2. `int_(0)^(5)(sqrt(x))/(sqrt(x)+sqrt(5-x))dx`

Prove that : int_(0)^(a) (sqrt(x))/(sqrt(x)+sqrt(a-x))dx=(a)/(2)

I=int_(2)^(3)(sqrt(x))/(sqrt(5-x)+sqrt(x))dx

Evaluate: int_(1)^(2) (sqrt(x))/(sqrt(3-x) + sqrt(x)) dx .

int_2^5 (sqrt(x))/(sqrt(x)+sqrt(7-x)) dx

Prove that : int_(2)^(7) (sqrt(x))/(sqrt(9-x)+sqrt(x))dx=(5)/(2)

int_(0)^(9)sqrt(x)/(sqrt(x)+sqrt(9-x))dx=(9)/(2)

int_(a)^(b) ( sqrt(x))/( sqrt(x) + sqrt(a+b-x))dx is equal to

Evaluate : (i) int_(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) int_(0)^(1)x cos(tan^(1)x)dx

Evaluate of each of the following integral: int_0^a(sqrt(x))/(sqrt(x)+sqrt(a-x))dx

By using the properties of definite integrals, evaluate the integrals int_0^a(sqrt(x))/(sqrt(x)+sqrt(a-x))dx