Read the following sentences:

I want to write a letter.
I ought to have written a letter.
I can write a letter.
I could have written a letter.

In the first two sentences, the infinitives are used with to, and in the
next two sentences they are used without to. These two kinds of infinitives
are known by the names ‘to-infinitives’ and ‘bare infinitives’.

Uses of the bare infinitives
Infinitives are used without to after the auxiliaries shall, should, will,
would, can, could, may, might and might.

I will invite them.
I shall say what I like.
He can go.
It may rain this evening.
You must obey my instructions.

Dare and need are sometimes followed by bare infinitives. When they are used as principal verbs, they are followed by to infinitives.

After bid, watch, see, let, help, make, hear etc.

Infinitives are used without to after the verbs bid, watch, see, let, make,
help and hear.

They made the child drink the milk.
She helped the boy lift the box.
I bade him come.
Let them go.
We heard her cry.
We saw him do it.

After rather, better and had better

Infinitives are used without to after rather, better and had better

We would rather wait.
You had better mend your ways.
Better get some help while you can.

After certain prepositions like except, but, save, than
Certain prepositions like except, but, save and than are followed by
infinitives without to.

She did nothing except cry.
She can do everything but cook.
The men said they would die rather than surrender.

Note that bare infinitives can often be replaced by to-infinitives without altering the meaning of the sentence.

She can knit. (= She is able to knit.)
I bade him go. (= I asked him to go.)
Let him speak. (= Allow him to speak.)
I must go now. (= I ought to go now.)

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