`intx/(sqrt(x+a)-sqrt(x+b)) dx`

Explanation

` int frac{x}{sqrt{x+a}-sqrt{x+b}} d x`
` = int frac{x}{sqrt{x+a}-sqrt{x+b}} times frac{sqrt{x+a}+sqrt{x+b}}{sqrt{x+a}+sqrt{x+b}} d x `
`
= int frac{x(sqrt{x+a}+sqrt{x+b})}{(sqrt{x+a})^{2}-(sqrt{x+b})^{2}} d x
`
`= int frac{x(sqrt{x+a}+sqrt{x+b})}{x+a-x-b} d x
`
`= frac{1}{a-b} int x(sqrt{x+a}+sqrt{x+b}) d x
`
`= frac{1}{a-b}[int x(sqrt{x+a}) d x+int x(sqrt{x+b}) d x]
`
`= frac{1}{a-b}[int(x+a-a)(sqrt{x+a}) d x+int(x+b-b)(sqrt{x+b}) d x] }`
`
=frac{1}{a-b}[int(x+a)(sqrt{x+a}) d x-a int(sqrt{x+a}) d x+int(x+b)(sqrt{x+b}) d x-b int(sqrt{x+b}) d x] `
`
=frac{1}{a-b}[int(x+a)^{frac{3}{2}} d x-a int(x+a)^{frac{1}{2}} d x+int(x+b)^{frac{3}{2}} d x-b int(x+b)^{frac{1}{2}} d x] `
`
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