x/√(2+2x-x^2)积分怎么求
问题描述：
x/√(2+2x-x^2)积分怎么求
答
∫x/√(2+2x-x^2)dx=∫x/√1-(1-x)^2dx
令1-x=cosy
则：x=1-cosy
上式：∫x/√1-(1-x)^2dx==∫(1-cosy)/|siny|d(1-cosy)=-∫(1-cosy)/|siny|(-siny)dy=∫(1-cosy)/|siny|.siny.dy=∫sin^2(y/2)/|sin(y/2)cos(y/2)|sin(y/2)cos(y/2)d(y/2)
变形即可.