Function Expression :
\[f(x)=\frac{\sqrt{1-x}}{2x-6} \]Domain
\[\left]-\infty, 1\right] \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 \sqrt{1 - x}}{\left(2 x - 6\right)^{2}} - \frac{1}{2 \sqrt{1 - x} \left(2 x - 6\right)} \]\[f^{\,\prime}(x)=\frac{x + 1}{4 \sqrt{1 - x} \left(x - 3\right)^{2}} \]
\[ \]
Integral
\[F(x) = \begin{cases} i \sqrt{x - 1} - \sqrt{2} i \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x - 1}}{2} \right)} & \text{for}\: \left|{x - 1}\right| > 2 \\i \sqrt{x - 1} - \sqrt{2} i \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x - 1}}{2} \right)} & \text{otherwise} \end{cases} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0035 seconds