Wikipedia:

The infinitive, either marked with to or unmarked, is used as the complement of many auxiliary verbs:

I will write a novel about talking beavers; I am really going to write it.

Another site:

Modals (can, might, will, etc.) don’t inflect, but they
occur in environments requiring a finite verb with no
(other) finite verb around.

Can you explain this apparent contradiction?

I’ve always believed that the bare infinitive is used after modal auxiliaries, not a finite verb.

Sorry, too complicated for me.  I only taught high school. But luck!

To me, the first is correct and the second is wrong. I’m near-certain the bare infintive is used always, not a finite verb.

I will write a novel about talking beavers; I am really going to write it.

Going to is an idiom used to expess the future tense.

I am going to win (as opposed to I am going to bed.

I prefer bed to any sports competition myself.

I agree. I don’t activities during which I am going to sweat.

I mow the lawn: don’t like that.  But in winter have to shovel snow, so dammed if I do, dammed if I don’t.  How about Holly cutting: work up a sweat there I imagine.

Absolutely!. It can make you bleed if you’re not careful.

Bleeding sweat, or sweating blood. Neither sound too exciting.

Have you noticed the site is fixed.  I’ve sent a glorious email to our WonderGog.

I just noticed. Wonder of wonders.

Wonder of Wonders: Wonder Woman: Wonder Gog: Wonder Vikki: Vikki Wonder Gog.

I was meaning I thought the first site is correct, while the second is not.

You’ve got me, I only taught high school, they never needed to know much, would not learn it anyhow.

Wikipedia:
The infinitive, either marked with to or unmarked, is used as the complement of many auxiliary verbs:
Another site:
Modals (can, might, will, etc.) don’t inflect, but they occur in environments requiring a finite verb with no (other) finite verb around. Can you explain this apparent contradiction?

I think what is meant on the second site is that the modal serves as the finite verb (I could, you could, he could, etc.) but doesn’t change forms like other finite verb (I run, you run, he runs). There is really no contradiction between sites one and two, since one refers to infinitives following auxiliaries, and the other discusses the auxiliaries themselves.

with no (other) finite verb around

I should’ve payed more attention to this part of the sentence, and I could’ve answered this myself. More tuna for me.