How do I calculate the convolution of $\sinh(t)$ and $t\,\mu_3(t)$?
I tried the following:
$$\int_0^t\sinh(t-s)s\mu_3(s)\,ds$$ then change the variable:
$$\int_t^{0}\sinh(v)(t-v)\mu_3(v)\,dv$$
I can separate into two integrals, but I'm stuck in the following:
$$\int_t^0\sinh(v)v\mu_3(v)\,dv$$
If it were composed only of $\sinh(v)$ and $v$ I could integrate by parts but I don't know what to do with this step function, am I missing some propriety? It was not spoken about any in my classroom, I did some google search but could not find any related, specially with limits that don't go to infinity.