Awk - check that a field can be converted to an integer

Only print field if it can be converted to an integer

If I have this sample text file

1 cat
2 dog
3 7
4 fish5
5 22

I want my awk script to only print the field if it can be converted to an integer.

I don't want rows 1,2 and 4 to be printed.

example awk script

BEGIN {
   print "testing conversion to integer on " ARGV[1];
   myinteger = 0;  # my atmept to force this var to an integer
}
 myinteger = $2;
 myinteger != 0 { print $2; }

This doesn't work.

How can I get this to work?