The value of `int_2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s____`

Explanation

Consider `I=int_{2}^{3} frac{sqrt{x}}{sqrt{5-x}+sqrt{x}} d x`

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therefore I=int_{2}^{3} frac{sqrt{5-x}}{sqrt{x}+sqrt{5-x}} d x`



by add Eqs. (i) and (ii), we obtain

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2 I=int_{2}^{3} frac{sqrt{x}+sqrt{5-x}}{sqrt{x}+sqrt{5-x}} d x `

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=int_{2}^{3} 1 d x=3-2=1 `

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