∫[(x+2)/(x^2+2x+3)]dx=1/2∫[(2x+4)/(x^2+2x+3)]dx
=1/2∫[(2x+2+2)/(x^2+2x+3)]dx
=1/2[∫(2x+2)/(x^2+2x+3)dx+∫2/(x^2+2x+3)]dx
=1/2[∫1/(x^2+2x+3)d(x^2+2x+3)+2∫1/(x^2+2x+3)dx]
=1/2[ln(x^2+2x+3)+√2arctan(2x+2)/(2√2)+C]
∫[(x+2)/(x^2+2x+3)]dx
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