(2)[ln(2x+ 1)]/2+c

(3) sin e x+c

(4)ln(e^x+2)+c

(5) e (x+ 1)+c, where c is a constant.

The first derivative on the right can get the formula on the left, and you can check your own right and wrong.

These are all contents of calculus. If you are in college, there are similar examples and many formulas in mathematical analysis books. Just remember them. Actually, you weren't that skilled at first, but you've been practicing.