I don't see the way of applying partial fractions here. Do we have a typo?
Not a typo there neither. It's the integral of the square root of (x^2 + 2x) dx
Krizalid: If it isn't necessary I don't have to use trigonometric expressions. If it's the only way, please explain a bit further.
EDIT: If this helps, the solution given by the book is:
(1/2)[(x+1)Sqrt(x^2+2x)-ln|x+1+Sqrt(x^2+2x)|]+c