So before anyone asks yes this is a homework question but my professor has allowed us to use the internet for help. Anyways my professor would like us to evaluate this integral by parts. $$ \int t \sec^2 dt $$
Although when I tried it I got this. 
. This seems to easy to me and I feel that I am doing something wrong and I was hoping someone could explain to me what that is.
Given $\int t\sec^2(t)\ dt$
By integration by parts $u=t, v^{\prime}=\sec^2t$
$$=t\tan(t)-\int\tan(t)\ dt$$$$=t\tan(t)+\ln|\cos(t)|+C$$