Learn Swedish: Jag kan inte bestämma mig.

In Swedish, the verb bestämma (to decide) is used reflexively as bestämma sig when it means to make up one's mind. Since the subject is jag (I), the reflexive pronoun has to match, so it becomes mig (myself). Literally, you are saying I cannot decide myself.

Can I just say Jag kan inte bestämma without mig?

You can, but it changes the meaning. Without the reflexive pronoun, bestämma needs a direct object. For example, you would say Jag kan inte bestämma reglerna (I cannot decide the rules). To express that you cannot choose between personal options, you must use the reflexive form.

Why is inte placed between the two verbs?

In a standard Swedish main clause, the negation inte (not) is placed immediately after the first verb. Here, the first verb is kan (can), so inte goes right after it, pushing the second verb bestämma further back in the sentence.

Why does bestämma end in an 'a' instead of the present tense 'r'?

Because it follows the modal verb kan. Just like in English, where we say 'I can decide' rather than 'I can decides', Swedish modal verbs are always followed by the infinitive (the dictionary form) of the main verb. The infinitive form here is bestämma.