" 3.(i) "(x)/(1+sin x)

Find real x such that (3+2i sin x)/(1-2i sin x) is purely real.

" 4.(i) "int(sin x)/(1-sin^(2)x)dx

I= int ( sin 2 x)/( 1+ sin^(2) x) dx .

"I=int(sin x)/(1+sin x)*dx

Evaluate: (i) int(1)/(sin^(3)x cos^(5)x)dx (ii) int(1)/(sin^(3)x cos x)dx

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

Evaluate: (i) int(1+cos x)/((x+sin x)^(3))dx (ii) int(cos x-sin x)/(1+sin2x)dx

Evaluate: (i) int(sin2x)/(sin5x sin3x)dx (ii) int(1+cot x)/(x+log sin x)dx