（x²-x-1）/(x²+1)的不定积分

题目

（x²-x-1）/(x²+1)的不定积分

答案

(x²-x-1)/(x²+1)
=(x²+1-x-2)/(x²+1)
=1-x/(x²+1)-2/(x²+1)
原式=∫1dx-∫x/(x²+1)-2∫1/(x²+1)dx
=∫1dx-1/2∫d(x²+1)/(x²+1)-2∫1/(x²+1)dx
=x-1/2*ln(x²+1)-2arctanx+C