求个积分,凑个热闹

咱也无聊了，给你解解吧
2x-x^2=1-(x-1)^2
原式=根号【1-（x-1)^2】d(x-1)
令u=x-1
原式=根号（1-u^2）du
令u=sint -pi/2<t<pi/2
则，根号(1-u^2)=cost,du=costdt
原始=(cost)^2dt
=1/2积分号（cos2t+1)dt
=1/2t+1/4sin2t+c
=1/2arcsinu+1/2u根号（1-u^2）+c
=1/2arcsin(x-1)+1/2(x-1)根号(2x-x^2)+c

换元积分 x-1=sin u