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

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- Oct 22nd 2009, 10:32 AMcalvin_coolidgeIntegration problem
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

- Oct 22nd 2009, 10:56 AMtonio
- Oct 22nd 2009, 11:03 AMAmer
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 $