Integrate under assumptions

I am trying to solve the following integral:
$$int_0^infty u^{sigma-1} expleft[-c u^sigmaright] mathrm{d}u$$
under the assumptions $sigma in (0,1)$ and $c>0$.
I know the result is
$$dfrac{1}{c sigma}.$$
However, using the following code in Mathematica

 Integrate[ Power[u, sigma - 1] * Exp[-c*Power[u, sigma]] , {u, 0, Infinity},  Assumptions -> {c > 0 && 0 < sigma && sigma <1 && Element[c, Reals] && Element[sigma, Reals]}]

I obtain

Integrate Integral of e^(-c u^sigma) u^(-1+sigma) does not converge on {0,[Infinity]}.

Surprisingly, deleting just the assumption $sigma <1$, it works as expected, that is running

Integrate[Power[u, sigma - 1] * Exp[-c*Power[u, sigma]] , {u, 0, Infinity}, Assumptions -> {c > 0 && 0 < sigma && Element[c, Reals] &&Element[sigma, Reals]}]

I obtain

1/(c sigma).

I do not understand why to add an additional a restriction changes the general result, but I do not find my mistake.

Edit: In the version 12.2 of Mathematica both the expressions work correctly. I assume they fixed the bug.

Integrate[
 Power[u, sigma - 1]*Exp[-c*Power[u, sigma]], {u, 0, Infinity}, 
 Assumptions -> {c > 0 && 0 < sigma && Element[c, Reals] && 
    Element[sigma, Reals]}]

(*  1/(c sigma)  *)