Question

为什么-(xdx)/根号下(1-x^2)=dy/y两边积分后得根号下(1-x^2)=lny-lnc

Answer 1

(-xdx)/根号下(1-x^2)

=(1-x^2)^(-1/2)(-xdx)

=(1/2)*(1-x^2)^(-1/2)(-2xdx)

=(1/2)*(1-x^2)^(-1/2)d(1-x^2)

积分,得（1/2）*[1/（-1/2+1）]*（1-x^2)^(-1/2+1)

化简,得（1-x^2)^(1/2)

即,根号下（1-x^2)