Capture the results of the queries executed in mysqlclient in a file (no copy and paste)

One way is to copy the mysqlclient screen and paste it into a text file. The other way is to use tee.

mysql>
mysql> tee mysql-1.txt
Logging to file 'mysql-1.txt'
mysql> show databases;
+----------------+
| Database |
+----------------+
| test_db |
| db_3 |
| db_4 |
| db_5 |
+----------------+
4 rows in set (0.00 sec)

mysql> exit
Bye

[thiru@cu065 tmp]$ less mysql-1.txt

mysql> show databases;
+----------------+
| Database |
+----------------+
| test_db |
| db_3 |
| db_4 |
| db_5 |
+----------------+
4 rows in set (0.00 sec)

mysql> exit