$\lim_{x\to-1}\left(\frac{x^2+2x+4}{\left(x+1\right)^3}\right)=\mathrm{The\:limit\:does\:not\:exist}$
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Derivative
$\frac{d}{dx}\left(\frac{x^2+2x+4}{\left(x+1\right)^3}\right)=\frac{\left(2x+2\right)\left(x+1\right)^3+3\left(-x^2-2x-4\right)\left(x+1\right)^{2}}{\left(x+1\right)^{6}}$
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Integral
$\int\frac{x^2+2x+4}{\left(x+1\right)^3}dx=\frac{-1}{\left(x+1\right)^{2}}+\frac{1}{-2\left(x+1\right)^{2}}+\frac{2}{x+1}+\ln\left(x+1\right)+\frac{-2}{x+1}+C_0$
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