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

For x=2, equation: 0 = -A+1 i.e. 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-x) and f₂(x) = e^x in the second integral and keeping the first integral intact,

, where c is the integrating constant