" 15."int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

int_(0)^((pi)/(2))(x sin x*cos x)dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x) dx . Hence, evaluate int_(0)^(pi//2) (sin x - cos x)/(1+ sin x cos x) dx.

int_(0)^((pi)/(2))(sin x cos x)/(1+sin^(4)x)dx

Prove that int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x)dx = 0 .

int_(0)^(pi//2)(a sin x + b cos x)/(sin x + cos x) dx=

int_(0)^((pi)/(2))(x)/(sin x+cos x)dx

int_(0)^(pi//2) ""(sin x - cos x)/( 1-sin x * cos x) dx is equal to

int_ (0) ^ ((pi) / (2)) (sin x-cos x) / ((sin x + cos x) ^ (2)) dx