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

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

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

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

int_(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx

int_(0)^(9)[sqrt(t)]dt .

int_0^7sqrt(9+x)dx

STATEMENT-1 : int_(-3)^(3)|x|dx=9 STATEMENT-2 : int_(0)^(1)tan^(-1)xdx=(pi)/(4)-lnsqrt(2) STATEMENT-3 : int_(0)^(pi//2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx=(pi)/(4)

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

int(1)/(sqrt(x^(2) -9))dx

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