integral of constant raised to a power

Hi. What is the integral of a constant raised to a variable power? For example:

I imagined first that perhaps you could treat it like a variable raised to a constant power, but I'm not sure if that is correct, and my results didn't seem quite right when I looked at a graph of the function and an antiderivative together.

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Re: integral of constant raised to a power

Re: integral of constant raised to a power

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**infraRed** Hi. What is the integral of a constant raised to a variable power? For example:

If then so what is the answer to your question?

Re: integral of constant raised to a power

It might be even easier to recognize that , which is e to a constant times x. I'm guessing you know how to integrate that....

- Hollywood

Re: integral of constant raised to a power

I found in my calculus textbook a table of basic integration rules, which states that

Since I'm short on time, it's easiest just to go with that. I imagine that the hints provided above were leading me in that direction.

Re: integral of constant raised to a power

Yes,

is correct.

- Hollywood