3.2429 \(\int \frac{(5-x) \left (2+5 x+3 x^2\right )^{3/2}}{(3+2 x)^8} \, dx\)

Optimal. Leaf size=174 \[ -\frac{4892 \left (3 x^2+5 x+2\right )^{5/2}}{13125 (2 x+3)^5}-\frac{433 \left (3 x^2+5 x+2\right )^{5/2}}{1050 (2 x+3)^6}-\frac{13 \left (3 x^2+5 x+2\right )^{5/2}}{35 (2 x+3)^7}+\frac{4663 (8 x+7) \left (3 x^2+5 x+2\right )^{3/2}}{60000 (2 x+3)^4}-\frac{4663 (8 x+7) \sqrt{3 x^2+5 x+2}}{800000 (2 x+3)^2}+\frac{4663 \tanh ^{-1}\left (\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right )}{1600000 \sqrt{5}} \]

[Out]

(-4663*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(800000*(3 + 2*x)^2) + (4663*(7 + 8*x)*(
2 + 5*x + 3*x^2)^(3/2))/(60000*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(35*(
3 + 2*x)^7) - (433*(2 + 5*x + 3*x^2)^(5/2))/(1050*(3 + 2*x)^6) - (4892*(2 + 5*x
+ 3*x^2)^(5/2))/(13125*(3 + 2*x)^5) + (4663*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2
+ 5*x + 3*x^2])])/(1600000*Sqrt[5])

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Rubi [A]  time = 0.307453, antiderivative size = 174, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.185 \[ -\frac{4892 \left (3 x^2+5 x+2\right )^{5/2}}{13125 (2 x+3)^5}-\frac{433 \left (3 x^2+5 x+2\right )^{5/2}}{1050 (2 x+3)^6}-\frac{13 \left (3 x^2+5 x+2\right )^{5/2}}{35 (2 x+3)^7}+\frac{4663 (8 x+7) \left (3 x^2+5 x+2\right )^{3/2}}{60000 (2 x+3)^4}-\frac{4663 (8 x+7) \sqrt{3 x^2+5 x+2}}{800000 (2 x+3)^2}+\frac{4663 \tanh ^{-1}\left (\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right )}{1600000 \sqrt{5}} \]

Antiderivative was successfully verified.

[In]  Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^8,x]

[Out]

(-4663*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(800000*(3 + 2*x)^2) + (4663*(7 + 8*x)*(
2 + 5*x + 3*x^2)^(3/2))/(60000*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(35*(
3 + 2*x)^7) - (433*(2 + 5*x + 3*x^2)^(5/2))/(1050*(3 + 2*x)^6) - (4892*(2 + 5*x
+ 3*x^2)^(5/2))/(13125*(3 + 2*x)^5) + (4663*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2
+ 5*x + 3*x^2])])/(1600000*Sqrt[5])

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Rubi in Sympy [A]  time = 45.7406, size = 165, normalized size = 0.95 \[ - \frac{4663 \sqrt{5} \operatorname{atanh}{\left (\frac{\sqrt{5} \left (- 8 x - 7\right )}{10 \sqrt{3 x^{2} + 5 x + 2}} \right )}}{8000000} - \frac{4663 \left (8 x + 7\right ) \sqrt{3 x^{2} + 5 x + 2}}{800000 \left (2 x + 3\right )^{2}} + \frac{4663 \left (8 x + 7\right ) \left (3 x^{2} + 5 x + 2\right )^{\frac{3}{2}}}{60000 \left (2 x + 3\right )^{4}} - \frac{4892 \left (3 x^{2} + 5 x + 2\right )^{\frac{5}{2}}}{13125 \left (2 x + 3\right )^{5}} - \frac{433 \left (3 x^{2} + 5 x + 2\right )^{\frac{5}{2}}}{1050 \left (2 x + 3\right )^{6}} - \frac{13 \left (3 x^{2} + 5 x + 2\right )^{\frac{5}{2}}}{35 \left (2 x + 3\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**8,x)

[Out]

-4663*sqrt(5)*atanh(sqrt(5)*(-8*x - 7)/(10*sqrt(3*x**2 + 5*x + 2)))/8000000 - 46
63*(8*x + 7)*sqrt(3*x**2 + 5*x + 2)/(800000*(2*x + 3)**2) + 4663*(8*x + 7)*(3*x*
*2 + 5*x + 2)**(3/2)/(60000*(2*x + 3)**4) - 4892*(3*x**2 + 5*x + 2)**(5/2)/(1312
5*(2*x + 3)**5) - 433*(3*x**2 + 5*x + 2)**(5/2)/(1050*(2*x + 3)**6) - 13*(3*x**2
+ 5*x + 2)**(5/2)/(35*(2*x + 3)**7)

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Mathematica [A]  time = 0.186408, size = 107, normalized size = 0.61 \[ \frac{-4663 \sqrt{5} \log \left (2 \sqrt{5} \sqrt{3 x^2+5 x+2}-8 x-7\right )+\frac{10 \sqrt{3 x^2+5 x+2} \left (191232 x^6+2893088 x^5+16376240 x^4+55403520 x^3+64140640 x^2+15759118 x-6554463\right )}{21 (2 x+3)^7}+4663 \sqrt{5} \log (2 x+3)}{8000000} \]

Antiderivative was successfully verified.

[In]  Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^8,x]

[Out]

((10*Sqrt[2 + 5*x + 3*x^2]*(-6554463 + 15759118*x + 64140640*x^2 + 55403520*x^3
+ 16376240*x^4 + 2893088*x^5 + 191232*x^6))/(21*(3 + 2*x)^7) + 4663*Sqrt[5]*Log[
3 + 2*x] - 4663*Sqrt[5]*Log[-7 - 8*x + 2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2]])/8000000

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Maple [A]  time = 0.023, size = 253, normalized size = 1.5 \[ -{\frac{13}{4480} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-7}}-{\frac{433}{67200} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-6}}-{\frac{1223}{105000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-5}}-{\frac{4663}{240000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-4}}-{\frac{4663}{150000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-3}}-{\frac{144553}{3000000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-2}}-{\frac{135227}{1875000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{5}{2}}} \left ( x+{\frac{3}{2}} \right ) ^{-1}}+{\frac{4663}{15000000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{3}{2}}}}-{\frac{23315+27978\,x}{1000000}\sqrt{3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}}}}+{\frac{4663}{8000000}\sqrt{12\, \left ( x+3/2 \right ) ^{2}-16\,x-19}}-{\frac{4663\,\sqrt{5}}{8000000}{\it Artanh} \left ({\frac{2\,\sqrt{5}}{5} \left ( -{\frac{7}{2}}-4\,x \right ){\frac{1}{\sqrt{12\, \left ( x+3/2 \right ) ^{2}-16\,x-19}}}} \right ) }+{\frac{676135+811362\,x}{3750000} \left ( 3\, \left ( x+3/2 \right ) ^{2}-4\,x-{\frac{19}{4}} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((5-x)*(3*x^2+5*x+2)^(3/2)/(3+2*x)^8,x)

[Out]

-13/4480/(x+3/2)^7*(3*(x+3/2)^2-4*x-19/4)^(5/2)-433/67200/(x+3/2)^6*(3*(x+3/2)^2
-4*x-19/4)^(5/2)-1223/105000/(x+3/2)^5*(3*(x+3/2)^2-4*x-19/4)^(5/2)-4663/240000/
(x+3/2)^4*(3*(x+3/2)^2-4*x-19/4)^(5/2)-4663/150000/(x+3/2)^3*(3*(x+3/2)^2-4*x-19
/4)^(5/2)-144553/3000000/(x+3/2)^2*(3*(x+3/2)^2-4*x-19/4)^(5/2)-135227/1875000/(
x+3/2)*(3*(x+3/2)^2-4*x-19/4)^(5/2)+4663/15000000*(3*(x+3/2)^2-4*x-19/4)^(3/2)-4
663/1000000*(5+6*x)*(3*(x+3/2)^2-4*x-19/4)^(1/2)+4663/8000000*(12*(x+3/2)^2-16*x
-19)^(1/2)-4663/8000000*5^(1/2)*arctanh(2/5*(-7/2-4*x)*5^(1/2)/(12*(x+3/2)^2-16*
x-19)^(1/2))+135227/3750000*(5+6*x)*(3*(x+3/2)^2-4*x-19/4)^(3/2)

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Maxima [A]  time = 0.776782, size = 456, normalized size = 2.62 \[ \frac{144553}{1000000} \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}} - \frac{13 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{35 \,{\left (128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right )}} - \frac{433 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{1050 \,{\left (64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right )}} - \frac{4892 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{13125 \,{\left (32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right )}} - \frac{4663 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{15000 \,{\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )}} - \frac{4663 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{18750 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} - \frac{144553 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{5}{2}}}{750000 \,{\left (4 \, x^{2} + 12 \, x + 9\right )}} - \frac{13989}{500000} \, \sqrt{3 \, x^{2} + 5 \, x + 2} x - \frac{4663}{8000000} \, \sqrt{5} \log \left (\frac{\sqrt{5} \sqrt{3 \, x^{2} + 5 \, x + 2}}{{\left | 2 \, x + 3 \right |}} + \frac{5}{2 \,{\left | 2 \, x + 3 \right |}} - 2\right ) - \frac{88597}{4000000} \, \sqrt{3 \, x^{2} + 5 \, x + 2} - \frac{135227 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}}{750000 \,{\left (2 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^8,x, algorithm="maxima")

[Out]

144553/1000000*(3*x^2 + 5*x + 2)^(3/2) - 13/35*(3*x^2 + 5*x + 2)^(5/2)/(128*x^7
+ 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187) - 43
3/1050*(3*x^2 + 5*x + 2)^(5/2)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^
2 + 2916*x + 729) - 4892/13125*(3*x^2 + 5*x + 2)^(5/2)/(32*x^5 + 240*x^4 + 720*x
^3 + 1080*x^2 + 810*x + 243) - 4663/15000*(3*x^2 + 5*x + 2)^(5/2)/(16*x^4 + 96*x
^3 + 216*x^2 + 216*x + 81) - 4663/18750*(3*x^2 + 5*x + 2)^(5/2)/(8*x^3 + 36*x^2
+ 54*x + 27) - 144553/750000*(3*x^2 + 5*x + 2)^(5/2)/(4*x^2 + 12*x + 9) - 13989/
500000*sqrt(3*x^2 + 5*x + 2)*x - 4663/8000000*sqrt(5)*log(sqrt(5)*sqrt(3*x^2 + 5
*x + 2)/abs(2*x + 3) + 5/2/abs(2*x + 3) - 2) - 88597/4000000*sqrt(3*x^2 + 5*x +
2) - 135227/750000*(3*x^2 + 5*x + 2)^(3/2)/(2*x + 3)

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Fricas [A]  time = 0.282381, size = 236, normalized size = 1.36 \[ \frac{\sqrt{5}{\left (4 \, \sqrt{5}{\left (191232 \, x^{6} + 2893088 \, x^{5} + 16376240 \, x^{4} + 55403520 \, x^{3} + 64140640 \, x^{2} + 15759118 \, x - 6554463\right )} \sqrt{3 \, x^{2} + 5 \, x + 2} + 97923 \,{\left (128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right )} \log \left (\frac{\sqrt{5}{\left (124 \, x^{2} + 212 \, x + 89\right )} + 20 \, \sqrt{3 \, x^{2} + 5 \, x + 2}{\left (8 \, x + 7\right )}}{4 \, x^{2} + 12 \, x + 9}\right )\right )}}{336000000 \,{\left (128 \, x^{7} + 1344 \, x^{6} + 6048 \, x^{5} + 15120 \, x^{4} + 22680 \, x^{3} + 20412 \, x^{2} + 10206 \, x + 2187\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^8,x, algorithm="fricas")

[Out]

1/336000000*sqrt(5)*(4*sqrt(5)*(191232*x^6 + 2893088*x^5 + 16376240*x^4 + 554035
20*x^3 + 64140640*x^2 + 15759118*x - 6554463)*sqrt(3*x^2 + 5*x + 2) + 97923*(128
*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x^2 + 10206*x + 2187)
*log((sqrt(5)*(124*x^2 + 212*x + 89) + 20*sqrt(3*x^2 + 5*x + 2)*(8*x + 7))/(4*x^
2 + 12*x + 9)))/(128*x^7 + 1344*x^6 + 6048*x^5 + 15120*x^4 + 22680*x^3 + 20412*x
^2 + 10206*x + 2187)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \int \left (- \frac{10 \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right )\, dx - \int \left (- \frac{23 x \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right )\, dx - \int \left (- \frac{10 x^{2} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\right )\, dx - \int \frac{3 x^{3} \sqrt{3 x^{2} + 5 x + 2}}{256 x^{8} + 3072 x^{7} + 16128 x^{6} + 48384 x^{5} + 90720 x^{4} + 108864 x^{3} + 81648 x^{2} + 34992 x + 6561}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5-x)*(3*x**2+5*x+2)**(3/2)/(3+2*x)**8,x)

[Out]

-Integral(-10*sqrt(3*x**2 + 5*x + 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), x) - Integral(-2
3*x*sqrt(3*x**2 + 5*x + 2)/(256*x**8 + 3072*x**7 + 16128*x**6 + 48384*x**5 + 907
20*x**4 + 108864*x**3 + 81648*x**2 + 34992*x + 6561), x) - Integral(-10*x**2*sqr
t(3*x**2 + 5*x + 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), x) - Integral(3*x**3*sqrt(3*x**2
+ 5*x + 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), x)

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GIAC/XCAS [A]  time = 0.304167, size = 622, normalized size = 3.57 \[ \frac{4663}{8000000} \, \sqrt{5}{\rm ln}\left (\frac{{\left | -4 \, \sqrt{3} x - 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right |}}{{\left | -4 \, \sqrt{3} x + 2 \, \sqrt{5} - 6 \, \sqrt{3} + 4 \, \sqrt{3 \, x^{2} + 5 \, x + 2} \right |}}\right ) - \frac{6267072 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{13} + 122207904 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{12} + 3852187808 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{11} + 18344551344 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{10} + 131374293680 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{9} + 134399090784 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{8} - 264419126976 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{7} - 1446858601104 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{6} - 6675760646156 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{5} - 5954681858370 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{4} - 10149146991914 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{3} - 3640765552263 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{2} - 2268672558411 \, \sqrt{3} x - 208833935688 \, \sqrt{3} + 2268672558411 \, \sqrt{3 \, x^{2} + 5 \, x + 2}}{16800000 \,{\left (2 \,{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )}^{2} + 6 \, \sqrt{3}{\left (\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right )} + 11\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x^2 + 5*x + 2)^(3/2)*(x - 5)/(2*x + 3)^8,x, algorithm="giac")

[Out]

4663/8000000*sqrt(5)*ln(abs(-4*sqrt(3)*x - 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2
+ 5*x + 2))/abs(-4*sqrt(3)*x + 2*sqrt(5) - 6*sqrt(3) + 4*sqrt(3*x^2 + 5*x + 2)))
- 1/16800000*(6267072*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^13 + 122207904*sqrt(3
)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^12 + 3852187808*(sqrt(3)*x - sqrt(3*x^2 +
5*x + 2))^11 + 18344551344*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^10 + 1313
74293680*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^9 + 134399090784*sqrt(3)*(sqrt(3)*x
- sqrt(3*x^2 + 5*x + 2))^8 - 264419126976*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^7
- 1446858601104*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^6 - 6675760646156*(
sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^5 - 5954681858370*sqrt(3)*(sqrt(3)*x - sqrt(3
*x^2 + 5*x + 2))^4 - 10149146991914*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^3 - 3640
765552263*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2))^2 - 2268672558411*sqrt(3)*
x - 208833935688*sqrt(3) + 2268672558411*sqrt(3*x^2 + 5*x + 2))/(2*(sqrt(3)*x -
sqrt(3*x^2 + 5*x + 2))^2 + 6*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) + 11)^7