Hi everyone! If you integrate e^[(-1/2)x] you get -2e^[(-1/2)x]+C for an answer. Can someone explain if you take the integral of e^[(-1/2)x^2] , why you don't get -2^[(-1/2)x^2] as an answer?
Is it because of some sort of reverse chain rule concept? I'm fuzzy on this. Thanks! :o)

Question

Hi everyone! If you integrate e^[(-1/2)x] you get -2e^[(-1/2)x]+C for an answer. Can someone explain if you take the integral of e^[(-1/2)x^2] , why you don't get -2^[(-1/2)x^2] as an answer?
Is it because of some sort of reverse chain rule concept? I'm fuzzy on this. Thanks! :o)

anonymous · Answer

@UnkleRhaukus @ganeshie8

anonymous · Answer

Never mind...I think I just realized something...
This approach to integrating I think may only work when the "power" is a constant.
Since the the power is actually another function ie:x^2, this nasty little thing doesn't behave very nicely and is not an elementary function at all!
That must be what this is.
Now that I think about it, I think Richard Feynman came up with a technique to solve these by dividing by its derivative or something like that.
Regardless, thank you for your help anyway but never mind! :o)

anonymous · Answer

If anyone has anything to add however, please do! :o)

unklerhaukus · Answer

what do you get when you differentiate   -2e^[(-1/2)x^2] ?

anonymous · Answer

don't know...one sec

anonymous · Answer

@UnkleRhaukus 
it should be 2xe^[(-1/2)x^2] ...why?