Function Expression :
\[f(x)=\frac{(x^3+2x^2-7x+4 )}{(x+1 )^2} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(- 2 x - 2\right) \left(x^{3} + 2 x^{2} - 7 x + 4\right)}{\left(x + 1\right)^{4}} + \frac{3 x^{2} + 4 x - 7}{\left(x + 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{x^{3} + 3 x^{2} + 11 x - 15}{x^{3} + 3 x^{2} + 3 x + 1} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} - 8 \log{\left(x + 1 \right)} - \frac{12}{x + 1} \]Sign Table
Variation Table
Plot
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