A substitution that will simplify this integrand $$\iint_{R}^{} x \sin(6x + 7y) - 3y \sin(6x + 7y) dA$$
So I chose $u = 3y$ and $v = 6x + 7y$. So then $x$ will be replaced with $\frac{3u - 7v}{18}$. It seems correct, but does this truly "simplify" the integrand? Or have I done something incorrectly?

Note that after factoring, we have
$$\iint_{R}^{} x \sin(6x + 7y) - 3y \sin(6x + 7y)\,dA = \iint_{R}^{} (x-3y)\,\sin(6x + 7y)\,dA.$$
So a better substitution would probably be:
$$\begin{cases} u=x-3y,\\v=6x+7y.\end{cases}.$$
