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\[\int\limits_{0}^{1} (9x ^{e}+e ^{x})dx\]
Do I use u substitution?

Wait I'm confused on the last post. \[\frac{ x ^{n+1} }{ n+1 }\]
Isn't that the anti-derivative?

is that what an integral is?

Exactly! An integral is the anti-derivative.

the first part is correct,
for e^x
\(\int e^xdx=e^x+c\)

oh yeah that's right because the integral of e^x is itself right?

Yup

Ok so what's next? or is that all I have to do with it?

It just says evaluate the integral

Oh wait I just realized I typed the problem out. There is no 9 in front of the x^e

*typed it out wrong lol

The answer you posted above was correct for the anti-derivative of x^e, just take out the 9 then.

stupid question how do you get e^-1 from e^1-e^0?

so e^1 = e
e^0 = 1
So e^1 - e^0 = e - 1