NEW FUNCTION
Function Expression :
\[f(x)=ln(1+e^x
)-\frac{1}{1+e^x} \]
Domain
\[\left]-\infty, \infty\right[ \]
Limits
\[\lim_{x \rightarrow-\infty}f(x) = -1 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{e^{x}}{e^{x} + 1} + \frac{e^{x}}{\left(e^{x} + 1\right)^{2}} \]
\[f^{\,\prime}(x)=\frac{e^{x} + 2}{4 \cosh^{2}{\left(\frac{x}{2} \right)}} \]
\[ \]
Integral
\[F(x) = x \log{\left(e^{x} + 1 \right)} - \int \frac{x e^{x}}{e^{x} + 1}\, dx - \int \frac{1}{e^{x} + 1}\, dx \]
Sign Table
Variation Table
Plot
Elapsed Time: 0.0134 seconds