" 19."quad (i)int_(0)^( pi/2)(dx)/(5+4sin x)

int_(0)^(pi//2)(1)/(5+13 sin x) dx=

int_(0)^(pi//2)(1)/(13+5sin x)dx=

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

" 0."int_(0)^( pi/4)(dx)/(2+sin^(2)x)=

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

Suppose _((pi)/(2))cos(pi sin^(2)x)dx and I_(2)int_(0)^(3)cos(2 pi sin^(2)x)dx and I_(3)=int_(0)^((pi)/(2))cos(pi sin x)dx, then

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

(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)

Evaluate: int_(0)^(pi/2)(dx)/(4sin^(2)x+5cos^(2)x)