Least integral value ofx for which inequality `sin^-1(sin((2e^x+3)/(e^x+1)))>pi-5/2` holds is

Sum of all positive integral values of x satisfying the inequality ((x-1)(x-2)(sin x-2))/(e^((x-4))(x-101))>=0 is

If f(x)=1-3sqrt(e)x-ex^(3) then find least integral value of x satisfying the inequality f((e^(1/x))/(x-2))ltf(((e^((1)/(10))))/(8)sgn(1+sgn(|e^(x)-1|)))

The value of the integral int_(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx is

The least positive integral value of 'x' satisfying (e^(x)-2)(sin(x+(pi)/(4)))(x-log_(e)2)(sin x-cos x)<0

The number of integral values of X in the interval [0,pi] satisfying the inequality 2sin^(2)2x-3sin2x+1<0

he value of the integral int e^(sin^(2x))(cos x+cos^(3)x)sin xdx is