求「（3y-x）dx+（y-3x）dy」／（x+y）^3的原函数

∵令P(x,y)=(3y-x)/(x+y)^3,Q(x,y)=(y-3x)/(x+y)^3则可求得αP/αy=αQ/αx∴[(3y-x)dx+(y-3x)dy]/(x+y)^3存在原函数F(x,y)∵由公式得F(x,y)=∫P(x,0)dx+∫Q(x,y)dy=∫(-1/x^2)dx+∫[(y-3x)/(x+y)^3]dy=1/x-1+(x-y)/...