" 1."int sin(2x+(pi)/(2))dx" ."

If x in(-pi,pi) then int sqrt(1+sin((x)/(2)))dx

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

int_(pi)^((pi)/(2)) sin|2x|dx

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

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

If int_(0)^(pi//2) sin^(6) x dx = (pi)/(32) then int_(-pi)^(pi) (sin^(6)x + cos^(6) x)dx=

1) int_(-(pi)/(2))^(pi)sin^(-1)(sin x)dx 2) int_(-(pi)/(2))^((pi)/(2))(-(pi)/(2))/(sqrt(cos x sin^(2)x))dx 3) int_(0)^(2)2x[x]dx