Integral of?

How do u intergrate x(x-1)^-1???

How do u intergrate x(x-1)^-1???

do you know the formula
integrate (f'(x) / f(x)) = ln f(x) + c??

alter the integral to:

INT [(x-1)+1]/(x-1) dx

= INT [1 + 1/(x-1)] dx

= x + ln|x-1| + C

i genuinely cant believ i didnt get that but there u go...not done integration yet so a little iffy to say the least

as soon as you've seen it, you'll easliy spot where to use it

i still cant get the answer of the q tho...it is m3

10. A particle moves on the +ve x-axis. When its displacement from ) is x metres, its acceleration is of magnitude x^-3 and directed towards ). Initially, t=0, x=1, find time particle takes to reach x=1/4

which question is it? is it in the M3 book?

Edit: found it, Ex. 1B right? i'll have a look through this again, cos i've kinda forgotten it

yeh q10 :-)


trouble i seem to get ln l 1-x l and u have to let x =1 :-(

sorry mate, but i'm kinda lost....since we have acc. as a function of displacement, then surely we have to use v.dv/dx = a , but then where does the whole 'time' thing come in
i'm just glad i didn't get a similar question when i did M3

well v=dx/dt

then rearrange, so say v=f(x)
dx/f(x)=dt

then integrate both sides...hope this is enough info

r u sure this helps?

only in the sense that it could help in the same way Mockel used it

but in this case, isn't a = f(x) = x^-3 ???

well i mean f(X) as nething

well, i'm getting it completely wrong....hopefully elpaw, fermat etc will stumble across this thread

Actually this question came up a few days ago by someone else, the_anomaly, I think.
I answered and completely messed it up
Skip past my post and look at Jonny W's.
http://www.thestudentroom.co.uk/showthread.php?p=1252243&highlight=question#post1252243

Actually this question came up a few days ago by someone else, the_anomaly, I think.
I answered and completely messed it up
Skip past my post and look at Jonny W's.
http://www.thestudentroom.co.uk/showthread.php?p=1252243&highlight=question#post1252243