Building native extensions.  This could take a while...
ERROR:  Error installing mysql:
ERROR: Failed to build gem native extension.
/usr/bin/ruby1.8 extconf.rb --with-mysql-dir=/usr/include/mysql
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... yes
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
--without-opt-dir
--with-opt-include
--without-opt-include=${opt-dir}/include
--with-opt-lib
--without-opt-lib=${opt-dir}/lib
--with-make-prog
--without-make-prog
--srcdir=.
--curdir
--ruby=/usr/bin/ruby1.8
--with-mysql-config
--without-mysql-config
--with-mysql-dir
--with-mysql-include
--without-mysql-include=${mysql-dir}/include
--with-mysql-lib
--without-mysql-lib=${mysql-dir}/lib
--with-mysqlclientlib
--without-mysqlclientlib
--with-mlib
--without-mlib
--with-mysqlclientlib
--without-mysqlclientlib
--with-zlib
--without-zlib
--with-mysqlclientlib
--without-mysqlclientlib
--with-socketlib
--without-socketlib
--with-mysqlclientlib
--without-mysqlclientlib
--with-nsllib
--without-nsllib
--with-mysqlclientlib
--without-mysqlclientlib
--with-mygcclib
--without-mygcclib
--with-mysqlclientlib
--without-mysqlclientlib
Gem files will remain installed in /usr/lib/ruby/gems/1.8/gems/mysql-2.8.1 for inspection.
Results logged to /usr/lib/ruby/gems/1.8/gems/mysql-2.8.1/ext/mysql_api/gem_make.out

Can be solved by installing libmysqlclient15-dev

# apt-get install libmysqlclient15-dev