Integration problem

• Oct 22nd 2009, 10:32 AM
calvin_coolidge
Integration 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 AM
tonio
Quote:

Originally Posted by calvin_coolidge
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

First do integration by parts: $\displaystyle u=t^2 \Longrightarrow u'=2t\,,\,\,v'=e^{4t} \Longrightarrow v=\frac{1}{4}e^{4t}$

After this do ANOTHER integration by parts...and then you're left with an easy exponential integral.

Tonio
• Oct 22nd 2009, 11:03 AM
Amer
Quote:

Originally Posted by calvin_coolidge
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

$\displaystyle \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -(t \frac{e^{4t}}{8} - \int \frac{e^{4t}}{8}dt)$

$\displaystyle \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -t \frac{e^{4t}}{8} + \frac{e^{4t}}{32} +c$