Hard Integration of rational fraction

Question

For $j=0...n$ let be $a_j,b_j,c_j\in\mathbb{R}$ and $$B_j^n=\binom{n}{j}t^j(1-t)^{n-j}$$ the j-th Bernstein polynomial defined over the closed interval $[0,1]$. Any hint on how to find a closed form solution for: $$\int_0^1\frac{\sum_{j=0}^n\sum_{k=0}^n a_jc_kB_j^n(t)\frac{\mathrm{d} }{\mathrm{d} t}B_k^n(t)}{(\sum_{j=0}^nb_jB_j^n(t))^2}dt$$