This word is too popular. It is freely used where some other word such as need, cause, impose, necessitate, involve, might be more appropriate, or at least make a refreshing change. Sometimes entail intrudes where no verb is needed, a common habit of involve.
a statement in writing that you are willing to bear the cost entailed of opening the case, withdrawing this amount and resealing.
If entailed is used, the preposition should be in.