The square of X - 5x + 6 = (X-2) (x-3) why is x square and why should we reduce 5x? Why should we add 6 and ask for the help of God

Use yesterday's formula (complete sum of squares, complete difference of squares)

∫x/(x^2+5x+6)dx

∫ x/(x+2)(x+3)dx
=∫ x ×[1/(x+2) -1/(x+3)] dx
=∫ x/(x+2)-x/(x+3) dx
=∫ 1-2/(x+2)-1+3/(x+3) dx
=∫ 3/(x+3)-2/(x+2) dx
=3ln|x+3|-2ln|x+2| +C