高数积分：∫(x^2+2x+3)/(x^2+1)dx用什么方法求解?

网友回答

∫(x^2+2x+3)/(x^2+1)dx
=∫1+[(2x+2))/(x^2+1)dx
=∫1+(2x)/(x^2+1)+2/(x^2+1)dx
=∫dx+∫(2x)/(x^2+1)dx+∫2/(x^2+1)dx
=∫dx+∫1/(x^2+1)d(x^2+1)+∫2/(x^2+1)dx
=x+ln（x^+1）+2arctanx+C
其中C是任意常数