begin{equation}
begin{aligned}
&P(t_{n+1}-t_n>q) =expleft( -int_{t_n}^{t_n+q}lambda(t) dt right)notag\
&simeq e^{-lambda_0q}biggl(1 &&+ int_{t_n}^{t_n+q}lambda_1(t)dt \
& &&+ int_{t_n}^{t_n+q}int_{t_n}^{t_n+q}lambda_1(t)lambda_1(t')dtdt'  biggr),.
end{aligned}
end{equation}

documentclass{article}
usepackage{amsmath}
begin{document}
begin{equation}
begin{aligned}
&P(t_{n+1}-t_n>q) =expleft( -int_{t_n}^{t_n+q}lambda(t) dt right)notag\
&simeq e^{-lambda_0q}biggl(1
begin{aligned}[t]
&+ int_{t_n}^{t_n+q}lambda_1(t)dt \
&+ int_{t_n}^{t_n+q}int_{t_n}^{t_n+q}lambda_1(t)lambda_1(t')dtdt'  biggr),.
end{aligned}
end{aligned}
end{equation}
end{document}