sin^(-1)((sin x+cos x)/(sqrt(2)))

Express sin^(-1)((sin x+ cos x)/(sqrt2)) , where -(pi)/(4) lt x lt (pi)/(4) , in the simplest form.

Express sin^(-1)((sin x+ cos x)/(sqrt2)) , where -(pi)/(4) lt x lt (pi)/(4) , in the simplest form.

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

int(cos x-sin x)/(sqrt(8-sin2x))dx=sin^(-1)((sin x+cos x)/(a))+c

int sqrt(cos x(cos^(3) x + sin 2x))dx = (1- sinx)/(k)sqrt(1+2 sin x-sin^(2)x) + sin^(-1)((1-sinx)/(sqrt(2)))+c then 3k =

int((sin x+cos x)/(sqrt(sin2x))dx

int(sin^(3)x cos x)/(sqrt(a-sin^(2)x)sqrt(a+sin^(2)x))backslash dx=

sin x+cos x=sqrt(2)sin5x

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))