integrate y/(x+y)^2 with respect to x

Question

integrate the above with respect to x, meaning fix y integrate x

Answer 1

In this case y is treated as a constant, so there is no relationship between y and x.

Let z=x+y then dz=dx so the integrand become some (y/z²)dz=yz⁻²dz. Integrating: -yz⁻¹+C that is, -y/(x+y)+C, where C is the constant of integration.