Let `F(x)""=""f(x)""+""f(1/x),"w h e r e"f(x)=int_1^x(logt)/(1+t)dtdot` Then `2F(x)""= (1) `1/2` (2) 0 (3) 1 (4) 2

Let F(x) =f(x) +f((1)/(x)),"where" f(x)=int_(1)^(x) (log t)/(1+t) dt Then F (e) equals

For x >0,l e tf(x)=int_1^x((log)_e t)/(1+t)dtdot Find the function f(x)+f(1/x) and show that f(e)+f(1/e)=1/2dot

If f(x)=int_(1)^(x)(logt)(1+t+t^(2))dt AAxge1 , then prove that f(x)=f(1/x) .

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

Find (lim)_(x->1)f(x),""w h e r e""f(x)=[x^2-1, xlt=1-x^2-1, x >1

Iff(x)=int_1^x(logt)/(1+t+t^2)dxAAxlt=1,t h e np rov et h a tf(x)=f(1/x)dot

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

Statement-1: If f(x)=int_(1)^(x) (log_(e )t)/(1+t+t^(2))dt , then f(x)=f((1)/(x)) for all x gr 0 . Statement-2:If f(x) =int_(1)^(x) (log_(e )t)/(1+t)dt , then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

If f(x)=int_(1)^(x)(logt)/(1+t+t^(2)) , AAx ge 1 , then f(2) is equal to