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 $\mathrm{du}/\mathrm{dx}=1$, $\mathrm{du}=\mathrm{dx}$.

Thus, $\int x/(x-1{)}^2\mathrm{dx}$ can be written as

$\int (u+1)/u^2\mathrm{du}$

$=\int 1/u\mathrm{du}+\int 1/u^2\mathrm{du}$

$=\ln (u)+u^{-1}/(-1)$

$=\ln (u)-1/u$

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

thanks