`int_(0)^( pi)( sin x*cos^(3)x)dx`

int_(0)^( pi)x*sin x*cos^(4)x*dx

" (8) "int_(0)^( pi)sin x*cos^(4)x*dx

int_(0)^(pi) x sin x cos^(2)x\ dx

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

int_(0)^( pi/4)(sin x-cos x)dx

int_(0)^( pi/4)(x*sin x)/(cos^(3)x)dx

int_(0)^(pi) x sin x. cos^(2) x dx

int_(0)^(pi//6) (sin x) /(cos^(3)x) dx is

If I_(1)=int_(0)^( pi)xf(sin^(3)x+cos^(2)x)dx and I_(2)=int_(0)^((pi)/(2))f(sin^(3)x+cos^(2)x)dx, then relate I_(1) and I_(2)

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