I've just encountered the same problem but within my own application.
I didn't like the solution with copying the dll since it's not very convenient so I did some research and came up with the following programmatic solution. 
Basically, before doing any connections to SQL server, you have to add the sqljdbc_auth.dll to path.. which is easy to say:
PathHelper.appendToPath("C:\\sqljdbc_6.2\\enu\\auth\\x64");
once you know how to do it:
import java.lang.reflect.Field;
public class PathHelper {
    public static void appendToPath(String dir){
        String path = System.getProperty("java.library.path");
        path = dir + ";" + path;
        System.setProperty("java.library.path", path);
        try {
            final Field sysPathsField = ClassLoader.class.getDeclaredField("sys_paths");
            sysPathsField.setAccessible(true);
            sysPathsField.set(null, null);
        }
        catch (Exception ex){
            throw new RuntimeException(ex);
        }
    }
}
Now integration authentication works like a charm :).
Credits to https://stackoverflow.com/a/21730111/1734640 for letting me figure this out.