I
think it all depends on whether it is used as part of an adverbial
phrase when making comparisons, in which case the infinitive or
simple form of the verb is the norm, or whether it is used as a
conjunction introducing clauses of comparison and similar in meaning
to in addition to, in which case the '-ing' pattern is required.
Let us compare the two usages:
as + adj + as + clause/phrase
as
+ adv + as + clause/phrase
For
example:
'I saw as many as three thousand people at the concert.'
'He was badly injured, but I did as much as I could
to make him comfortable.'
'I waited for as long as I dared, but when it got dark,
I went home.'
'Please come as quickly as you can. My father is very
ill.'
'The Irish played as well as the Scots but didn't convert
as many attempts on goal.'
'Richardson was as good an actor as Gieldgud (was).'
Note
that if an adjective is placed between as and the noun, a / an must be placed after the adjective.
What
is interesting in your example, Van Anh, is that if you say: 'I
can swim as well as cook well', you are stating that these are two
things that you can do, whereas if you say: 'I can swim as well
as I can cook', you are stating that you can do both these things
to an equal degree of proficiency.
When
we use as well as - similar in meaning and usage to in
addition to - as a subordinating conjunction, the '-ing' form
in the verb which follows is required:
'As well as playing tennis with Steve three times during
the week, I (also) play badminton with my wife at the weekend.'
'In addition to working on his Ph.D. dissertation, he
(also) translates articles for The Weekly Review.'
Note
here that the adverb as well is similar in meaning to as
well as and is often used as an alternative to too. Note
that both as well and too must be used at the end of
the sentence:
'We enjoyed a rare night out last night. We ate at Luigi's,
and went to the cinema as well.' ( = As well as eating
out, we (also) went to the cinema.)
'We eat well here in Sardinia. The wine is excellent
too.'
'My wife is a chemist and both her parents were chemists as
well.'
Note
the special use of as long as which is similar in meaning and
use to provided that. Both are more emphatic forms of if
and are used to introduce conditions:
'As long as you promise to help me, I don't mind cooking
for twelve people on Easter Sunday.'
'I'll join you on this skiing holiday, provided I can
have my own room at the hotel.'
