Function Expression :
\[f(x)=\frac{2x^2+3x+5}{x+1} \]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
\[f^{\,\prime}(x)=\frac{4 x + 3}{x + 1} - \frac{2 x^{2} + 3 x + 5}{\left(x + 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x^{2} + 2 x - 1\right)}{x^{2} + 2 x + 1} \]
\[ \]
Integral
\[F(x) = x^{2} + x + 4 \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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