Hello John, I am not sure why you have an error when you press |ALPHA| |T|, but it might be because you have a variable called T in the directory that you are currently working, to check that press |VAR| and see if you have a variable T (you may have to press |NXT| to check the hole directory. If that is the case, purge the variable, press (I assume that you are working with RPN and soft menus) | ' | |ALPHA| |T| |ENTER| |TOOL| and select |PURGE| from the soft menu.
To find the antiderivative, you can use the command INT or INTVX, INT does not work with the default variable so you have to provide the name of the variable, INTVX in the other hand works with the default variable (saved in the VX variable in the CASDIR directory).
Let's try INTVX, make sure that 'X' is the default variable; press | ' | |6| |×| |ALPHA| |T| |×| |X| |ENTER| |Left-Shift| |CALC| and choose INVX from the soft menu, then press |EVAL| to simplify.
For the command INT, you have to enter the expression, which integral its to be evaluated, the variable name (in our case 'T') and a value of the upper limit of the integral, (the lower limit is always zero) we live this value as 'T' for this example; (leave 'X' as the default variable), press | ' | |6| |×| |ALPHA| |T| |×| |X| |ENTER| now enter the variable, press | ' | |ALPHA| |T| |ENTER|, duplicate the variable, press |ENTER|, now enter the command, |ALPHA| |ALPHA| | I | |N| |T| |ENTER|, then press |EVAL| to simplify.
I hope this helps you.
Juan