Q. 725.0( 1 Vote )

# 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

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