[SOLVED] Integration by parts - anyone feel like a bit of maths?

[GingerRobot]

Edit: unfortunately, i can't get the integral symbol to display, so im using f to represent it.

 

Eugh, well im a bit stuck with some integration by parts. I was beginning to get it, but i've some unstuck with problems similar to:

 

f (x/(x-1)^2) dx

 

The way ive gone about it is to let u=x and let dv/dx = (x-1)^2

 

So, du/dx = 1 and v = -(x-1)^-1   

 

Therefore, given the formula uv - f (v*du/dx) , i thought the answer should come about something like:

 

-x(x-1)^-1 - f(-(x-1)^-1). This is where the problem comes in. Im not entirely sure how to integrate this part. I thought it might be -ln(1-x), but im not completely sure.

 

For reference, the answer in the back is ln(x-1) - x/(x-1)

 

Ill completely understand if i get no replies here, but im rather confused and would appreciate a pointer. I suspect im doing somethinga bit stupid somewhere, but im not sure what. Thanks in advance if anyone does reply!

[GingerRobot]

Turns out i was missing something simple. Didn't notice the two negative signs. Whoops.