Let f:(0,∞)→R be given by f(x)=∫x1/xe(t+1t)dtt, then

Let f(x)=2x2−ln|x|,x≠0,thenf(x) is

Let f:(0,∞)→R be a differentiable function such that f′(x)=2−f(x)x for all xϵ(0,∞) and f(1)≠1. Then

Let f(x)= {x^2 ; x>=0

{ax ; x<0

Find a for which f(x) is monotonically increasing function at x=0.

Let g(x)=∫x0f(t)dt and f(x) satisfies the equation f(x+y)=f(x)+f(y)+2xy−1 for all x, yϵR and f′(0)=2 then

For x>0, let f(x)=∫x1log t1+t dt. Then f(x)+f(1x) is equal to