I want to plot the following integral as a function of $x$ but Mathematica fails to draw it even using the numerical integration. $$f(x)=\displaystyle\int_0^{\infty } \left(\sum _{n=1}^{\infty } n^4e^{-e^{4 u} n^2 \pi }\right) (e^{9 u}\text{Cosh}(xu)) \, du$$ How should I plot it, say on some finite interval?
EDIT: Here is what I tried for numerical plot: $$ g[u\_]=\sum _{n=1}^{\infty } e^{-e^{4 u} n^2 \pi } \left(e^{9 u} n^4 \right)*(Cosh[x*u]){FunctionExpand}\text{\\\\}$$
$$f[x\_]:=({NIntegrate}[g[u],\{u,0,10\}]) $$
$$Plot[f[x], \{x, 1, 5\}] $$ .
The output I get is: