Question: How to find the inverse function of a variable in a definite integral?

In

I want to compute x__0 as a function of alpha. I tried fsolve but could not make it work (see attached).

What did I do wrong? Are there other ways in Maple to solve such problems?

I am stuck here and would very much appreciate help.

inverse_function_with_fsolve.mw

Update:

Its likely that the recently introduced warnings for definite integrals would have helped in this case to find a solution on my own. When I run this worksheet with Maple 2023, it immediately suggests the use of assumptions.

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