The value of `int_2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dx` is ______

Explanation

Let `I=int_(2)^(3)(sqrt(x))/(sqrt(5-x)+sqrt(x))dx` . . . (i)
`rArrI=int_(2)^(3)(sqrt(2+3-x))/(sqrt((2+3)-(5-x))+sqrt(2+3-x))dx`
`rArr I=int_(2)^(3)(sqrt(5-x))/(sqrt(x)+sqrt(5-x))dx` . . . (ii)
On adding Eqs . (i) and (ii) , we get
`2I=int_(2)^(3)(sqrt(x)+sqrt(5-x))/(sqrt(5-x)+sqrt(x))dx rArr 2I = int_(2)^(3)1 dx =1 rArr I=(1)/(2)`