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int1/(sqrt(x+1)+sqrt(x))\ dx...

`int1/(sqrt(x+1)+sqrt(x))\ dx`

Text Solution

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`=int1/(sqrt(x+1)+sqrt(x))\ dx`

Multiplying by its conjugate

`=int(sqrt(x+1)-sqrt(x))/((sqrt(x+1)-sqrt(x))(sqrt(x+1)+sqrt(x)))\ dx`

`=int(sqrt(x+1)-sqrt(x))/((x+1)-(x))\ dx`

`=int(sqrt(x+1)-sqrt(x)) dx`

`=(2(x+1)^(3/2))/(3)-(2(x)^(3/2))/(3)+C`

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