Function Expression :
\[f(x)=1+ln(2x-1 )-x \]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
\[f^{\,\prime}(x)=-1 + \frac{2}{2 x - 1} \]\[f^{\,\prime}(x)=\frac{3 - 2 x}{2 x - 1} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + x \log{\left(2 x - 1 \right)} - \frac{\log{\left(2 x - 1 \right)}}{2} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0048 seconds