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Límite de la función/ -4*sqrt((4+x)/(6+x))+(-1+6*x+6*x^2)/(-1-x-x^2-2*x^3)

Límite de la función -4*sqrt((4+x)/(6+x))+(-1+6*x+6*x^2)/(-1-x-x^2-2*x^3)

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Ha introducido [src] 
     /        _______                  2  \
     |       / 4 + x     -1 + 6*x + 6*x   |
 lim |- 4*  /  -----  + ------------------|
x->oo|    \/   6 + x              2      3|
     \                  -1 - x - x  - 2*x /
$$\lim_{x \to \infty}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right)$$ 
Limit(-4*sqrt((4 + x)/(6 + x)) + (-1 + 6*x + 6*x^2)/(-1 - x - x^2 - 2*x^3), x, oo, dir='-')
Método de l'Hopital
Tenemos la indeterminación de tipo
oo/-oo,

tal que el límite para el numerador es
$$\lim_{x \to \infty}\left(8 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 4 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 x^{2} + 4 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 x + 4 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} - 1\right) = \infty$$
y el límite para el denominador es
$$\lim_{x \to \infty}\left(- 2 x^{3} - x^{2} - x - 1\right) = -\infty$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to \infty}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to \infty}\left(\frac{6 x^{2} + 6 x - 4 \sqrt{\frac{x + 4}{x + 6}} \left(- 2 x^{3} - x^{2} - x - 1\right) - 1}{- 2 x^{3} - x^{2} - x - 1}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \left(8 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 4 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 x^{2} + 4 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 x + 4 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} - 1\right)}{\frac{d}{d x} \left(- 2 x^{3} - x^{2} - x - 1\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{- \frac{4 x^{4}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} - \frac{18 x^{3}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{4 x^{3}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 24 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} - \frac{10 x^{2}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2 x^{2}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 8 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x - \frac{10 x}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2 x}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 4 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 - \frac{8}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}}{- 6 x^{2} - 2 x - 1}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \left(- \frac{4 x^{4}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} - \frac{18 x^{3}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{4 x^{3}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 24 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} - \frac{10 x^{2}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2 x^{2}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 8 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x - \frac{10 x}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2 x}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 4 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 - \frac{8}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{2}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}\right)}{\frac{d}{d x} \left(- 6 x^{2} - 2 x - 1\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{- \frac{2 x^{7}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{41 x^{6}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{2 x^{6}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{8 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{317 x^{5}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{33 x^{5}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{2 x^{5}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{84 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{1129 x^{4}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{185 x^{4}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{21 x^{4}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{2 x^{4}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{236 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{4 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1800 x^{3}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{389 x^{3}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{59 x^{3}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{13 x^{3}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{28 x^{3}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{140 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1204 x^{2}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{244 x^{2}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{35 x^{2}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{7 x^{2}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{106 x^{2}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{24 x^{2}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 48 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + \frac{136 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1056 x}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{228 x}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{34 x}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{7 x}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{38 x}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{8 x}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 8 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + \frac{96 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} + 12 - \frac{576}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{144}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{24}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{6}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{18}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{4}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}}{- 12 x - 2}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \left(- \frac{2 x^{7}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{41 x^{6}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{2 x^{6}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{8 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{317 x^{5}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{33 x^{5}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{2 x^{5}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{84 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{1129 x^{4}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{185 x^{4}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{21 x^{4}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{2 x^{4}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{236 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{4 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1800 x^{3}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{389 x^{3}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{59 x^{3}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{13 x^{3}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{28 x^{3}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{140 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1204 x^{2}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{244 x^{2}}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{35 x^{2}}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{7 x^{2}}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{106 x^{2}}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{24 x^{2}}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 48 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + \frac{136 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} - \frac{1056 x}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{228 x}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{34 x}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{7 x}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{38 x}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{8 x}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + 8 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + \frac{96 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{5}}{x + 6} + \frac{28 x^{4}}{x + 6} + \frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}} - \frac{2 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}} + 12 - \frac{576}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{144}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{24}{\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{6}{\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{18}{x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{4}{x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}\right)}{\frac{d}{d x} \left(- 12 x - 2\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{x^{15}}{\frac{12 x^{18} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1224 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{58896 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1776288 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{37627200 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{594470016 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7259196672 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{70051557888 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{541537311744 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3378603571200 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{17051219767296 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{69443710083072 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{226523709554688 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{583778193997824 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1162401767424000 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1725474407841792 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1797987381018624 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1173581721501696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{361102068154368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{6 x^{17}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{576 x^{16}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25992 x^{15}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{732192 x^{14}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{14420448 x^{13}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{210712320 x^{12}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2365324416 x^{11}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{20833832448 x^{10}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{145765661184 x^{9}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{814707818496 x^{8}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3637362972672 x^{7}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{12897677205504 x^{6}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{35875791544320 x^{5}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{76634347732992 x^{4}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{121394797314048 x^{3}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{134368420036608 x^{2}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{92783170289664 x}{x^{3} + 18 x^{2} + 108 x + 216} 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\frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{7 x^{5}}{\frac{6 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{204 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2880 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{21600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{90720 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{202176 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{x^{5}}{\frac{3 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{102 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1440 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10800 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{45360 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{101088 x 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+ 18 x^{2} + 108 x + 216} + \frac{26531214336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{52686194688 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{71753195520 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{59982446592 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{23219011584 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{22434 x^{3}}{\frac{x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{72 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2388 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48304 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{664800 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{6573312 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48034944 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{262642176 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1074394368 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3247257600 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7047668736 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10400182272 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9352101888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3869835264 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{3346 x^{3}}{\frac{x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{66 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1992 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{36352 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{446688 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3893184 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{24675840 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{114587136 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{386871552 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{926028288 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1491499008 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1451188224 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{644972544 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{715 x^{3}}{\frac{x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{60 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1632 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{26560 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{287328 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2169216 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{11660544 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{44623872 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{119128320 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{211258368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{223948800 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{107495424 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{6781 x^{3}}{\frac{12 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{8208 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{77760 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{440640 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1492992 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2799360 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2239488 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{271 x^{3}}{\frac{6 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{240 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 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\frac{1159 x^{3}}{\frac{12 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{408 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5760 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{43200 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{181440 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{404352 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{373248 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{59 x^{3}}{\frac{6 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{204 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2880 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{21600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{90720 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{202176 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{185 x^{3}}{3 \left(\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{x^{3}}{\frac{12 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3744 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{20736 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{57024 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{62208 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{33 x^{3}}{\frac{3 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{84 x^{4} \sqrt{\frac{x}{x 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\frac{6573312 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48034944 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{262642176 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1074394368 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3247257600 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7047668736 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10400182272 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9352101888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3869835264 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{1872 x}{\frac{x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{66 x^{11} 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x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{17 x}{\frac{3 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{102 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1440 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10800 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{45360 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{101088 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{93312 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{320 x}{3 \left(\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{5 x}{\frac{12 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3744 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{20736 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{57024 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{62208 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{29 x}{\frac{3 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{84 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{936 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{14256 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15552 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{35 x}{6 \left(\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{x}{\frac{12 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{264 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2160 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{7776 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{13 x}{\frac{6 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{132 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1080 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{7 x}{6 \left(\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{25 x}{3 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 108 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{53 x}{3 \left(x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}\right)} - \frac{6 x}{x \sqrt{\frac{x}{x + 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\sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{664800 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{6573312 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48034944 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{262642176 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1074394368 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3247257600 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7047668736 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10400182272 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9352101888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3869835264 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{864}{\frac{x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{66 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1992 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{36352 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{446688 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3893184 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{24675840 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{114587136 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{386871552 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{926028288 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1491499008 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1451188224 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{644972544 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{216}{\frac{x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{60 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1632 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{26560 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{287328 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2169216 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{11660544 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{44623872 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{119128320 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{211258368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{223948800 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{107495424 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{212}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{50}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{2}{\frac{6 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{168 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1872 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28512 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{41}{6 \left(\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{1}{\frac{12 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{264 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2160 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{7776 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{19}{12 \left(\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{4}{3 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 108 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{19}{6 \left(x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}\right)} - \frac{1}{3 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 18 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} - \frac{2}{3 \left(x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{x^{15}}{\frac{12 x^{18} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1224 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{58896 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1776288 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{37627200 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{594470016 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7259196672 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{70051557888 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{541537311744 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3378603571200 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{17051219767296 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{69443710083072 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{226523709554688 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{583778193997824 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1162401767424000 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1725474407841792 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1797987381018624 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1173581721501696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{361102068154368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{6 x^{17}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{576 x^{16}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25992 x^{15}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{732192 x^{14}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{14420448 x^{13}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{210712320 x^{12}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2365324416 x^{11}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{20833832448 x^{10}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{145765661184 x^{9}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{814707818496 x^{8}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3637362972672 x^{7}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{12897677205504 x^{6}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{35875791544320 x^{5}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{76634347732992 x^{4}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{121394797314048 x^{3}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{134368420036608 x^{2}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{92783170289664 x}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{30091839012864}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{43 x^{14}}{\frac{8 x^{18} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{816 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{39264 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1184192 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25084800 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{396313344 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4839464448 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{46701038592 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{361024874496 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2252402380800 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{11367479844864 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{46295806722048 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{151015806369792 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{389185462665216 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{774934511616000 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1150316271894528 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1198658254012416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{782387814334464 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{240734712102912 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{x^{14}}{\frac{12 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1152 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{51984 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1464384 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{28840896 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{421424640 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4730648832 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{41667664896 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{291531322368 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1629415636992 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7274725945344 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25795354411008 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{71751583088640 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{153268695465984 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{242789594628096 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{268736840073216 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{185566340579328 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{60183678025728 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{121 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{12 x^{17}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1152 x^{16}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{51984 x^{15}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1464384 x^{14}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{28840896 x^{13}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{421424640 x^{12}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4730648832 x^{11}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{41667664896 x^{10}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{291531322368 x^{9}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1629415636992 x^{8}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7274725945344 x^{7}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25795354411008 x^{6}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{71751583088640 x^{5}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{153268695465984 x^{4}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{242789594628096 x^{3}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{268736840073216 x^{2}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{185566340579328 x}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{60183678025728}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{7 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{\frac{6 x^{16}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{540 x^{15}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{22752 x^{14}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{595680 x^{13}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10846368 x^{12}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{145634112 x^{11}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1491519744 x^{10}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{11884713984 x^{9}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{74457377280 x^{8}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{367963554816 x^{7}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1429581643776 x^{6}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4320187342848 x^{5}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9954667487232 x^{4}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{16906342809600 x^{3}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{19956740456448 x^{2}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{14627977297920 x}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5015306502144}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{3809 x^{13}}{\frac{24 x^{18} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2448 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{117792 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3552576 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{75254400 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1188940032 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{14518393344 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{140103115776 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1083074623488 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{6757207142400 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + 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\frac{1159 x^{3}}{\frac{12 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{408 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5760 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{43200 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{181440 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{404352 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{373248 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{59 x^{3}}{\frac{6 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{204 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2880 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{21600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{90720 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{202176 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{185 x^{3}}{3 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\frac{4}{x + 6}}}{x + 6} + \frac{2052 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{19440 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{110160 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{373248 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{699840 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{559872 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{1231 x^{2}}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{35 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\sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{5 x^{2}}{\frac{12 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3744 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{20736 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{57024 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{62208 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{55 x^{2}}{\frac{2 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{56 x^{4} \sqrt{\frac{x}{x + 6} + 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+ \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{150847488 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1075700736 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5955358464 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25595108352 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{84692957184 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{211873480704 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{387870363648 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{490501619712 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{383113691136 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{139314069504 \sqrt{\frac{x}{x + 6} + 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\frac{6573312 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48034944 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{262642176 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1074394368 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3247257600 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7047668736 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10400182272 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9352101888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3869835264 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{1872 x}{\frac{x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{66 x^{11} 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\frac{211258368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{223948800 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{107495424 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{68 x}{\frac{3 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{120 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2052 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{19440 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{110160 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{373248 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{699840 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{559872 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{1487 x}{3 \left(\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{17 x}{\frac{3 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{102 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1440 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10800 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{45360 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{101088 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{93312 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{320 x}{3 \left(\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} - \frac{5 x}{\frac{12 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3744 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{20736 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{57024 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{62208 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{29 x}{\frac{3 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{84 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{936 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{14256 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15552 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{35 x}{6 \left(\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{x}{\frac{12 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{264 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2160 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{7776 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{13 x}{\frac{6 x^{4} \sqrt{\frac{x}{x + 6} 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\frac{312 x^{3}}{x + 6} + \frac{1728 x^{2}}{x + 6} + \frac{4752 x}{x + 6} + \frac{5184}{x + 6}\right)} + \frac{\sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{2 \left(\frac{x^{3}}{x + 6} + \frac{16 x^{2}}{x + 6} + \frac{84 x}{x + 6} + \frac{144}{x + 6}\right)} + \frac{17915904}{\frac{x^{18} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{102 x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4908 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{148024 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3135600 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{49539168 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{604933056 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5837629824 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 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\sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{30091839012864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{4478976}{\frac{x^{17} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{96 x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{4332 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{122032 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2403408 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{35118720 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{394220736 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3472305408 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{24294276864 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{135784636416 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{606227162112 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2149612867584 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5979298590720 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{12772391288832 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{20232466219008 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{22394736672768 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{15463861714944 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5015306502144 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{746496}{\frac{x^{16} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{90 x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3792 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{99280 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1807728 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{24272352 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{248586624 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1980785664 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{12409562880 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{61327259136 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{238263607296 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{720031223808 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1659111247872 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2817723801600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3326123409408 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2437996216320 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{835884417024 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{186624}{\frac{x^{15} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{84 x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3288 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{79552 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1330416 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{16289856 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{150847488 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1075700736 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{5955358464 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{25595108352 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{84692957184 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{211873480704 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{387870363648 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{490501619712 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{383113691136 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{139314069504 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{20736}{\frac{x^{14} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{78 x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2820 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{62632 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{954624 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10562112 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{87474816 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{550851840 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2650247424 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9693623808 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{26531214336 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{52686194688 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{71753195520 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{59982446592 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{23219011584 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{5184}{\frac{x^{13} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{72 x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2388 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48304 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{664800 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{6573312 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{48034944 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{262642176 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1074394368 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3247257600 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{7047668736 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{10400182272 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{9352101888 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3869835264 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{864}{\frac{x^{12} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{66 x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1992 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{36352 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{446688 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{3893184 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{24675840 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{114587136 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{386871552 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{926028288 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1491499008 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1451188224 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{644972544 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} - \frac{216}{\frac{x^{11} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{60 x^{10} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{1632 x^{9} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{26560 x^{8} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{287328 x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{2169216 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{11660544 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{44623872 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{119128320 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{211258368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{223948800 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216} + \frac{107495424 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x^{3} + 18 x^{2} + 108 x + 216}} + \frac{212}{\frac{x^{7} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{40 x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{684 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{6480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{36720 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{124416 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{233280 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{186624 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{50}{\frac{x^{6} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{34 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{480 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{3600 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{15120 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{33696 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{2}{\frac{6 x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{168 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1872 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28512 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{31104 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} - \frac{41}{6 \left(\frac{x^{5} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{28 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{312 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{1728 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{4752 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{5184 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{1}{\frac{12 x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{264 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{2160 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{7776 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{10368 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}} + \frac{19}{12 \left(\frac{x^{4} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{22 x^{3} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{180 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{648 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6} + \frac{864 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}}{x + 6}\right)} + \frac{4}{3 x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 108 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} + \frac{19}{6 \left(x^{2} \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 12 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 36 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}\right)} - \frac{1}{3 x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 18 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}} - \frac{2}{3 \left(x \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}} + 6 \sqrt{\frac{x}{x + 6} + \frac{4}{x + 6}}\right)}\right)$$
=
$$-4$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 3 vez (veces)
Gráfica
Trazar el gráfico
Respuesta rápida [src] 
-4
$$-4$$
Abrir y simplificar
Otros límites con x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = -4$$
$$\lim_{x \to 0^-}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = 1 - \frac{4 \sqrt{6}}{3}$$
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = 1 - \frac{4 \sqrt{6}}{3}$$
Más detalles con x→0 a la derecha
$$\lim_{x \to 1^-}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = - \frac{4 \sqrt{35}}{7} - \frac{11}{5}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = - \frac{4 \sqrt{35}}{7} - \frac{11}{5}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(- 4 \sqrt{\frac{x + 4}{x + 6}} + \frac{6 x^{2} + \left(6 x - 1\right)}{- 2 x^{3} + \left(- x^{2} + \left(- x - 1\right)\right)}\right) = -4$$
Más detalles con x→-oo
    © Sr Examen