f(x)=log_(2)((sin x-cos x+3sqrt(2))/(sqrt(2)))

Find the range of the function y = log_2 (sin x + cos x + 3sqrt2)/sqrt2

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

int_(0)^((pi)/(2))(cos^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))(log(sqrt(2)+1))

The domain of the function f(x)=log_(10)(sin(x-3))+sqrt(16-x^2) is.

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

3((1)/(2)+log_(3)(cos x+sin x))-2^(log_(2)(cos x-sin x))=sqrt(2)

The domain of the function f(x)=log_(10) sin(x-3)+sqrt(16-x^(2)) is

The range of f(x)=log_(sqrt(5))(sqrt(2)(sin x-cos x)+3) is

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

The domain of the function f(x)=sqrt(-log_(0.3) (x-1))/(sqrt(x^(2)+2x+8))" is"