How can I compute $\int\frac1{e^{ct}} dt $ $$ \displaystyle \int \dfrac{1}{e^{ct}} dt $$
How do I do this, I've tried substitution. Rewrite the above integral as $\displaystyle \int e^{-ct} dt $, then we have $u=-ct$, but at this point derivatives and integrals are confusing me. If we want $[e^u]'$, we just have $[e^u]u'$, but for integrals I've forgotten how to tackle this.

No need for the u-sub. The anti derivative is the e-power again. You just need to "account for" the derivative of your exponent, which is $-c$. So divide by that and you are done
