Mac OS X 10.5.8（Leopard）ruby1.9.3p0gemバージョン1.8.14sqlite3バージョン3.7.9の使用
Xcode 3.1.4もインストールしました（これがgemのインストールに使用されているかどうかはわかりません）。
sqlite3gemをフェッチしました
gem fetch sqlite3
それからそれを開梱しました
gem unpack sqlite3-1.3.5.gem
そして、新しいディレクトリにcdしました
cd sqlite3-1.3.5
実行
ruby setup.rb config
次に、ext/sqlite3にcdします
その後、makeを実行しました
これにより、次のエラーメッセージが返されます。
usernamemac:sqlite3 username$ make
compiling backup.c
compiling database.c
database.c: In function 'initialize':
database.c:47: error: 'SQLITE_OPEN_READWRITE' undeclared (first use in this function)
database.c:47: error: (Each undeclared identifier is reported only once
database.c:47: error: for each function it appears in.)
database.c:47: error: 'SQLITE_OPEN_CREATE' undeclared (first use in this function)
database.c:79: error: 'SQLITE_OPEN_READONLY' undeclared (first use in this function)
database.c:81: warning: implicit declaration of function 'sqlite3_open_v2'
database.c: In function 'set_sqlite3_func_result':
database.c:285: error: 'sqlite3_int64' undeclared (first use in this function)
database.c:285: error: syntax error before 'long'
make: *** [database.o] Error 1
gemのREADME.rdocファイルで、「オプションSQLITE_ENABLE_COLUMN_METADATAの有効化（詳細についてはwww.sqlite.org/compile.htmlを参照）」について読みましたが、何をすべきか理解できませんでした。
誰かが私がこの問題を解決するのを手伝ってくれますか？
バンドルインストール中にMySqlでエラーなどの他のアプローチを試し ましたが、 sqlite3 gemをインストールできませんが、これらは機能しませんでした。
更新：試してみると同様の問題があります
rails new app1 -d mysql
create vendor/plugins/.gitkeep
run bundle install
/Users/username/.rbenv/versions/1.9.3-p0/lib/ruby/gems/1.9.1/gems/railties-3.1.3/lib/rails/generators/app_base.rb:232: warning: Insecure world writable dir /usr/local in PATH, mode 040777
/Users/username/.rbenv/versions/1.9.3-p0/lib/ruby/gems/1.9.1/gems/bundler-1.0.21/lib/bundler.rb:209: warning: Insecure world writable dir /usr/local in PATH, mode 040777
Fetching source index for http://rubygems.org/
Installing rake (0.9.2.2)
...
Installing jquery-rails (1.0.19)
Installing mysql2 (0.3.11) with native extensions
Gem::Installer::ExtensionBuildError: ERROR: Failed to build gem native extension.
/Users/username/.rbenv/versions/1.9.3-p0/bin/ruby extconf.rb
checking for rb_thread_blocking_region()... yes
checking for rb_wait_for_single_fd()... yes
checking for mysql_query() in -lmysqlclient... no
checking for main() in -lm... yes
checking for mysql_query() in -lmysqlclient... no
checking for main() in -lz... yes
checking for mysql_query() in -lmysqlclient... no
checking for main() in -lsocket... no
checking for mysql_query() in -lmysqlclient... no
checking for main() in -lnsl... no
checking for mysql_query() in -lmysqlclient... no
checking for main() in -lmygcc... no
checking for mysql_query() in -lmysqlclient... no
*** extconf.rb failed ***
Could not create Makefile due to some reason, probably lack of
necessary libraries and/or headers. Check the mkmf.log file for more
details. You may need configuration options.
Provided configuration options:
--with-opt-dir
... (list of switches)
Gem files will remain installed in /Users/username/a/app1/vendor/bundle/gems/mysql2-0.3.11 for inspection.
Results logged to /Users/username/a/app1/vendor/bundle/gems/mysql2-0.3.11/ext/mysql2/gem_make.out
An error occured while installing mysql2 (0.3.11), and Bundler cannot continue.
Make sure that `gem install mysql2 -v '0.3.11'` succeeds before bundling.
私はすでにgemmysql2（0.3.11）をインストールしています。
アップデート2：実行時
gem update
sqlite3-ruby gemが更新されているときに、次のようになります。
Updating sqlite3-ruby
Building native extensions. This could take a while...
/Users/username/.rbenv/versions/1.9.3-p0/lib/ruby/site_ruby/1.9.1/rubygems/ext/builder.rb:48: warning: Insecure world writable dir /usr/local in PATH, mode 040777
ERROR: Error installing sqlite3-ruby:
ERROR: Failed to build gem native extension.
/Users/username/.rbenv/versions/1.9.3-p0/bin/ruby extconf.rb
checking for sqlite3.h... yes
checking for sqlite3_libversion_number() in -lsqlite3... yes
checking for rb_proc_arity()... yes
checking for sqlite3_initialize()... no
checking for sqlite3_backup_init()... no
checking for sqlite3_column_database_name()... no
checking for sqlite3_enable_load_extension()... no
checking for sqlite3_load_extension()... no
creating Makefile
make
compiling backup.c
compiling database.c
database.c: In function 'initialize':
database.c:47: error: 'SQLITE_OPEN_READWRITE' undeclared (first use in this function)
database.c:47: error: (Each undeclared identifier is reported only once
database.c:47: error: for each function it appears in.)
database.c:47: error: 'SQLITE_OPEN_CREATE' undeclared (first use in this function)
database.c:79: error: 'SQLITE_OPEN_READONLY' undeclared (first use in this function)
database.c:81: warning: implicit declaration of function 'sqlite3_open_v2'
database.c: In function 'set_sqlite3_func_result':
database.c:285: error: 'sqlite3_int64' undeclared (first use in this function)
database.c:285: error: syntax error before 'long'
make: *** [database.o] Error 1
Gem files will remain installed in /Users/username/.rbenv/versions/1.9.3-p0/lib/ruby/gems/1.9.1/gems/sqlite3-1.3.5 for inspection.
Results logged to /Users/username/.rbenv/versions/1.9.3-p0/lib/ruby/gems/1.9.1/gems/sqlite3-1.3.5/ext/sqlite3/gem_make.out
Gems updated: activesupport, activemodel, rack, journey, sprockets, actionpack, railties, coffee-rails, jquery-rails, minitest, rubygems-update, sass-rails
Installing ri documentation for activesupport-3.2.0.rc2...
ありがとう