Function Expression :
\[f(x)=\frac{x^2}{(x-5 )(x-1 )} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, 5\right[ \cup \left]5, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow5} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow5} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x^{2} \cdot \left(6 - 2 x\right)}{\left(x - 5\right)^{2} \left(x - 1\right)^{2}} + 2 x \frac{1}{\left(x - 5\right) \left(x - 1\right)} \]\[f^{\,\prime}(x)=\frac{2 x \left(- x \left(x - 3\right) + \left(x - 5\right) \left(x - 1\right)\right)}{\left(x - 5\right)^{2} \left(x - 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = x + \frac{25 \log{\left(x - 5 \right)}}{4} - \frac{\log{\left(x - 1 \right)}}{4} \]Sign Table
Variation Table
Plot
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