Question

For x > 0, let f(x) = ∫(lnt/(1 + t)) dt for t ∈ [0,x]. Find the function f(x) + f(1/x) and show that f(e) + f(1/e) = 1/2. Here, lnt = log_et

Answer 1

We have,

The given integral reduces to

Adding Eqs (i) and (ii), we get