I=int(cos^(2)x*cos^(5)x)/(sin^(2)x+sin^(2)x)*sec(pi)/(x)*pi+sin x=

Show that int_(0)^(pi//4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4)x) = (pi)/(2)

(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4) (ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)

Find int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

int_(0)^((pi)/(2))((cos x)/(6-5sin x+sin^(2)x))dx

Show that int_(0)^(pi/4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4) x) = pi/2

int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=

(cos(pi-x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x

(cos(pi-x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x

int_(-pi//2)^(pi//2) ( sin ^(3) x . cos ^(3) x)/(cos^(2) x - sin ^(2) x) dx = . . . .