integrate 1/[(x-a)(x-b)]^1/2

Let I = \int \frac{dx}{\sqrt{(x - a) (x - b)}} = \int \frac{dx}{\sqrt{x^{2} - (a + b) x + ab}} = \int \frac{dx}{\sqrt{x^{2} - (a + b) x + {(\frac{a + b}{2})}^{2} + ab - {(\frac{a + b}{2})}^{2}}} = \int \frac{dx}{\sqrt{{[x - (\frac{a + b}{2})]}^{2} - {(\frac{a - b}{2})}^{2}}} = \log |[x - (\frac{a + b}{2})] + \sqrt{{[x - (\frac{a + b}{2})]}^{2} - {(\frac{a - b}{2})}^{2}}| + C = \log |[x - (\frac{a + b}{2})] + \sqrt{x^{2} - (a + b) x + ab}| + C

integrate 1/[(x-a)(x-b)]​1/2