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Posted by **Barbara** on Monday, February 16, 2009 at 7:51pm.

(integral sign) 3te^2tdt

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

- Calculus -
**Barbara**, Monday, February 16, 2009 at 8:24pmExcuse 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 8:34pmdo 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 8:35pmthen multiply by 3

- Calculus -
**Reiny**, Monday, February 16, 2009 at 8:37pmintegral(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 8:37pmLet 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 8:39pmThank You Damon, Reiny and Drwls for your help

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

- Calculus -
**Reiny**, Monday, February 16, 2009 at 8:49pmall 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 8:51pmbecause 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 8:55pmoooo okay Thank You

- Calculus -
**Anonymous**, Monday, February 16, 2009 at 8:58pmyeah 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 9:10pmUmmm 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