Function Expression :
\[f(x)=-x+ln(2x2+1 ) \]Domain
\[\left]- \frac{1}{4}, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow- \frac{1}{4}} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=-1 + \frac{4}{2 x 2 + 1} \]\[f^{\,\prime}(x)=\frac{3 - 4 x}{4 x + 1} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + x \log{\left(4 x + 1 \right)} - x + \frac{\log{\left(4 x + 1 \right)}}{4} \]Sign Table
Variation Table
Plot
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