$\displaystyle \int 2^t dt$

I know the derivative of $\displaystyle 2^t$ is $\displaystyle 2^tln2$, but I can't figure out the anitderivative

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- Apr 5th 2009, 04:53 PMcammywhiteAntiderivative of 2^t
$\displaystyle \int 2^t dt$

I know the derivative of $\displaystyle 2^t$ is $\displaystyle 2^tln2$, but I can't figure out the anitderivative - Apr 5th 2009, 04:54 PMMush
- Apr 5th 2009, 05:49 PMcammywhite
- Apr 5th 2009, 05:50 PMJhevon
- Apr 5th 2009, 05:58 PMcammywhiteCan I simplify the following function?
what do you mean?

Oh is it $\displaystyle 2^x$ - Apr 5th 2009, 06:05 PMJhevon
where is $\displaystyle x$ coming from? it is $\displaystyle 2^t$.

in general, $\displaystyle \int a^x~dx = \frac {a^x}{\ln a} + C$, for $\displaystyle a > 1$ a constant

and we derive this in the same way you did here, by considering $\displaystyle \int e^{x \ln a}~dx$ - Apr 5th 2009, 06:13 PMcammywhite
- Apr 5th 2009, 06:18 PMJhevon
- Apr 5th 2009, 06:31 PMKrizalid
- Apr 5th 2009, 06:32 PMJhevon
- Apr 5th 2009, 08:07 PMReckoner
- Apr 6th 2009, 07:00 PMJhevon