Function Expression :
\[f(x)=\frac{x^2+1}{\sqrt{x+2}} \]Domain
\[\left]-2, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x}{\sqrt{x + 2}} - \frac{x^{2} + 1}{2 \left(x + 2\right)^{\frac{3}{2}}} \]\[f^{\,\prime}(x)=\frac{3 x^{2} + 8 x - 1}{2 \left(x + 2\right)^{\frac{3}{2}}} \]
\[ \]
Integral
\[F(x) = \frac{2 \left(x + 2\right)^{\frac{5}{2}}}{5} - \frac{8 \left(x + 2\right)^{\frac{3}{2}}}{3} + 10 \sqrt{x + 2} \]Sign Table
Variation Table
Plot
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