$\displaystyle \int 2^t dt$
I know the derivative of $\displaystyle 2^t$ is $\displaystyle 2^tln2$, but I can't figure out the anitderivative
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 $\displaystyle \int e^{x \ln a}~dx$