MEI core 3 integration. Help!

Question 1 (i haven't gotten very far!)
i) integrate x/(x^2-1)^3 dx

I got:
1/6(x^2-1)^3 (3/2x^-2/3) + c

No idea if this is right or not though?

ii) integrate e^x/(1+e^x) dx

if e^x integrates to the same thing, wouldn't it just be ln(1+e^x) ??

I would really appreciate any help!
Thank you

Reply 1

technicolour

Could you show your working for part 1? I'm not too sure about it.
Part 2 is right.

Reply 2

scifilover

ok, for the first part i did:

u=x so 1/2du/dx=xdx
= u/(u^2 -1)^2 [times] 1/2 du
= integral (u^2-1)^2 (u)^(-1/2) [times] 1/2 du
= 1/2 [times] ((u^2 -1)^3)/3 [times] (u^-2/3)/(2/3)

and then just expand out?

should the very last bit be to the power of 3/2 not 2/3?
I am very confused!

thanks for the help!

Reply 3

Skadoosh

Your u isn't right here, or at least isn't the easy way of doing it.

Reply 4

scifilover

Whats the easy way of doing it?

make u = x^2 - 1

try using (x^2-1) for u.
then go about it the same way, using substitution.

Reply 7

scifilover

Thanks guys! I will try that

Cheers for all the help! :biggrin:

Reply 8

username219321

For the first one the easiest way is to guess it'll be a multiple of (x^2 - 1) ^-2, differentiate that then find out what the multiple actually is.

Second one is right