求详细过程，谢谢啦！
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dy/dx = 1/(x+y)^2
let
u = x+y
du/dx = 1+ dy/dx
dy/dx = 1/(x+y)^2
du/dx -1 = 1/u^2
du/dx = (u^2+1)/u^2
∫[u^2/(u^2+1) ] du = ∫dx
∫[1 - 1/(u^2+1) ] du = ∫dx
u - arctanu = x + C
x+y - arctan(x+y ) = x + C
y- arctan(x+y ) = C
let
u = x+y
du/dx = 1+ dy/dx
dy/dx = 1/(x+y)^2
du/dx -1 = 1/u^2
du/dx = (u^2+1)/u^2
∫[u^2/(u^2+1) ] du = ∫dx
∫[1 - 1/(u^2+1) ] du = ∫dx
u - arctanu = x + C
x+y - arctan(x+y ) = x + C
y- arctan(x+y ) = C
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