To integrate xy^2 + 3y + zxy^2 + 3y with respect to y, we treat x and z as constants and apply the power rule of integration.

∫(xy^2 + 3y + zxy^2 + 3y) dy

= ∫xy^2 dy + ∫3y dy + ∫zxy^2 dy + ∫3y dy

= x * ∫y^2 dy + 3 * ∫dy + z * ∫y^2 dy + 3 * ∫dy

= x * (y^3 / 3) + 3y + z * (y^3 / 3) + 3y + C

= (x+z) * (y^3 / 3) + 6y + C

where C is the constant of integration.
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