I need to compute the following:
$E\left[ B_t \int_0^tB_s^2 \, ds \right]$ for $t≥0$
Where $B_t$ is a standard Brownian motion.
I'm thinking this is really obvious, But I cannot get my head round it. I thought about using Fubinis theorem to move the expectation inside of the integral to get an $s$, but I don't think that works seeing as there's a product.