Hi
How do you go about integrating equations like x/((x-1)² )

Hi,
I believe I can help on this one, if the Nrich team do not mind...

This is called integration by substitution, and you can find it in most A-level textbooks. It goes like this:

If you substitute u=x-1,

then x=u+1

and du/dx=1, du=dx.

Thus, òx/(x-1)² dx can be written as

ò(u+1)/u² du

=ò1/u du+ò1/u² du

=ln(u)+u^-1/(-1)

=ln(u)-1/u

=ln(x-1)-1/(x-1)+c
Hope this helps.
Cheers,
Chi Kin Ho

thanks