Let `int(10lnx)/(x^(2))dx=f(x),` for all positive x. If `f(e )=(1)/(e )`, then `f(2)+f(4)` is equal to

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

Let f(x)=(x^2-x)/(x^2+2x) then d(f^(-1)x)/(dx) is equal to

int (f'(x))/( f(x) log(f(x)))dx is equal to

If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f'(1)=1, then f(e) is.

If f (6-x ) =f (x), for all then 1/5 int _(2)^(3) x [f (x) + f (x+1)]dx is equal to :

If f(x) = log_(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to :

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

Let f(x)=sinx,g(x)=x^(2) and h(x)=log_(e)x. If F(x)=("hog of ")(x)," then "F''(x) is equal to

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for all x,y, in R, if int_0^2 f(x)dx=alpha, then int_-2^2 f(x) dx is equal to