(x^2+1)/((x+2)^2(x^2+2x+3)^2)不定积分
问题描述：
(x^2+1)/((x+2)^2(x^2+2x+3)^2)不定积分
答
答：∫ (x+2)/(x^2+2x+3) dx=∫ (x+1+1)/(x^2+2x+3) dx=1/2*ln(x^2+2x+3)+∫ 1/[(x+1)^2+2] dx=1/2*ln(x^2+2x+3)+1/2*∫ 1/([(x+1)/√2]^2+1) dx=1/2*ln(x^2+2x+3)+1/2*√2*arctan((x+1)/√2) + C=1/2*ln(x^2+2x+3)+...