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Here's one i'm stuck on, and my working thus far:

Integrate with respect to x:

x^2/(x-2) dx

I rewrote it as: x^2.(x-2)^-1

I then tried to use integration by parts, thinking that eventually i would be able to bring the x^2 down to 2, and produce an integral i could solve.

V = x^2, dv/dx = 2x, du = (x-2)^-1, u = ln[x-2].

So:

x^2ln[x-2] - integral of (2xln[x-2])

So i thought i would need to use integration by parts again, to solve the above integral and bring the 2x to a 2.

Integral of (2xln[x-2])

v = 2x, dv/dx = 2, du = ln[x-2], u = ?, where's where i'm having problems, i've tried using integration by parts again to calculate ln[x-2] but simply can't do it, as the new expression is becoming constantly more difficult.

I thought about substitution, but i would need to take u = x^2, with du/dx as 2x, however, this would only produce u/(du/dx - 2) dx, which isn't going anywhere.

Some help would be much appreciated. Thanks.