Question

integrate e^x seems pretty easy when x is just x but what about when x is more complicated like: integrate e^(-x/2)?

Answer 1

just use u substitution:
u = (-x/2)
du = (-1/2) dx

Answer 2

Now since you don't have (-1/2)dx in the original equation, multiply by -2 (so that it cancels out and becomes 1)

Answer 3

-2*Int(e^(-x/2) * (-1/2)dx)

Answer 4

-2*Int(e^u du)
-2*e^u + C

Answer 5

okay, I just busted out the u sub everytime I hit an e to the something and was starting to think I was just being unimaginative

Answer 6

now substitute back in for u:
-2*e^(-x/2) + C