[int_(0)^( pi/4)sqrt((1-sin2x)/(1+sin2x))dx=],[" A.O log "2],[" B.O "(1)/(2)log2],[" D."4log2]

int_(0)^((pi)/(2))log(sin2x)dx

int_(0)^((pi)/(2))(2log cos x-log sin2x)dx

int_0^(pi/2)sin2x log(tanx)dx

int_(0)^(1)((sin^(-1)x)/(x))dx=(pi)/(2)(log2)

Show that int_(0)^(pi//2)(cos x)/((1+sin x )(2 + sin x))dx = log (4/3)

int_(0)^(1) ln Sin((pi x)/(2))dx=

[int_(-pi/4)^( pi/4)log(cos x+sin x)dx=(1)/(2)],[[" 1) "pi log2," 2) "-pi log2," 3) "-(pi)/(4)log2," 4) "-(pi)/(2)log2]]

Given int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=log2. Then the value of integral int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to (1)/(2)log2(b) is (pi)/(2)-log2(pi)/(4)-(1)/(2)log2(d)(pi)/(2)+log2

Show that int_(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3))