Function Expression :
\[f(x)=3x^3+2ln(x^2-4x ) \]Domain
\[\left]-\infty, 0\right[ \cup \left]4, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow4} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=9 x^{2} + \frac{2 \cdot \left(2 x - 4\right)}{x^{2} - 4 x} \]\[f^{\,\prime}(x)=\frac{9 x^{3} \left(x - 4\right) + 4 x - 8}{x \left(x - 4\right)} \]
\[ \]
Integral
\[F(x) = \frac{3 x^{4}}{4} + 2 x \log{\left(x^{2} - 4 x \right)} - 4 x - 8 \log{\left(x - 4 \right)} \]Sign Table
Variation Table
Plot
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