`Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto"` 4 (b) 1n 8 (c) 1n 4 (d) none of these

If int_(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6) then x is equal to

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If sin^(-1)x-cos^(-1)x=pi/6 , then x= 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

int_1^(e^(17))(pi"sin"(pi(log)_e x))/x dx is equal to (A) 2 (B) -2 (C) 2//pi (D) none of these

int(x^(n-1))/(sqrt(1+4x^(n)))dx

int_(-(pi)/(2))^((pi)/(2))(e^(|sin x|)cos x)/(1+e^(tan x))dx is equal to (a) e+1 (b) 1-(pi)/(2)e(c)e-1(d) none of these

If 8f(x)+6f((1)/(x))=x+5 and y=x^(2)(f(x), then (dy)/(dx) at x=-1 is equal to 0( b) (1)/(14)(c)-(1)/(4)(d) None of these

tan((pi)/(4)+(1)/(2)cos^(-1)x)+tan((pi)/(4)-(1)/(2)cos^(-1)x),x!=0 is equal to x( b) 2x( c) (2)/(x) (d) none of these

The minimum value of (x)/((log)_(e)x) is e(b)1/e(c)1(d) none of these

S_(n)=[(1)/(1+sqrt(n))+(1)/(2+sqrt(2n))+...+(1)/(n+sqrt(n^(2)))] then (lim_(n rarr oo)S_(n) is equal to (A)log2(B)log4 (C) log 8 (D) none of these