i know this probably seems really trivial, but in college calc we basically have to teach ourselves.. and i don't understand where i'm going wrong >.<

the problem is, integral (e^x)(cosx)dx

so i figured this is something you'd go about by using parts

u= e^x v= sinx

du= e^xdx dv= cosxdx

then you get e^x(sinx)- integral e^x(sinx)

doing parts again.. u= sin x v= e^x

du= cosxdx dv= e^xdx

and it seems like i'm going to get e^x(sinx)-e^x(sinx) * integral (e^x)(cosx)dx which is where i started..

this is a mistake that i often make in parts.. please help? i need to be able to understand/explain what i did