Expand the square on the right giving you a sixth order polynomial in x, then integrate term by term
CB
Since there is a term with y in it on the right hand side, it's possible that the real question is not to integrate but to solve a differential equation. The OP will need to clarify the situation.
No, you shoudn't. Since there is no "du" already in the integrand, it is far easier to just multiply it out and integrate the polynomial as Captain Black first said.