gerauchert
2011-09-19 19:27:04
I've been pulling my hair out over this problem for some time now… was hoping someone could lend a hand?
I'm solving for the indefinite integral of:
(t+3)^2/(t^4)
This is from the "Integration by Substitution" section, so there is a way to do this by substitution… I just keep getting stuck.
Any help would be appreciated :)
Thanks
Nava2
2011-09-19 19:47:01
err, expand the quadratic then distribute the denominator.
then..
http://www.wolframalpha.com/input/?i=integrate+[[t%2B3]^2]%2F[t^4]
sf411
2011-09-19 20:39:06
WOLFRAM YEAH!Here is a proper link just click the show steps button to see how WFA did the problem. Nava2, I dont think the forums like your link or maybe it just miss typed.
Nava2
2011-09-19 21:25:03
Nope, the forums did not like it. Haha, its the use of brackets instead of using parenthesis.
gerauchert
2011-09-21 13:49:23
Ah thanks a lot man. The problem was throwing me off since I was thinking in terms of substitution. :duh:
And wow… that site is really legit. Definitely using that a lot this semester :D
Thanks again
sf411
2011-09-21 14:29:56
Yup, wolfram is amazing. Using it in the CalcII class I am taking now.
You can use it for just about anything you want like definitions, nutritional facts, etc.
gerauchert
2011-09-21 23:17:28
Thats pretty sweet man. Calc II for me as well… gah… calculus :frusty:
sf411
2011-09-21 23:24:18
Yeah were getting into Integration and Differentation of Ln. It still shows I hate the chain rule….
owain jones
2012-01-07 15:47:33
No need for substitution, it wouldn't make the problem any easier.
(t+3)^2= t^2+6t+9
For simplicities sake, lets split it up.
(t^-4)(t^2+6t+9)= t^-2+6t^-3+9t^-4
From there it should be easy. When integrating you add one to the exponent and divide by the new exponent.
Thus it's -t^-1-3t^-2-3t^-3
simplified, but still overcomplicated as I'm typing on a computer lol
-1/t((1)+(3t^-1)+(3t^-2))
t^-3 is the same as 1/t^3, it really helps with calculus to simplify like this. Cheers.