For x=-1, equation: -2 = C i.e. C = -2

For x=0, equation: -1 = A+B-2 i.e. A+B = 1

For x=1, equation: 0 = 4A+2B-2

i.e. 2(A+B+A) = 2

⇨1+A = 1

⇨A = 0

And, B = 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)² and f₂(x) = e^x in the first integral and keeping the second integral intact,

, where c is the integrating constant