Integration/log question (urgent!) (1 Viewer)

[kloudsurfer]

Hey,

Im really stuck on this question, and i have an assessment tommorow so im freaking out that ill get a question like this and i wont know how to do it! Could someone please help me?
Heres the question

Find the exact value of:

(3x^2+1)/(x^3+x) dx lim 4-2(dunno how to do the squiggly thingy...)

So heres my working out:

= xloge(x^3+x) lim 4-2 (im not sure if the first x is right...)
= 4log68 - 2loge10
....
and now im just kinda lost...because i know i cant get a correct answer with this...

The answer is loge6.8. Which is the same as loge34/5. Which is the same as loge68/10. So i must be doing something right....

Can anyone help me?

Thanks in advance!

 

[eam]

log laws... the 2nd log law (from memory) says that logax - logbx = log a/b or something similar... so, from your working, then next step is log 68/10, which as you said, is log 34/5... i cant remember what happens to the numbers in front of the logs, sorry... Im sure you textbook can tell you.

 

[SoulSearcher]

Integral, right?

Well, the end integral would be
[ln |x³+x|] (4-->2)
= ln (64 + 4) - ln (8 + 2)
= ln 68 - ln 10
= ln (68/10)
= ln 6.8, which is your answer.

 

[kloudsurfer]

Ahhh wait, i made a silly mistake when I was working it out on paper!

Ooops.

Serves me right for doing late night revision the night before!

Thanks anyway guys.