I know that the actuarial present value of a whole life insurance is:

$\displaystyle \bar{A}_x= \int^\infty_0v^t[_tp_x]\mu_x(t).dt$

Under constant force of mortality, it becomes $\displaystyle \frac{\mu}{\mu+\delta}$

Then How it can be shown that $\displaystyle \bar{A}_x=\displaystyle\sum_{k=0}^{\infty}v^{k+1}[_kp_x]\mu_x(k)\frac{i+q_{x+k}}{\delta+\mu_x(k)}$ ?

where $\displaystyle \mu_x(k)=-log(p_{x+k})$