Evaluate the following integrals:
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) = ex in the first integral and keeping the second integral intact,
, where c is the integrating constant