Function Expression :
\[f(x)=ln(1+\sqrt{x} ) \]Domain
\[\left[0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{2 \sqrt{x} \left(\sqrt{x} + 1\right)} \]\[f^{\,\prime}(x)=\frac{1}{2 \left(\sqrt{x} + x\right)} \]
\[ \]
Integral
\[F(x) = \sqrt{x} + x \log{\left(\sqrt{x} + 1 \right)} - \frac{x}{2} - \log{\left(\sqrt{x} + 1 \right)} \]Sign Table
Variation Table
Plot
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