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gerauchert
09-19-2011, 11:27 PM
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
09-19-2011, 11:47 PM
err, expand the quadratic then distribute the denominator.

then.. http://www.wolframalpha.com/input/?i=integrate+[[t%2B3]^2]%2F[t^4]

sf411
09-20-2011, 12:39 AM
WOLFRAM YEAH! (http://www.wolframalpha.com/input/?i=integrate+%28%28t%2B3%29^2%29%2Ft^4)

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
09-20-2011, 01:25 AM
Nope, the forums did not like it. Haha, its the use of brackets instead of using parenthesis.

gerauchert
09-21-2011, 05:49 PM
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
09-21-2011, 06:29 PM
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
09-22-2011, 03:17 AM
Thats pretty sweet man. Calc II for me as well... gah... calculus :frusty:

sf411
09-22-2011, 03:24 AM
Yeah were getting into Integration and Differentation of Ln. It still shows I hate the chain rule....

owain jones
01-07-2012, 08:47 PM
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.