How to solve this integral?

Question

∫ (x+1)/(x^2+5x+6) dx

Please show all your work and tell me the right answer. Thanks.

Answer 1

∫(x+1)dx/(x² +5x +6)= ∫(x +1)dx/ (x+2)(x+3). using partial fractions (x+1)/(x+2)(x+3) = A/(x+2) +B/(x+3) and so matching coefficients x+1= A(x+3) +B(x+2)= x(A+B) +3A +2B which gives A+B=1 and 3A+2B=1. Solving for A and B gives A=-1 and B=2. So the original integral =∫-dx/(x+2) +2∫ dx/(x+3) and this equals -ln|x+2| + 2ln|x+3| + C and this equals ln|x+3|² -ln|x+2| +C which equals ln| (x+3)²/(x+2)| +C.