How do you get the antiderivated of e^(2x). I'm having a massive smelly brain fart.

Question

anonymous · Answer

derivative* (I can't even spell)

amistre64 · Answer

lol ... or just multiply by 2/2

jim_thompson5910 · Answer

hint: let u = 2x, so du = 2dx ----> dx = du/2

So now you need to integrate e^(u)(du/2)

amistre64 · Answer

$$\frac{1}{2}\int 2e^{2x}dx$$

amistre64 · Answer

what i do is think of where e^2x would have come from:  well, e^2x of course, then derive it and adjust.

[e^2x]' = 2 e^2x ; so we have to divide off a two to get our answer

anonymous · Answer

that is so much work.  you know that it will look like 
$$?e^{2x}$$ because the input will never change. so just think "what would i differentiate to get 
$$e^{2x}$$ and you should come up with 
$$\frac{1}{2}e^{2x}$$ by dint of reasoning

amistre64 · Answer

any of this make any sense?

anonymous · Answer

I get the u-substitution version. Thanks guys