Function Expression :
\[f(x)=\frac{(x-1 )ln x}{x+1}+1 \]Domain
\[\left]0, \infty\right[ \]Limits
\[ \]Derivate
\[ \]Integral
\[F(x) = x \log{\left(x \right)} - \begin{cases} - \operatorname{Li}_{2}\left(x + 1\right) & \text{for}\: \frac{1}{\left|{x + 1}\right|} < 1 \wedge \left|{x + 1}\right| < 1 \\i \pi \log{\left(x + 1 \right)} - \operatorname{Li}_{2}\left(x + 1\right) & \text{for}\: \left|{x + 1}\right| < 1 \\- i \pi \log{\left(\frac{1}{x + 1} \right)} - \operatorname{Li}_{2}\left(x + 1\right) & \text{for}\: \frac{1}{\left|{x + 1}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x + 1} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x + 1} \right)} - \operatorname{Li}_{2}\left(x + 1\right) & \text{otherwise} \end{cases} - \log{\left(x \right)} \log{\left(x + 1 \right)} - \operatorname{Li}_{2}\left(x e^{i \pi}\right) \]Sign Table
Variation Table
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