Make your integer 5 8-bit bytes long (by adding a byte with a random value if your integer is 32-bit), that's 40 bits of data.
Cryptographically encrypt the 5 bytes of your integer using some key, which you probably want to keep private.
Slice the 40 encrypted bits into 8 5-bit parts. Encode each part using 32 alphanumeric characters. You may choose to use different 32 (out of the total 36) characters for each part.
The reverse operation is trivial.