If `2f(x)+f(-x)=1/xsin(x-1/x)`then the value of `int_(1/e)^e f(x)d x` is

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

If f(x)=1+1/x int_1^x f(t) dt, then the value of (e^-1) is

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

Let f(x)=e^(x)+2x+1 then find the value of int_(2)^(e+3)f^(-1)(x)dx

If f(x)=1+(1)/(x)int_(1)^(x)f(t)dt, then the value of (e^(-1)) is

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx