`int_0^(pi/4)sin^(- 1)sqrt(x/(a+x))dx`

int_0^(pi/2) sin x dx

int_(0)^(pi^(2)//4) sin sqrt(x)dx equals to

If I_(1)=int_(0)^( pi/2)(sin x)^(sqrt(3)+1)dx,I_(2)=int_(0)^(pi/2)(sin x)^(sqrt(3)-1))dx then (I_(1))/(I_(2))=

int_0^1 sin^-1x/sqrt(1+x)dx

int_(0)^( pi/4)sin|x|dx

int_(0)^(pi//2)tan^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]\ dx

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

int_(0)^(pi)(cos x)/(1+sqrt(sin x))dx=