Solution of Partial differential equations by direct integration method

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In this video I have discussed how to find the solution for partial differential equations by direct integration method.
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Very good sir... But in ur question x is squared and in ur answer u integrated by x once and u integrated with y twice... Please explain why sir

chatiwaishmael
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sir i have a doubt plz ans
potential energy = U = xy - yz -xz^2
force = f = - (∂ U/∂x) icap - (∂U/∂y) jcap - (∂U/∂z) kcap
force = f = (z^2-y) i + (z-x) j + (2xz+y) k
i know how to do partial differentiation but not partial integration
how do i integrate this force to again get the same above potential energy ???
plz ans

universallawismyname
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I can't understand when to integrate with respect to x and y

xavier