f’(x)=x^2+2ax+1
△=4a^2-4=4(a+1)(a-1)
①当△≤0,
即-1≤a≤1,
有 f’(x)≥0,
所以f(x)在R上单增.
②当△>0
即a<-1 or x>1,
若x<-a-√(a^2-1),x>-a+√(a^2-1)
则f’(x)>0,f(x)单增
若-a-√(a^2-1)则f’(x)<0,f(x)单减