`(xsin x)/(1+cos x)`

int e ^(xsin x +cos x )((x ^(4) cos ^(3) x-x sin x +cos x)/(x ^(2) cos ^(2) x )) dx =

logsqrt((1-cos x)/(1+cos x))

Evaluate: int(cos2xsin4x dx)/(cos^4x(1+cos^2 2x)

xsin 2y = y cos 2x

if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

int_(0)^(pi) xsin x cos^(4)x dx=

(lim)_(x->0)((sqrt(1+xsin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/6 b. 6 c. 3 d. 2

IfI_1=int_0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I_2=int_0^(pi/2)(sin^2x)/(1+sin^2x)dx I_3=int_0^(pi/2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx ,t h e n I_1=I_2> I_3 (b) I_3> I_1=I_2 I_1=I_2=I_3 (d) none of these

If I_1=int_0^(pi//2)(cos^2x)/(1+cos^2x)dx , I_2=int_0^(pi//2)(sin^2x)/(1+sin^2x)dx and I_3=int_0^(pi//2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx , then (a) I_1=I_2 > I_3 (b) I_3> I_1=I_2 (c) I_1=I_2=I_3 (d) none of these

int x^2/(xsin x+cosx)^2dx is equal to