Function Expression :
\[f(x)=\frac{1}{2}x^2+x+ln(x+1 ) \]Domain
\[\left]-1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=x + 1 + \frac{1}{x + 1} \]\[f^{\,\prime}(x)=x + 1 + \frac{1}{x + 1} \]
\[f^{\,\prime}(x)=\frac{x \left(x + 1\right) + x + 2}{x + 1} \]
Integral
\[F(x) = \frac{x^{3}}{6} + \frac{x^{2}}{2} + x \log{\left(x + 1 \right)} - x + \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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