Though normal in speech, contracted forms are generally not used in university and research writing. For example, rather than don’t, isn’t and aren’t, you should write do not, is not and are not.

Examples of spoken forms and their formal written equivalents are given below.

Spoken form University and Research Writing
it’s it is
who’s who is
we’re we are
they’re they are
he’ll he will or shall
gonna going to or will
isn’t is not
ain’t am, is, are not or has, have not
aren’t are not
don’t do not
can’t cannot (see note)
didn’t did not
won’t will not
wouldn’t would not
shouldn’t should not

An exception to this rule is when you wish to specifically cite spoken language, for example in quoting interview responses.

Note: cannot is written as one word even in formal writing.