Hi Deathfish!

If your result is

[tex]-\frac{x+4}{16x^2}+\frac{1}{16(x+4)}[/tex]

then it is completely correct!!

Now, why does mathematica give another result? Well, the above result can be put in a form that is even more convenient. Indeed, the term [itex]\frac{x+4}{16x^2}[/itex] can be "simplified" further as

[tex]\frac{x+4}{16x^2}=\frac{1}{16x}+\frac{1}{4x^2}[/tex]

This is a better form since it's more suitable for integration purposes. But your result isn't wrong!