Integrate $$\int e^{x+e^{x+e^{x}}} \mathrm{d}x$$
This is a question from the book I am reading, no solution or an answer is provided. I am learning integration from a book by myself so let me know if I did anything incorrectly. I have searched for this integral with approach0 and SearchOnMath but nothing relevant came up.
So far here is what I did -
$$\int e^{x+e^{x+e^{x}}} \mathrm{d}x \implies \int e^x e^{e^xe^{e^x}} \mathrm{d}x$$
Substituting $u = e^x \implies \mathrm{d}u = e^x$
$$\therefore \int {u e^{ue^u} \over u} \mathrm{d}u \implies \int { e^{ue^u}} \mathrm{d}u $$
But I am not sure how to proceed or if all this is even correct. Any hints will do.
Thanks.