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Integration by substitution
By Anonymous on Sunday, September 3, 2000 - 02:55 pm:

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

By Chi Kin Ho (P1942) on Sunday, September 3, 2000 - 05:35 pm:

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, ò x/(x-1)2 dx can be written as

ò (u+1)/u2du

= ò 1/u du + ò 1/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

By Tim Garton (P2843) on Sunday, September 3, 2000 - 08:55 pm:

thanks