Posted by Barbara on Monday, February 16, 2009 at 7:51pm.
Find the indefinite integral
(integral sign) 3te^2tdt

Calculus  Anonymous, Monday, February 16, 2009 at 8:13pm
use a calculator, that's what calculus is all about. duh!

Calculus  Barbara, Monday, February 16, 2009 at 8:24pm
Excuse you that DUH is not necessary and if I could use the calculator I would have used it but my teacher did not teach me to how to use the calculator for this so please mind your business

Calculus  Damon, Monday, February 16, 2009 at 8:34pm
do t e^(2t) dt
and multiply by 3 later
by parts
u = t
du = dt
dv = e^(2t) dt
v = (1/2) e^(2t)
u v = (1/2) t e^(2t)
v du = (1/2)e^(2t) dt
integral v du = e^(2t)
u v  integral v du = (1/2) t e^(2t) e^(2t) 
Calculus  Damon, Monday, February 16, 2009 at 8:35pm
then multiply by 3

Calculus  Reiny, Monday, February 16, 2009 at 8:37pm
integral(u dv) = uv  integral(v du)
let u = 3t
du/dt = 3 , so du = 3 dt
let dv = e^(2t)dt
v = (1/2)e^(2t)
so integral(3t(e^(2t)))dt = 3t(1/2)e^(2t)  integral((1/2)e^(2t)(3 dt)
= (3/2)te^(2t)  (3/4)e^(2t)
I don't know how much further you want to simplify this, but I differentiated my last answer and it works 
Calculus  drwls, Monday, February 16, 2009 at 8:37pm
Let 3t = u and e^2t dt = dv
du = 3 dt v = (1/2) e^2t
The integral is
uv  INTEGRAL v du
= (3/2)t e^2t  INTEGRAL (3/2)e^2t
= (3/2)t e^2t  (3/4)e^2t 
Calculus  Barbara, Monday, February 16, 2009 at 8:39pm
Thank You Damon, Reiny and Drwls for your help

Calculus  Barbara, Monday, February 16, 2009 at 8:43pm
but why does v=(1/2)e^2t

Calculus  Reiny, Monday, February 16, 2009 at 8:49pm
all three of us had chosen
let dv = e^(2t)dt
or dv/dt = e^(2t)
wouldn't you have to integrate that to get v ?
v = (1/2)e^(2t)
I hope you recognized that we used a method called integration by parts
in choosing the "u" and "dv"
let u be something that you can differentiate, and
let dv be the part that you can integrate,
then hope for the best 
Calculus  Damon, Monday, February 16, 2009 at 8:51pm
because d/dt of e^2t = 2 e^2t
so you need the (1/2) to get one of them instead of 2 
Calculus  Barbara, Monday, February 16, 2009 at 8:55pm
oooo okay Thank You

Calculus  Anonymous, Monday, February 16, 2009 at 8:58pm
yeah you better say thank you and if i were to mind my own business then why did you post a question where everyone can see dufus?

Calculus  Barbara, Monday, February 16, 2009 at 9:10pm
Ummm because I wasn't looking for help from you and of course I'm going to say Thank You because i have manners unlike you you don't have any and you don't address people that's looking for help form you like that so Goodbye and Have a nice day