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