Function Expression :
\[f(x)=x+\sqrt{x^2+3x} \]Domain
\[\left]-\infty, -3\right] \cup \left[0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = - \frac{3}{2} \]\[\lim_{x \overset{<}{\rightarrow-3} }f(x) = -3 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x + \frac{3}{2}}{\sqrt{x^{2} + 3 x}} + 1 \]\[f^{\,\prime}(x)=\frac{x + \sqrt{x \left(x + 3\right)} + \frac{3}{2}}{\sqrt{x \left(x + 3\right)}} \]
\[f^{\,\prime}(x)=\frac{2 x + 2 \sqrt{x \left(x + 3\right)} + 3}{2 \sqrt{x \left(x + 3\right)}} \]
Integral
\[F(x) = \int \left(x + \sqrt{x^{2} + 3 x}\right)\, dx \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0076 seconds