How to solve this indefinite integral using integral substitution? So while working on some physics problem for differential equations,  I landed at this weird integral $$ \int \frac 1 {\sqrt{1-\left(\frac 2x\right)}}\,dx $$
So since there is a square root, I thought I could use trig substitution, but I couldn't find anything that works out. How can one solve this integral in a nice simple manner? If you can solve it in a different way, it is still fine. $Thank$ $you!$
This is the answer given to me by symbolab $$ 4\left(-\frac{1}{4\left(\sqrt{1-\frac{2}{x}}-1\right)}-\frac{1}{4\left(\sqrt{1-\frac{2}{x}}+1\right)}-\frac{1}{4}\ln \left|\sqrt{1-\frac{2}{x}}-1\right|+\frac{1}{4}\ln \left|\sqrt{1-\frac{2}{x}}+1\right|\right)+C $$

$u=\sqrt{1-\frac{2}{x}} \implies u^2=1-\frac{2}{x} \implies 2u du=\frac{2}{x^2} dx \implies du=\frac{1}{x^2} \frac{1}{u} dx \implies du=\frac{1}{x^2} \frac{1}{\sqrt{1-\frac{2}{x}}} dx \text{ So now back to the integral } \int \frac{1}{\sqrt{1-\frac{2}{x}}}dx=\int \frac{x^2}{x^2 \sqrt{1-\frac{2}{x}}}dx \\ \text{ now putting in the sub } \int (\frac{2}{1-u^2})^2 du \text{ Note: I solve for }x^2 \text{ from my sub to plug in also }  \\ \text{ That is I solved } u^2=1-\frac{2}{x} \text{ for } x \text{ then squared result } \\ \text{  Then you can do partial fractions. } $
