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