Is this integral possible:
$$\int\left(f(a \cdot b,x)g(c \cdot d,x)\right)dx= h(a \cdot c,x)j(b \cdot d,x)$$
with $(a \cdot b\neq a \cdot c)$ and $(c \cdot d \neq b \cdot d)$ and $f \neq g \neq h \neq j$?
If this is possible, what are the functions $f$, $g$, $h$, and $j$?
I'm trying to find nontrivial instances of these functions such that they all include $x$, and that $(a\cdot b)$ isn't multiplied by $c \cdot d$ in the integral, and that $a \cdot c$ isn't multiplied by $b \cdot d$ in the result.