Cauchy Riemann equations, application

Question

For $u: \Bbb C \to \Bbb R$ with
$$u(x + iy) = 2x^3 – 6xy^2 + x^2 – y^2$$
find a function $v: \Bbb C \to \Bbb R$ s.t. $f = u + iv$ is holomorphic.

I see that I have to verify the Cauchy Riemann equations, but I did not get the right solution…

Answer 1

$\dfrac{\partial u }{\partial x}=6x^2-6y^2+2x=\dfrac{\partial v}{\partial y}$

$\dfrac{\partial u}{\partial y}=-12xy-2y=-\dfrac{\partial v}{\partial x}$

$v=6x^2y-2y^3+2xy+f(x)$

$v=6x^2y+2xy+f(y)$

Can you take it from here?