Function Expression :
\[f(x)=ln(\sqrt{1+9x^2}+3x ) \]Domain
\[\left]-\infty, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\frac{9 x}{\sqrt{9 x^{2} + 1}} + 3}{3 x + \sqrt{9 x^{2} + 1}} \]\[f^{\,\prime}(x)=\frac{3}{\sqrt{9 x^{2} + 1}} \]
\[ \]
Integral
\[F(x) = x \log{\left(3 x + \sqrt{9 x^{2} + 1} \right)} - \frac{\sqrt{9 x^{2} + 1}}{3} \]Sign Table
Variation Table
Plot
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