp[(c*d*f + a*e*g)*(m + 1) - c*(e*f - d*g)*(m + 2*p + 3)*x, x], x], x] /; Fr
eeQ[{a, c, d, e, f, g, p}, x] && NeQ[c*d^2 + a*e^2, 0] && LtQ[m, -1] && (IntegerQ[m] || IntegerQ[p] || Integer
sQ[2*m, 2*p])

Rule 807

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> -Simp[((e*f - d*g
)*(d + e*x)^(m + 1)*(a + c*x^2)^(p + 1))/(2*(p + 1)*(c*d^2 + a*e^2)), x] + Dist[(c*d*f + a*e*g)/(c*d^2 + a*e^2
), Int[(d + e*x)^(m + 1)*(a + c*x^2)^p, x], x] /; FreeQ[{a, c, d, e, f, g, m, p}, x] && NeQ[c*d^2 + a*e^2, 0]
&& EqQ[Simplify[m + 2*p + 3], 0]

Rule 721

Int[((d_) + (e_.)*(x_))^(m_)*((a_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> -Simp[((d + e*x)^(m + 1)*(-2*a*e + (2*c*
d)*x)*(a + c*x^2)^p)/(2*(m + 1)*(c*d^2 + a*e^2)), x] - Dist[(4*a*c*p)/(2*(m + 1)*(c*d^2 + a*e^2)), Int[(d + e*
x)^(m + 2)*(a + c*x^2)^(p - 1), x], x] /; FreeQ[{a, c, d, e}, x] && NeQ[c*d^2 + a*e^2, 0] && EqQ[m + 2*p + 2,
0] && GtQ[p, 0]

Rule 725

Int[1/(((d_) + (e_.)*(x_))*Sqrt[(a_) + (c_.)*(x_)^2]), x_Symbol] :> -Subst[Int[1/(c*d^2 + a*e^2 - x^2), x], x,
(a*e - c*d*x)/Sqrt[a + c*x^2]] /; FreeQ[{a, c, d, e}, x]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin{align*} \int \frac{(5-x) \left (2+3 x^2\right )^{5/2}}{(3+2 x)^{10}} \, dx &=-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{1}{315} \int \frac{(-369+78 x) \left (2+3 x^2\right )^{5/2}}{(3+2 x)^9} \, dx\\ &=-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}+\frac{\int \frac{(24072-2916 x) \left (2+3 x^2\right )^{5/2}}{(3+2 x)^8} \, dx}{88200}\\ &=-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}+\frac{2847 \int \frac{\left (2+3 x^2\right )^{5/2}}{(3+2 x)^7} \, dx}{42875}\\ &=-\frac{949 (4-9 x) \left (2+3 x^2\right )^{5/2}}{3001250 (3+2 x)^6}-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}+\frac{2847 \int \frac{\left (2+3 x^2\right )^{3/2}}{(3+2 x)^5} \, dx}{300125}\\ &=-\frac{2847 (4-9 x) \left (2+3 x^2\right )^{3/2}}{42017500 (3+2 x)^4}-\frac{949 (4-9 x) \left (2+3 x^2\right )^{5/2}}{3001250 (3+2 x)^6}-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}+\frac{25623 \int \frac{\sqrt{2+3 x^2}}{(3+2 x)^3} \, dx}{21008750}\\ &=-\frac{25623 (4-9 x) \sqrt{2+3 x^2}}{1470612500 (3+2 x)^2}-\frac{2847 (4-9 x) \left (2+3 x^2\right )^{3/2}}{42017500 (3+2 x)^4}-\frac{949 (4-9 x) \left (2+3 x^2\right )^{5/2}}{3001250 (3+2 x)^6}-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}+\frac{76869 \int \frac{1}{(3+2 x) \sqrt{2+3 x^2}} \, dx}{735306250}\\ &=-\frac{25623 (4-9 x) \sqrt{2+3 x^2}}{1470612500 (3+2 x)^2}-\frac{2847 (4-9 x) \left (2+3 x^2\right )^{3/2}}{42017500 (3+2 x)^4}-\frac{949 (4-9 x) \left (2+3 x^2\right )^{5/2}}{3001250 (3+2 x)^6}-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}-\frac{76869 \operatorname{Subst}\left (\int \frac{1}{35-x^2} \, dx,x,\frac{4-9 x}{\sqrt{2+3 x^2}}\right )}{735306250}\\ &=-\frac{25623 (4-9 x) \sqrt{2+3 x^2}}{1470612500 (3+2 x)^2}-\frac{2847 (4-9 x) \left (2+3 x^2\right )^{3/2}}{42017500 (3+2 x)^4}-\frac{949 (4-9 x) \left (2+3 x^2\right )^{5/2}}{3001250 (3+2 x)^6}-\frac{13 \left (2+3 x^2\right )^{7/2}}{315 (3+2 x)^9}-\frac{27 \left (2+3 x^2\right )^{7/2}}{2450 (3+2 x)^8}-\frac{4741 \left (2+3 x^2\right )^{7/2}}{1800750 (3+2 x)^7}-\frac{76869 \tanh ^{-1}\left (\frac{4-9 x}{\sqrt{35} \sqrt{2+3 x^2}}\right )}{735306250 \sqrt{35}}\\ \end{align*}

Mathematica [A]  time = 0.314704, size = 185, normalized size = 1.03 \[ \frac{1}{315} \left (-\frac{243 \left (3 x^2+2\right )^{7/2}}{70 (2 x+3)^8}-\frac{13 \left (3 x^2+2\right )^{7/2}}{(2 x+3)^9}-\frac{3 \left (406540750 \left (3 x^2+2\right )^{7/2}+2847 (2 x+3) \left (-945 (9 x-4) \sqrt{3 x^2+2} (2 x+3)^4-3675 (9 x-4) \left (3 x^2+2\right )^{3/2} (2 x+3)^2-17150 (9 x-4) \left (3 x^2+2\right )^{5/2}+162 \sqrt{35} (2 x+3)^6 \tanh ^{-1}\left (\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right )\right )\right )}{1470612500 (2 x+3)^7}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^10,x]

[Out]

((-13*(2 + 3*x^2)^(7/2))/(3 + 2*x)^9 - (243*(2 + 3*x^2)^(7/2))/(70*(3 + 2*x)^8) - (3*(406540750*(2 + 3*x^2)^(7
/2) + 2847*(3 + 2*x)*(-945*(3 + 2*x)^4*(-4 + 9*x)*Sqrt[2 + 3*x^2] - 3675*(3 + 2*x)^2*(-4 + 9*x)*(2 + 3*x^2)^(3
/2) - 17150*(-4 + 9*x)*(2 + 3*x^2)^(5/2) + 162*Sqrt[35]*(3 + 2*x)^6*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2
])])))/(1470612500*(3 + 2*x)^7))/315

________________________________________________________________________________________

Maple [B]  time = 0.033, size = 320, normalized size = 1.8 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x)

[Out]

-4741/230496000/(x+3/2)^7*(3*(x+3/2)^2-9*x-19/4)^(7/2)-949/96040000/(x+3/2)^6*(3*(x+3/2)^2-9*x-19/4)^(7/2)-854
1/1680700000/(x+3/2)^5*(3*(x+3/2)^2-9*x-19/4)^(7/2)-82563/29412250000/(x+3/2)^4*(3*(x+3/2)^2-9*x-19/4)^(7/2)-8
45559/514714375000/(x+3/2)^3*(3*(x+3/2)^2-9*x-19/4)^(7/2)-9198657/9007501562500/(x+3/2)^2*(3*(x+3/2)^2-9*x-19/
4)^(7/2)[phone]/157631277343750*x*(3*(x+3/2)^2-9*x-19/4)^(5/2)-106771041/157631277343750/(x+3/2)*(3*(x+3/2)
^2-9*x-19/4)^(7/2)+8993673/1801500312500*x*(3*(x+3/2)^2-9*x-19/4)^(3/2)+691821/51471437500*x*(3*(x+3/2)^2-9*x-
19/4)^(1/2)-76869/25735718750*35^(1/2)*arctanh(2/35*(4-9*x)*35^(1/2)/(12*(x+3/2)^2-36*x-19)^(1/2))+1229904/788
15638671875*(3*(x+3/2)^2-9*x-19/4)^(5/2)+76869/25735718750*(12*(x+3/2)^2-36*x-19)^(1/2)+102492/450375078125*(3
*(x+3/2)^2-9*x-19/4)^(3/2)-13/161280/(x+3/2)^9*(3*(x+3/2)^2-9*x-19/4)^(7/2)-27/627200/(x+3/2)^8*(3*(x+3/2)^2-9
*x-19/4)^(7/2)

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Maxima [B]  time = 1.61425, size = 586, normalized size = 3.26 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x, algorithm="maxima")

[Out]

27595971/9007501562500*(3*x^2 + 2)^(5/2) - 13/315*(3*x^2 + 2)^(7/2)/(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x
^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683) - 27/2450*(3*x^2 + 2)^(7/2)/(256*x^
8 + 3072*x^7 + 16128*x^6 + 48384*x^5 + 90720*x^4 + 108864*x^3 + 81648*x^2 + 34992*x + 6561) - 4741/1800750*(3*
x^2 + 2)^(7/2)/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187) - 949/1500
625*(3*x^2 + 2)^(7/2)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729) - 8541/52521875*(3*x^
2 + 2)^(7/2)/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243) - 82563/1838265625*(3*x^2 + 2)^(7/2)/(16*x^
4 + 96*x^3 + 216*x^2 + 216*x + 81) - 845559/64339296875*(3*x^2 + 2)^(7/2)/(8*x^3 + 36*x^2 + 54*x + 27) - 91986
57/2251875390625*(3*x^2 + 2)^(7/2)/(4*x^2 + 12*x + 9) + 8993673/1801500312500*(3*x^2 + 2)^(3/2)*x + 102492/450
375078125*(3*x^2 + 2)^(3/2) - 106771041/9007501562500*(3*x^2 + 2)^(5/2)/(2*x + 3) + 691821/51471437500*sqrt(3*
x^2 + 2)*x + 76869/25735718750*sqrt(35)*arcsinh(3/2*sqrt(6)*x/abs(2*x + 3) - 2/3*sqrt(6)/abs(2*x + 3)) + 76869
/12867859375*sqrt(3*x^2 + 2)

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Fricas [A]  time = 1.97265, size = 701, normalized size = 3.89 \begin{align*} \frac{691821 \, \sqrt{35}{\left (512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right )} \log \left (-\frac{\sqrt{35} \sqrt{3 \, x^{2} + 2}{\left (9 \, x - 4\right )} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right ) - 35 \,{\left (10968696 \, x^{8} + 30006612 \, x^{7} - 620594352 \, x^{6} - 25197346566 \, x^{5} + 9750269970 \, x^{4} - 11567526201 \, x^{3} + 42455611758 \, x^{2} + 11990965797 \, x + 15948113036\right )} \sqrt{3 \, x^{2} + 2}}{463242937500 \,{\left (512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x, algorithm="fricas")

[Out]

1/463242937500*(691821*sqrt(35)*(512*x^9 + 6912*x^8 + 41472*x^7 + 145152*x^6 + 326592*x^5 + 489888*x^4 + 48988
8*x^3 + 314928*x^2 + 118098*x + 19683)*log(-(sqrt(35)*sqrt(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 +
12*x + 9)) - 35*(10968696*x^8 + 30006612*x^7 - 620594352*x^6 - 25197346566*x^5 + 9750269970*x^4 - 11567526201
*x^3 + 42455611758*x^2 + 11990965797*x + 15948113036)*sqrt(3*x^2 + 2))/(512*x^9 + 6912*x^8 + 41472*x^7 + 14515
2*x^6 + 326592*x^5 + 489888*x^4 + 489888*x^3 + 314928*x^2 + 118098*x + 19683)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5-x)*(3*x**2+2)**(5/2)/(3+2*x)**10,x)

[Out]

Timed out

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Giac [B]  time = 1.36062, size = 672, normalized size = 3.73 \begin{align*} \frac{76869}{25735718750} \, \sqrt{35} \log \left (-\frac{{\left | -2 \, \sqrt{3} x - \sqrt{35} - 3 \, \sqrt{3} + 2 \, \sqrt{3 \, x^{2} + 2} \right |}}{2 \, \sqrt{3} x - \sqrt{35} + 3 \, \sqrt{3} - 2 \, \sqrt{3 \, x^{2} + 2}}\right ) - \frac{9 \,{\left (1093248 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{17} + 27877824 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{16} + 3126615774 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{15} - 956098170 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{14} + 3010876470 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{13} - 85987901496 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{12} - 181405205604 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{11} - 331045664193 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{10} - 68739446745 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{9} - 544736640510 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{8} + 854568812592 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{7} - 908850124224 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{6} + 271848650976 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{5} - 115517223360 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{4} - 158685613440 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{3} - 565618176 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{2} + 422125056 \, \sqrt{3} x - 17333248 \, \sqrt{3} - 422125056 \, \sqrt{3 \, x^{2} + 2}\right )}}{94119200000 \,{\left ({\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )}^{2} + 3 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 2}\right )} - 2\right )}^{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5-x)*(3*x^2+2)^(5/2)/(3+2*x)^10,x, algorithm="giac")

[Out]

76869/25735718750*sqrt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sq
rt(35) + 3*sqrt(3) - 2*sqrt(3*x^2 + 2))) - 9/94119200000*(1093248*(sqrt(3)*x - sqrt(3*x^2 + 2))^17 + 27877824*
sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^16 + 3126615774*(sqrt(3)*x - sqrt(3*x^2 + 2))^15 - 956098170*sqrt(3)*(sq
rt(3)*x - sqrt(3*x^2 + 2))^14 + 3010876470*(sqrt(3)*x - sqrt(3*x^2 + 2))^13 - 85987901496*sqrt(3)*(sqrt(3)*x -
sqrt(3*x^2 + 2))^12 - 181405205604*(sqrt(3)*x - sqrt(3*x^2 + 2))^11 - 331045664193*sqrt(3)*(sqrt(3)*x - sqrt(
3*x^2 + 2))^10 - 68739446745*(sqrt(3)*x - sqrt(3*x^2 + 2))^9 - 544736640510*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 +
2))^8 + 854568812592*(sqrt(3)*x - sqrt(3*x^2 + 2))^7 - 908850124224*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^6 +
271848650976*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 - 115517223360*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^4 - 15868561
3440*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 565618176*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 422125056*sqrt(3)*x
- 17333248*sqrt(3) - 422125056*sqrt(3*x^2 + 2))/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x - sqr
t(3*x^2 + 2)) - 2)^9