Integrate (e(-0.08)×0.8)^t w.r.t t

Question

How do you work it out? I know the answer is ((e^(-0.08)*0.8)^t)/ log(e^(-0.08)*0.8) but how do we get there?

Also, why can you not just calculate (0.8×e^(-0.08)) and let that equal x. Now, integral of x^t= (x^t+1)/t+1 ?

Answer 1

Hint

Write $0.8e^{0.08}=k$ so you have to integrate $k^t$ with respect to $t$. But $k^t=e^{t \log(k)}$.

I am sure that you can take from here.