B is a Brownian motion with values in $\mathbb{R}$. I have to find a process $(F_t)_{t\in[0,T]}$ such that $X=E[X]+\int_0^T F_s dB_s$, for $X=B_T$, $X=\int_0^T B_tdt$, $X=B^2_T$, $X=B^3_T$ and find a stochastic process $(F_t)_{t\in[0,T]}$ for the random variable $X=cos B_T$ such that the equation is hold.
I have already shown that $B^2_T=2\int_0^T B_sdB_s+T$. So i thought $F_s=2B_s$ might be a good choice for that case. For $X=B_T$ i took $F_s=1$. I determined $B_T^3$with Ito's Formula. My result was $B_T^3=3\int_0^T B_T^2 dB_T+3\int_0^T B_T ds$, but i cannot see how my $F$ looks like. Could you please help me with the rest?