Let $b\in(0,1)$ and $c, n$ positive constants. Is it possible to find a function $a(x)$ independent from $b$ such that
$$\int_0^\infty a(x)x^2b^xdx=\frac{c^nb^n}{(c^n-b^n)^2}?$$
Thank you
2026-04-24 19:20:03.1777058403
Inverse of an integral
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