（x+1）/(x^2+x+1)对x的不定积分怎么求?

Question

（x+1）/(x^2+x+1)对x的不定积分怎么求?

Answer 1

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