Single Variable CalculusIntegral FormulaIntegral with √[±(x-a)/(x-b)]On this pageIntegral with ±x−ax−b\sqrt{\pm\frac{x-a}{x-b}}±x−bx−a 79 ∫x−ax−b dx=(x−b)x−ax−b+(b−a)ln(∣x−a∣+∣x−b∣)+C\int{\sqrt{\frac{x-a}{x-b}}}\ \mathrm{d}x=(x-b)\sqrt{\frac{x-a}{x-b}}+(b-a)\ln{\left(\sqrt{\left|x-a\right|}+\sqrt{\left|x-b\right|}\right)}+C∫x−bx−a dx=(x−b)x−bx−a+(b−a)ln(∣x−a∣+∣x−b∣)+C Derivation 80 ∫x−ab−x dx=(x−b)x−ab−x+(b−a)arcsinx−ab−a+C\int{\sqrt{\frac{x-a}{b-x}}}\ \mathrm{d}x=(x-b)\sqrt{\frac{x-a}{b-x}}+(b-a)\arcsin{\sqrt{\frac{x-a}{b-a}}}+C∫b−xx−a dx=(x−b)b−xx−a+(b−a)arcsinb−ax−a+C Derivation