Putnam 1946 A2

If $a(x), b(x), c(x)$ and $d(x)$ are polynomials in $x$ , show that $$\int_{1}^{x} a(x) c(x) dx \cdot \int_{1}^{x} b(x) d(x) dx - \int_{1}^{x} a(x) d(x) dx \cdot \int_{1}^{x} b(x) c(x) dx$$ is divisible by $(x-1)^4.$