(2+3x^(2)-x sin x)/(x)

int_( equal to )^((x-sin x)^((3)/(2))){(6x^(2)sin^(2)((x)/(2)))/(x-sin x)+3x}dx is

int (3 cos 3x-2 sin 2x)/(cos 2x+ sin 3x)dx=

the value of lim_(x rarr0)((sin2x)/(3x)+(x sin x^(2))/(sin x^(3))) is

Prove that cos8x-cos5x=-2sin((13x)/(2))sin((3x)/(2))

(cos 4x sin 3x -cos 2x sin x )/(sin 4x sin x+ cos 6x cos x)= tan 2x

Solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sin x-2)(x+1)^(2)x)<=0 is

Evaluate the following limit : lim_(x rarr 0)(sin 2x + 3x)/(2x+sin 3x) .

Solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sin x-2)(x+1)^(2)x)<=0 is [(3)/(2),oo) b.(-oo,-1)uu[(3)/(2),oo) c.[-1,0)uu[(3)/(2),oo) d.R-{0,-1}

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. The value of ((alpha)/(2))^(2) + ((beta)/(2 )) ^(2) + ((gamma)/(2 ))^(2) =

Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin theta + (x -x ^(2)) cos theta + (x-1) sin theta cos theta =0 whose roots are alpha, beta , gamma. The value of ((alpha)/(2))^(2) + ((beta)/(2 )) ^(2) + ((gamma)/(2 ))^(2) =