I attached a picture of my attempt, it seems to loop back... Maybe I made a mistake... If not how am I suppose to integrate this? Thank you!
Stop at the third line. Now move the integral of cos(x)*e^x on the right to the left. Then you are basically done. The third line gives you an equation where the only integral is cos(x)*e^x. Solve for it.
Oh I see, I got
But how did I get :
∫(e^xcosx dx)=e^xsinx+e^xcosx-∫(e^xcosx dx) (in the third step)
∫(e^xcosx dx)=∫(e^xcosx dx) (in the last step)
The two are not the same thing?