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Now there is also mention of doing "a series expansion of the
integral at a=0", and the Taylor series is shown up to O(a^5).
This amounts to doing the series expansion of the integrand
e^(-(a t)) about (a t) = 0, then taking the definite integral
of each term, and simplifying slightly. If this is the
"textbook answer" for the numerical question that John refers
to, I only point out that if 0 << a t1, taking only 5 terms in
the series expansion may not get us very close to the correct
answer, and each term may involve significant errors due to
subtracting large quantities: a^n (t2^n - t1^n).