Question

If L = ∫(log(1 + x)/(1 + x2)) dx for x ∈ [0,1] and M = ∫log(1 + tanθ) dθ for θ ∈ [0,π/4] such that L + M = (π/A)log B, find the value of A + B + 3.

Answer 1

Let

Let x = tan θ

dx = sec2 θ dθ

and Let

So, A = 4 and B = 2

Hence, the value of

A + B + 3 = 9