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int1/(sqrt(x+a)+sqrt(x+b))\ dx...

`int1/(sqrt(x+a)+sqrt(x+b))\ dx`

Text Solution

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`=int1/(sqrt(x+a)+sqrt(x+b))\ dx`

Multiplying by its conjugate

`=int(sqrt(x+a)-sqrt(x+b))/((sqrt(x+a)-sqrt(x+b))(sqrt(x+a)+sqrt(x+b)))\ dx`

`=int(sqrt(x+a)-sqrt(x+b))/(a-b)\ dx`

`=(2(x+a)^(3/2))/(3(a-b))-(2(x+b)^(3/2))/(3(a-b))+C`

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