How to integrate : $\sqrt{\frac{a-x}{x-b}}$ Problem : 
How to integrate : $\sqrt{\frac{a-x}{x-b}}$
Unable to find the substitution for this : 
$\sqrt{\frac{a-x}{x-b}}$
Please help how to proceed ...........thanks..

Why so much regress maths in simple Solutions.
I think it's a good solution.
$$\begin{align}&\int\sqrt{\frac{a-x}{x-b}}dx\\ & =\int \frac{a-x}{\sqrt{(a-x)(x-b)}} dx \\ &= \int \frac{\frac12(a+b-2x)}{\sqrt{(a-x)(x-b)}} dx+\int \frac{(\frac a2-\frac b2)}{\sqrt{(a-x)(x-b)} } dx \\ &=\sqrt{(a-x)(x-b)}+\frac{(a-b)}{2}\int\frac{dx}{\sqrt{(\frac{a+b}2)^2-(x-\frac{a+b}2)^2-ab}}\\ &=\sqrt{(a-x)(x-b)}+\frac{(a-b)}{2}\int\frac{dx}{\sqrt{{{(\frac{a-b}2)^2}}-(x-\frac{a+b}2)^2}}\\ &=\sqrt{(a-x)(x-b)}+\left(\frac{a-b}2\right)\arcsin\left(\frac{x-\frac{a+b}2}{\frac{a-b}{2}}\right)+C\end{align}$$
