Function Expression :
\[f(x)=(2x+2 )ln(x+1 ) \]Domain
\[\left]-1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 \log{\left(x + 1 \right)} + \frac{2 x + 2}{x + 1} \]\[f^{\,\prime}(x)=2 \log{\left(x + 1 \right)} + 2 \]
\[f^{\,\prime}(x)=2 \left(\log{\left(x + 1 \right)} + 1\right) \]
Integral
\[F(x) = x^{2} \log{\left(x + 1 \right)} - \frac{x^{2}}{2} + 2 x \log{\left(x + 1 \right)} - x + \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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