Do investigations ever change

[Corvo]

i have the old jagras quests there sitting ,if i make them all finished they dissapear and get better quests? I want upgrade my longsword and i need hunt tobi monsters so i just go without any quest cause theres no quest for him and go hunt him in free world ? do i alwa ys need a quest when i go out or can i explore only or is it waste of time

[Flyin' High]

Assigned quests progress the game's story and unlocks more monsters as you go
Optional quests will sometimes unlock new optional quests on completion or give you new interaction prompts with NPCs, which can also sometimes give you a new optional quest
investigations are unlocked mostly by tracking or hunting a monster, and the investigation is typically for that specific monster you're tracking or hunting

You can hunt in expeditions but it's not really worth the trouble most of the time if it's to get materials, monsters can leave the region abruptly during expeditions which isn't great for hunting, and it's difficult to know how much longer you have until they leave.
Optional quests are repeatable infinitely with a couple of exceptions, if you've hunted a tobi-kadachi in the assigned quests you should have an optional one to hunt another one. Optional quests with a speechbubble usually also unlock new items or upgrades.
As you hunt monsters or gather tracks you sometimes will unlock investigations for that monster, these are generally the best for getting materials but each investigation has different criteria (e.g sometimes you have less time or aren't allowed to faint) and can only be done a few times before you need to unlock a new investigation.
Generally I recommend just progressing the assigned quests until you unlock tobi-kadachi if you don't already have an optional quest or investigations for them.

tldr do the optional quest if you don't have any investigations for a tobi-kadachi
if you don't have the optional quest progress the story line, if you're really desperate for materials you can hunt them in expeditions but it's inefficient

[Seth Abercromby]

Investigations are something you select and activate manually. You have to speak to the character that handles bounties for the research commission, there you can check on the investigations you currently have available (capped to 100, with new ones replacing the oldest). Once you've selected an investigation to be active, it'll show up at the quest counter.

[LastTourniquet]

I believe there is a cap to how many investigations can be offered to you at a time. You need to get rid of some investigations to make room for new ones (you can simply delete them, you don't need to complete them!).

[Omnicide]

Tracking/Hunting/Capturing monsters contributes to investigations becoming available, though you won't always get the one you are looking for right away.

The list naturally cycles itself and is pretty long so you can go back and find lower ones if you need for quite some time. The number of investigations you can have 'registered' at a time is more limited. These are the ones you'll be able to see on the quest board, you can (un)register them at the resource center.

There's no need to ever actually delete any of them but it is possible to do so, be careful not to wipe the whole list unless you have the ones you want registered already.

There's also nothing innately wrong with just doing expeditions, you still get your carves, you still get bonus rewards at the end of the expedition for your hunts. You just don't get the investigation bonuses which is money and guaranteed reward rarity implied by the bronze/silver/gold squares. They are helpful when you are looking for rare drops but I don't do them that often myself.

Later on they become one of the ways of farming skill decorations for your gear when you start getting tempered monsters.

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Originally posted by LastTourniquet:

You need to get rid of some investigations to make room for new ones (you can simply delete them, you don't need to complete them!).

No, you don't need to manually delete investigations. New ones will replace the oldest ones that you haven't registered.

[Farsha]

Originally posted by #!:

No, you don't need to manually delete investigations. New ones will replace the oldest ones that you haven't registered.

This!

[Bobucles]

Investigations are collected randomly from doing things. You will automatically stockpile up to 400 idle investigations, then they start going into the trash.
Investigations have to be activated by choosing them in town. Up to 75 can be chosen, they will show up as your investigation quests. There is a button to automatically delete the rest.