For x=1, equation: 0 = A+B

For x=1/e, equation: -1 = B i.e. B = -1

So, A = 1

The given equation becomes

Tip – If f₁(x) and f₂(x) are two functions, then an integral of the form can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = 1/(1+logx) and f₂(x) = 1in the second integral and keeping the first integral intact,

, where c is the integrating constant