Add SqLite to PHP5

I'm using Ubuntu 14.04 64 bit and installed the php5 package from the repositories which brought Apache with it. Php itself works but when I try to use new SQLiteDatabase([...]), the error

Fatal error: Class 'SQLiteDatabase' not found in [...] on line [...]

is printed.

The php.ini in use is /etc/php5/apache2/php.ini (according to phpinfo()). I noticed that in the php.ini the block

[sqlite]
; http://ift.tt/1iAwEzy
;sqlite.assoc_case = 0

[sqlite3]
;sqlite3.extension_dir =

doesn't set an extension directory. I tried finding files called sqlite3 on my system and putting a path to their directories in there, but it didn't work (and I restarted my machine after changing the php.ini).

The package php5-sqlite3 doesn't exist for Ubuntu 14.04 but php5-sqlite does and I installed it before trying anything else. I then also installed the packages sqlite3 and sqlite, but again: I doesn't work.