# Another integral, general power formula.

• May 8th 2013, 03:31 PM
togo
Another integral, general power formula.
Hi thanks for the help lately its been good. I don't post these unless a day goes by without a solution.

28-1-20

Integrate:

(int) 2 sqrt(1- e^(-x)) (e^-x) dx

therefore,
u = 1 - e^(-x)
du = - e^(-x)

General power form:
[1 - e^(-x)]^(3/2) / (3/2) + C
=
4/3 [1 - e^(-x)]^(3/2) + C

however here is the ti-89 answer:

http://i44.tinypic.com/k170ut.jpg

somehow something has been added in the nominator.
how did I go wrong? Thanks!
• May 8th 2013, 03:48 PM
Soroban
Re: Another integral, general power formula.
Hello, togo!

Quote:

$\displaystyle \int \sqrt{1-e^{-x}}\cdot e^{-x}\,dx$

Therefore:

$\displaystyle u \:=\: 1 - e^{-x}$

$\displaystyle du \:=\: - e^{-x}dx$ . . . . no

$\displaystyle \text{If }u \:=\:1-e^{-x}$

. . $\displaystyle \text{then: }\:du \:=\:\left[0-e^{-x}(\text{-}1)\right]dx \:=\:e^{-x}dx$
• May 8th 2013, 05:03 PM
togo
Re: Another integral, general power formula.
but, that doesn't really change what I did at all

its the added e^(-3x/2) that is confusing me in the nominator
• May 8th 2013, 05:18 PM
Prove It
Re: Another integral, general power formula.
Quote:

Originally Posted by togo
but, that doesn't really change what I did at all

its the added e^(-3x/2) that is confusing me in the nominator

Well it DOES change what you did, because if you followed your own logic, you should have ended up with a negative answer. I'm not sure where your negative has gone.
• May 8th 2013, 08:00 PM
togo
Re: Another integral, general power formula.
I have been having trouble with losing the negative and have retraced it twice in homework the last couple days.

This is something I can do myself and I'm not sure what to do in order to complete the answer besides this. I'll rework the question soon and hopefully it does give me the answer shown on the ti-89.
• May 9th 2013, 11:33 AM
togo
Re: Another integral, general power formula.
ya that change does not give me a complete answer.