= Solution
Insert $f_i=h_iF_i$ and $F_i=e^{-H_i}$ into the <survival likelihood>. Each individual's log contribution simplifies to
$$
v_i\log h_i(x_i;\theta)+\log F_i(x_i;\theta).
$$
Therefore
$$
\boxed{\ell(\theta)=\sum_{i=1}^n\{v_i\log h_i(x_i;\theta)-H_i(x_i;\theta)\}+\text{constant}.}
$$
Failures contribute a log <hazard function> term as well as exposure, whereas both failures and censored subjects contribute the negative <cumulative hazard function> over their observed follow-up.
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