∫ 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
∫x/(x^2+5x+6)dx
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