For `x>0` ,if `f(x)=int_(1)^(x)(log_(c)t)/((1+t))dt` ,then `f(e)+f((1)/(e))` is equal to :

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

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 int_(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x) , then int_(0)^(1)f^(')(x) dx is equal to

If f(x)=int_(0)^(1)(dt)/(1+|x-t|),x in R . The value of f'(1//2) is equal to

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

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

If f(x)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))}, then f'((1)/( e )) is equal to

Let f(x)=int_(0)^(x)(e^(t))/(t)dt(xgt0), then e^(-a)[f(x+1)-f(1+a)]=

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