A basic calculus question: The integral of e^2x is [(e^2x)/2] + C. Why do we only multiply by 1/2 without increasing the power?

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A basic calculus question: The integral of e^2x is [(e^2x)/2] + C. Why do we only multiply by 1/2 without increasing the power?

Mathematics
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you increase the power when it is x to the power of some number, when it is some number to the power or x or 2x, the rules are different.
Can you help me understand why the rule is different for e^2x than for x^2?
well, integration is (sort of) the opposite of differentiation, do you know why the derivative of x^2 is 2x?

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Other answers:

Yes, I understand the concept.
This is an analysis question more than it is a calculus question, I suppose. Looking for what is happening under the hood conceptually to make the exp function work differently when integrating that the way other functions like the power function for instance.
e^x will stay e^x when integrated or derivative because e is a number but the power is variable
Suzi20, okay, so if I had x^2N would I not increment that exponent when integrating because it includes the variable N?
if you are integrating with respect to x, then n is not a variable, it is a constant. this is really tough to explain, maybe try khan acadmy, http://www.khanacademy.org/ they have a video that proves that the derivative of e^x is e^x.
Okay, I see the two are different and obey different rules of the road. That is what I needed to confirm. I am brand new to this and trying to get it!! THANKS. Case closed for now.

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