If `f(x)=underset(1)overset(x)int (log t)/(1+t) dt"then" f(x)+f((1)/(x))` is equal to

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

For x>0, let f(x)=int_(1)^(x)(log t)/(1+t)dt. Find the function f(x)+f((1)/(x)) and find the value of f(e)+f((1)/(e))

For x>0, let f(x)=int_(1)^(x)(log_(t)t)/(1+t)dt. Find the function f(x)+f((1)/(x)) and show that f(e)+f((1)/(e))=(1)/(2)

If f(x)=int_(1)^(x)(log t)/(1+t+t^(2))dx AA x<=1, then prove that f(x)f((1)/(x))

f(x)=int_(log ex)^(x)(dt)/(x+t), then find f'(x)

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

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

Let f be a real-valued function on the interval (-1,1) such that e^(-x) f(x)=2+underset(0)overset(x)int sqrt(t^(4)+1), dt, AA x in (-1,1) and let f^(-1) be the inverse function of f. Then [f^(-1) (2)] is a equal to:

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :