Function Expression :
\[f(x)=x-\frac{2}{\sqrt{x+1}} \]Domain
\[\left]-1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 + \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} \]\[f^{\,\prime}(x)=1 + \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} \]
\[f^{\,\prime}(x)=\frac{\left(x + 1\right)^{\frac{3}{2}} + 1}{\left(x + 1\right)^{\frac{3}{2}}} \]
Integral
\[F(x) = \frac{x^{2}}{2} - 2 \left(\begin{cases} 2 \sqrt{x + 1} & \text{for}\: \frac{1}{\left|{x + 1}\right|} < 1 \vee \left|{x + 1}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + 1} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 & \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + 1} \right)} & \text{otherwise} \end{cases}\right) \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0116 seconds