Hello, I'm having difficulties with this indefinite integral:
(t^2)(e^4t) dt. Do I use a u/v substitution for this?
Thanks,
~CC
let v=t^2 and du = e^4t dv=2t and u=e^4t/4
$\displaystyle \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 - \int t\frac{e^{4t}}{2} dt $
use derive by part again for the integral let
v=t and du=e^4t dv=1 and u=e^4t/4
$\displaystyle \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -(t \frac{e^{4t}}{8} - \int \frac{e^{4t}}{8}dt)$
$\displaystyle \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -t \frac{e^{4t}}{8} + \frac{e^{4t}}{32} +c $