Límite de la función e^(-x)*sqrt(4+x)

Tenemos la indeterminación de tipo

oo/oo,

tal que el límite para el numerador es
$$\lim_{x \to \infty} \sqrt{x + 4} = \infty$$
y el límite para el denominador es
$$\lim_{x \to \infty} e^{x} = \infty$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to \infty}\left(e^{- x} \sqrt{x + 4}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to \infty}\left(\sqrt{x + 4} e^{- x}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \sqrt{x + 4}}{\frac{d}{d x} e^{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{e^{- x}}{2 \sqrt{x + 4}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \frac{1}{\sqrt{x + 4}}}{\frac{d}{d x} 2 e^{x}}\right)$$
=
$$\lim_{x \to \infty}\left(- \frac{e^{- x}}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \frac{1}{x \sqrt{x + 4} + 4 \sqrt{x + 4}}}{\frac{d}{d x} \left(- 4 e^{x}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{- \frac{x}{2 \sqrt{x + 4}} - \sqrt{x + 4} - \frac{2}{\sqrt{x + 4}}}{- 4 x^{3} e^{x} - 48 x^{2} e^{x} - 192 x e^{x} - 256 e^{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \left(- \frac{x}{2 \sqrt{x + 4}} - \sqrt{x + 4} - \frac{2}{\sqrt{x + 4}}\right)}{\frac{d}{d x} \left(- 4 x^{3} e^{x} - 48 x^{2} e^{x} - 192 x e^{x} - 256 e^{x}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{x}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)} + \frac{1}{x \sqrt{x + 4} + 4 \sqrt{x + 4}} - \frac{1}{\sqrt{x + 4}}}{- 4 x^{3} e^{x} - 60 x^{2} e^{x} - 288 x e^{x} - 448 e^{x}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \frac{1}{- 4 x^{3} e^{x} - 60 x^{2} e^{x} - 288 x e^{x} - 448 e^{x}}}{\frac{d}{d x} \frac{1}{\frac{x}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)} + \frac{1}{x \sqrt{x + 4} + 4 \sqrt{x + 4}} - \frac{1}{\sqrt{x + 4}}}}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{1}{\left(\frac{x^{2}}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} + \frac{x \sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{x}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} + \frac{\sqrt{x + 4}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{2}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{3}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)}\right) \left(\frac{16 x^{6} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{480 x^{5} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{5904 x^{4} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{38144 x^{3} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{136704 x^{2} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{258048 x e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{200704 e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{\frac{d}{d x} \frac{1}{\frac{x^{2}}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} + \frac{x \sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{x}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} + \frac{\sqrt{x + 4}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{2}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{3}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)}}}{\frac{d}{d x} \left(\frac{16 x^{6} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{480 x^{5} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{5904 x^{4} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{38144 x^{3} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{136704 x^{2} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{258048 x e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{200704 e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{- \frac{x^{2} \left(- \frac{4 x^{3}}{\sqrt{x + 4}} - 24 x^{2} \sqrt{x + 4} - \frac{48 x^{2}}{\sqrt{x + 4}} - 192 x \sqrt{x + 4} - \frac{192 x}{\sqrt{x + 4}} - 384 \sqrt{x + 4} - \frac{256}{\sqrt{x + 4}}\right)}{\left(8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}\right)^{2}} - \frac{x \sqrt{x + 4} \left(- 3 x^{2} - 24 x - 48\right)}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{2 x}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} - \frac{x \left(- \frac{x^{3}}{2 \sqrt{x + 4}} - 3 x^{2} \sqrt{x + 4} - \frac{6 x^{2}}{\sqrt{x + 4}} - 24 x \sqrt{x + 4} - \frac{24 x}{\sqrt{x + 4}} - 48 \sqrt{x + 4} - \frac{32}{\sqrt{x + 4}}\right)}{\left(x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}\right)^{2}} - \frac{x}{8 \sqrt{x + 4} \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{\sqrt{x + 4} \left(- 3 x^{2} - 24 x - 48\right)}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{\sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{1}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{2 \left(- \frac{x^{3}}{2 \sqrt{x + 4}} - 3 x^{2} \sqrt{x + 4} - \frac{6 x^{2}}{\sqrt{x + 4}} - 24 x \sqrt{x + 4} - \frac{24 x}{\sqrt{x + 4}} - 48 \sqrt{x + 4} - \frac{32}{\sqrt{x + 4}}\right)}{\left(x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}\right)^{2}} + \frac{3 \left(- \frac{x}{2 \sqrt{x + 4}} - \sqrt{x + 4} - \frac{2}{\sqrt{x + 4}}\right)}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)^{2}} - \frac{1}{2 \sqrt{x + 4} \left(x^{3} + 12 x^{2} + 48 x + 64\right)}}{\left(\frac{x^{2}}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} + \frac{x \sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{x}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} + \frac{\sqrt{x + 4}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{2}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{3}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)}\right)^{2} \left(\frac{32 x^{6} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{16 x^{6} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{1056 x^{5} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{480 x^{5} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{14208 x^{4} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{5904 x^{4} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{99904 x^{3} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{38144 x^{3} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{387840 x^{2} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{136704 x^{2} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{789504 x e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{258048 x \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{659456 e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{200704 \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}}\right)}\right)$$
=
$$\lim_{x \to \infty}\left(\frac{- \frac{x^{2} \left(- \frac{4 x^{3}}{\sqrt{x + 4}} - 24 x^{2} \sqrt{x + 4} - \frac{48 x^{2}}{\sqrt{x + 4}} - 192 x \sqrt{x + 4} - \frac{192 x}{\sqrt{x + 4}} - 384 \sqrt{x + 4} - \frac{256}{\sqrt{x + 4}}\right)}{\left(8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}\right)^{2}} - \frac{x \sqrt{x + 4} \left(- 3 x^{2} - 24 x - 48\right)}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{2 x}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} - \frac{x \left(- \frac{x^{3}}{2 \sqrt{x + 4}} - 3 x^{2} \sqrt{x + 4} - \frac{6 x^{2}}{\sqrt{x + 4}} - 24 x \sqrt{x + 4} - \frac{24 x}{\sqrt{x + 4}} - 48 \sqrt{x + 4} - \frac{32}{\sqrt{x + 4}}\right)}{\left(x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}\right)^{2}} - \frac{x}{8 \sqrt{x + 4} \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{\sqrt{x + 4} \left(- 3 x^{2} - 24 x - 48\right)}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{\sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{1}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{2 \left(- \frac{x^{3}}{2 \sqrt{x + 4}} - 3 x^{2} \sqrt{x + 4} - \frac{6 x^{2}}{\sqrt{x + 4}} - 24 x \sqrt{x + 4} - \frac{24 x}{\sqrt{x + 4}} - 48 \sqrt{x + 4} - \frac{32}{\sqrt{x + 4}}\right)}{\left(x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}\right)^{2}} + \frac{3 \left(- \frac{x}{2 \sqrt{x + 4}} - \sqrt{x + 4} - \frac{2}{\sqrt{x + 4}}\right)}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)^{2}} - \frac{1}{2 \sqrt{x + 4} \left(x^{3} + 12 x^{2} + 48 x + 64\right)}}{\left(\frac{x^{2}}{8 x^{3} \sqrt{x + 4} + 96 x^{2} \sqrt{x + 4} + 384 x \sqrt{x + 4} + 512 \sqrt{x + 4}} + \frac{x \sqrt{x + 4}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{x}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} + \frac{\sqrt{x + 4}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{2}{x^{3} \sqrt{x + 4} + 12 x^{2} \sqrt{x + 4} + 48 x \sqrt{x + 4} + 64 \sqrt{x + 4}} - \frac{3}{4 \left(x \sqrt{x + 4} + 4 \sqrt{x + 4}\right)}\right)^{2} \left(\frac{32 x^{6} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{16 x^{6} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{1056 x^{5} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{480 x^{5} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{14208 x^{4} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{5904 x^{4} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{99904 x^{3} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{38144 x^{3} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{387840 x^{2} e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{136704 x^{2} \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{789504 x e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{258048 x \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}} + \frac{659456 e^{2 x}}{\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}} + \frac{200704 \left(- \frac{x^{5} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} - \frac{13 x^{4} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{31 x^{4} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{72 x^{3} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{8 x^{3} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{131 x^{3} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{183 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{88 x^{3} e^{x}}{2 x^{2} + 16 x + 32} + \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} - \frac{4 x^{3} e^{x}}{x + 4} + \frac{4 x^{3} e^{x}}{\left(x + 4\right)^{2}} + \frac{408 x^{2} \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{144 x^{2} \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{322 x^{2} \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1037 x^{2} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{624 x^{2} e^{x}}{2 x^{2} + 16 x + 32} + \frac{168 x^{2} e^{x}}{x^{2} + 8 x + 16} - \frac{84 x^{2} e^{x}}{x + 4} + \frac{72 x^{2} e^{x}}{\left(x + 4\right)^{2}} + \frac{736 x \left(- 4 x - 16\right) e^{x}}{\left(2 x^{2} + 16 x + 32\right)^{2}} + \frac{816 x \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{776 x \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1420 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{1552 x e^{x}}{2 x^{2} + 16 x + 32} + \frac{1104 x e^{x}}{x^{2} + 8 x + 16} - \frac{552 x e^{x}}{x + 4} + \frac{408 x e^{x}}{\left(x + 4\right)^{2}} + \frac{1472 \left(- 2 x - 8\right) e^{x}}{\left(x^{2} + 8 x + 16\right)^{2}} - \frac{736 \left(- 3 x^{2} - 24 x - 48\right) e^{x}}{\left(x^{3} + 12 x^{2} + 48 x + 64\right)^{2}} - \frac{1512 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} + \frac{736 e^{x}}{2 x^{2} + 16 x + 32} + \frac{2288 e^{x}}{x^{2} + 8 x + 16} - \frac{1144 e^{x}}{x + 4} + \frac{736 e^{x}}{\left(x + 4\right)^{2}}\right) e^{2 x}}{\left(\frac{x^{5} e^{x}}{4 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} + \frac{13 x^{4} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{4 x^{4} e^{x}}{2 x^{2} + 16 x + 32} + \frac{131 x^{3} e^{x}}{2 \left(x^{3} + 12 x^{2} + 48 x + 64\right)} - \frac{72 x^{3} e^{x}}{2 x^{2} + 16 x + 32} - \frac{8 x^{3} e^{x}}{x^{2} + 8 x + 16} + \frac{4 x^{3} e^{x}}{x + 4} + \frac{322 x^{2} e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{408 x^{2} e^{x}}{2 x^{2} + 16 x + 32} - \frac{144 x^{2} e^{x}}{x^{2} + 8 x + 16} + \frac{72 x^{2} e^{x}}{x + 4} + \frac{776 x e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{736 x e^{x}}{2 x^{2} + 16 x + 32} - \frac{816 x e^{x}}{x^{2} + 8 x + 16} + \frac{408 x e^{x}}{x + 4} + \frac{736 e^{x}}{x^{3} + 12 x^{2} + 48 x + 64} - \frac{1472 e^{x}}{x^{2} + 8 x + 16} + \frac{736 e^{x}}{x + 4}\right)^{2}}\right)}\right)$$
=
$$0$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 6 vez (veces)