(v)cos2x log((cos x+sin x)/(cos x-sin x))

int cos2x*log((cos x+sin x)/(cos x-sin x))backslash dx

int cos2x*log((cos x+sin x)/(cos x-sin x))dx

(cos2x)/(cos x-sin x)=cos x+sin x

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

A: int (2cos x +3sin x)/(4cos x+5 sin x)dx= (-2)/(41)log|4cos x+5Sinx|+(23)/(41)x+c R: int (a cos x+b sin x)/(c cos x+d sin x)dx= (ac+bd)/(c^(2)+d^(2))x+(ad-bc)/(c^(2)+d^(2))log|c cos x+d sin x |+k

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .

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