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Evaluate: intx/(sqrt(x+a)-sqrt(x+b))\ dx...

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

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`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} iint(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]`
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