You have written this:
\(\displaystyle \int\frac{(2x+5)(x+2)(x-1)}{x-1}\;dx\)
This simplifies trivially for any region not containing x = 1, to \(\displaystyle \int (2x+5)(x+2)\;dx\)
The real question is your intent. Methinks you have forgotten your Order of Operations. If you mean this
\(\displaystyle \int\frac{(2x+5)}{(x-1)(x+2)(x-1)}\;dx\)
You probably should write that. Parentheses help [(2x+5)/((x-1)(x+2)(x-1))].
If you mean the second version, you'll need to warm up your Partial Fraction Decomposition skills.