" (3) "e^(x)((cos x-sin x)/(sin^(2)x))

Evaluate : int e^(x) [(cos x - sin x)/(sin^(2) x)] dx.

int e^(x)(sin x-cos x)/(sin^(2)x)dx

"int e^(sin x)((x cos^(2)x-sin x)/(cos^(2)x))dx

e^(x)((2+ sin 2x)/(1 + cos 2 x ))

Evaluate : int_(0)^((pi)/(2))e^(x){cos(sin x)(cos^(2)x)/(2)+sin(sin x)(sin^(2)x)/(2)}dx

int ((sin x + cos x)(2-sin 2x))/(sin^(2)2x)dx= a) (sin x+cos x)/(sin 2x) +C b) (sin x- cos x)/(sin 2x)+C c) (sin x)/(sin x+cos x)+C d) (sin x)/(sin x-cos x)+C

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) .

The value of the definite integral int_(0)^( pi)((1-x sin2x)e^(cos^(2)x)+(1+x sin2x)e^(sin^(2)x)) dx is equal to

" "int(sin x cos x-1)/(sin^(2)x)*e^(x)dx

int(e^(x)-sin x)/(cos x+e^(x))dx