Question

solve:

e^integral(-2/t)dt

Any help is appreciated.

Kind regards

Answer 1

\[\huge e^{\int -\frac 2t dt}\]
do you know the value of \[\huge \int -\frac 2t dt\]

Answer 2

I think it is -2ln(t)

Answer 3

right

Answer 4

now apply the log rule.. \[\huge a \ln b \implies \ln b^a\]

Answer 5

so what will be the value of -2 ln t

Answer 6

-1 minute plse ...screen has gone blank

Answer 7

sure sure

Answer 8

busy powering up imac ...1 more minute plse

Answer 9

no rush :D

Answer 10

I'm assuming you want the integral of e^(2t) dt
The integral is simply (1/2)*e^(2t) + c (c is a constant)
This is because the integral of an exponential, e^(at) dt is:
(1/a)e^(at) + c

Answer 11

for some reason openstudy wont open on imac...this could be a while ...sorry....let me log off on the windos pc...mebbe that the problem ;)

Answer 12

haha take your time. just tag me when you're ready

Answer 13

the answer is lnt^-2

Answer 14

right.. so..
\[\LARGE e^{\int -\frac 2t dt} \implies e^{-2 \ln t} \implies e^{\ln (t^{-2})}\]

Answer 15

okay

Answer 16

do you know how to simplify that?

Answer 17

yes, t^-2 = 1/t^2

Answer 18

right

Answer 19

does the ln cancel the e out

Answer 20

yup \[\huge e^{\ln a} = a\]

Answer 21

excellent - where do i find all these rules..do you know of a good resource

Answer 22

i have written a list of log rules before in this site...it also comes with a brief description and examples... http://openstudy.com/updates/4fa45f8fe4b029e9dc34e0b5

Answer 23

Wow...That's amazing....I didn't even know we had such excellent resources here on openstudy....Thank you very much ....Much appreciated

Answer 24

welcome ^_^ btw...you wouldnt be happening to be studying integrating factors in differential equations, would you?

Answer 25

yep...thats exactly why i posted this question..it is part of an Integrating Factor problem...How did you guess.?

Answer 26

because it didnt look like a normal integration problem =)) the only time i saw that kind of integration is from integrating factor

Answer 27

You are spot on....nice! Its not too hard now...we move on to 2nd order next semester. Is that difficult?

Answer 28

well...hmm...not really...you just have to remember solutions

Answer 29

okay...If you have any more tips on how to solve these IF problems that would be much appreciated. I struggle sometimes with the exp function...but with the help of the great people (like you) at openstudy my task has been made more easier... :)

Answer 30

hmm i dont know shortcuts to IF haha

Answer 31

okay...;) anyway ..thanks for your help .....i really aprreciate it...take care . :)

Answer 32

welcome ^_^