How "step by step" evaluate the following integral to the hypergeometric Guassian form 2F1.
$$\int \frac{(a-be^{-ct})^{\alpha-1}} {e^{t(\alpha-1)(g+f)}} dt $$
where:
$\alpha$ $\;$ is a parameter from 0 to 1
a, b, c, f, g $\;$ are parameters, real positive.
2026-03-25 07:40:12.1774424412
evaluate Integral using hypergeometric function (how to get to 2F1)
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