Function Expression :
\[f(x)=ln(2x+1 )-6e^x \]Domain
\[\left]- \frac{1}{2}, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow- \frac{1}{2}} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 6 e^{x} + \frac{2}{2 x + 1} \]\[f^{\,\prime}(x)=\frac{2 \left(- 3 \cdot \left(2 x + 1\right) e^{x} + 1\right)}{2 x + 1} \]
\[ \]
Integral
\[F(x) = x \log{\left(2 x + 1 \right)} - x - 6 e^{x} + \frac{\log{\left(2 x + 1 \right)}}{2} \]Sign Table
Variation Table
Plot
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