- #1

QuickQThrowaway

- 2

- 1

I just stumbled upon this integral while doing ODEs...

∫x*(x-2)

^{-2}dx

I used integration by parts

u=x

du/dx=1

dv/dx=(x-2)

^{-2}

v=-(x-2)

^{-1}

Thus

∫x*(x-2)

^{-2}dx=-x(x-2)

^{-1}-∫1*-(x-2)

^{-1}dx=-x*(x-2)

^{-1}+ln(x-2)+C

Now... I don't see anything wrong with this...

But every single online integration calculator as well as the ODE solution solves this integral by doing 1/(x-2)+2/(x-2)

^{2}and they all get

-2*(x-2)

^{-1}+ln(x-2)+C

as a result...

What am I doing wrong in my integration by parts? What am I missing? Oo