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
答
∫(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