$\int_0^x \cfrac{1}{1+\int_0^t \cfrac{1}{2+\int_0^{t_1} \cfrac{1}{3+\int_0^{t_2} \cfrac{1}{\cdots} dt_3} dt_2} dt_1} dt =f(x)$
$\int_{0}^{x} \frac{1}{n+h_{n+1}(t)}{d} t=h_n(x)$
$h'_n(x)(n+h_{n+1}(x))=1$ $h'_{n+1}(x)(n+1+h_{n+2}(x))=1$
I need to find $ h_1(x)=f(x)$
Please help me how to express $f(x)$ as known functions or power series?
Thanks a lot for answers