Question

evaluate :
$I=\int \frac{2x}{x^2-60x+6}dx$

Answer 1

$f\left(x\right)=\frac{\sqrt{2}\cos x-1}{\cot x-1},x\ne \frac{x}{4}$

$\underset{x\to \frac{x}{4}}{lim}f\left(x\right)=\underset{x\to \frac{x}{9}}{lim}\frac{\sqrt{2}\cos x-1}{\cot x-1}$ $|\frac{0}{0}$ from

$=\underset{x\to \frac{x}{4}}{lim}\frac{-\sqrt{2}\sin x}{-cose{c}^{2}x}$

$=\frac{-\sqrt{2}\times \frac{1}{\sqrt{2}}}{-(\sqrt{2}{)}^2}$

$\underset{x\to \frac{x}{4}}{lim}f\left(x\right)=\frac{1}{2}$

so f(x) to be contentious a $fx=\frac{x}{4}$

$\underset{x\to \frac{x}{4}}{lim}f\left(x\right)$ has to be equal to $f\left(\frac{x}{4}\right)$

$\therefore f\left(\frac{x}{4}\right)=\frac{1}{2}$