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Evaluate: int0^1 1/(1+x+sqrt(x))dx...

Evaluate: `int_0^1 1/(1+x+sqrt(x))dx`

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`int_(0)^(1)(1)/(sqrt(1+x)+sqrtx)dx`
`=int_(0)^(1)(1)/(sqrt(1+x)+sqrtx)xx(sqrt(1+x)-sqrtx)/(sqrt(1+x)-sqrtx)dx`
`=int_(0)^(1)(sqrt(1+x)-sqrtx)/(1+x-x)dx`
`=int_(0)^(1)(sqrt(1+x)-sqrtx)dx`
`=int_(0)^(1)(1+x)^((1)/(2))dx-int_(0)^(1)x^((1)/(2))dx`
`=[((1+x)^((3)/(2)))/(3//2)]_(0)^(1)-[(x^((3)/(2)))/(3//2)]_(0)^(1)=(2)/(3)[(1+x)^((3)/(2))]_(0)^(1)-(2)/(3)[(x^((3)/(2)))]_(0)^(1)`
`(2)/(3)[(2^((3)/(2))-1^((3)/(2)))-(2)/(3)(1-0)]`
`=(2)/(3)(2sqrt2-1-1)=(2)/(3)(2sqrt2-2)=(4)/(3)(sqrt2-1)`
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