Function Expression :
\[f(x)=ln(1+e^x )+ln2 \]Domain
\[\left]-\infty, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \log{\left(2 \right)} \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{e^{x}}{e^{x} + 1} \]\[ \]
Integral
\[F(x) = x \log{\left(e^{x} + 1 \right)} - \int \left(- \frac{\log{\left(2 \right)}}{e^{x} + 1}\right)\, dx - \int \frac{x e^{x}}{e^{x} + 1}\, dx - \int \left(- \frac{e^{x} \log{\left(2 \right)}}{e^{x} + 1}\right)\, dx \]Sign Table
Variation Table
Plot
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