一道微积分题目求∫(2x+3)/(x^2+2x+2)dx

问题描述:

一道微积分题目
求∫(2x+3)/(x^2+2x+2)dx

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