Function Expression :
\[f(x)=ln(2x-5 )+ln(1+x )-2ln2 \]Domain
\[\left]\frac{5}{2}, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow\frac{5}{2}} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2}{2 x - 5} + \frac{1}{x + 1} \]\[f^{\,\prime}(x)=\frac{4 x - 3}{\left(x + 1\right) \left(2 x - 5\right)} \]
\[ \]
Integral
\[F(x) = x \log{\left(x + 1 \right)} + x \log{\left(2 x - 5 \right)} - 2 x - 2 x \log{\left(2 \right)} + \log{\left(x + 1 \right)} - \frac{5 \log{\left(2 x - 5 \right)}}{2} \]Sign Table
Variation Table
Plot
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