Integration with $e$ What are the steps in this integration : 

$$
\int4e^{t(u-4)}dt = \frac{-4}{u-4}e^{t(u-4)}
$$

I've calculated simpler integration formulas such as 
$$
\int x^2dt = \frac{x^3}{3} 
$$

but I'm unsure how integral above is calculated as there is an $e$ involved.
$$I=\int4e^{(u-4)t}dt=4\int e^{(u-4)t}dt$$
Substitute $$w=(u-4)t\\\Rightarrow dw=(u-4)dt\\\Rightarrow \frac{dw}{u-4}=dt$$
Hence $$I=4\int e^{w}\frac{dw}{u-4}=\frac{4}{u-4}\int e^wdw$$
Since $\frac{d}{dx}e^x=e^x$,
$$I=\frac{4}{u-4}e^w+C$$
Re-substitute:
$$I=\frac{4}{u-4}e^{(u-4)t}+C$$
Substituting $$m=t(u-4)$$ then you will get $$dm=(u-4)dt$$