Integrate : $\int a^{\large a^{\Large a^{\Large a^{x}}}}.a^{\large a^{\Large a^{x}}}.a^{a^{x}}.a^{x}$$.dx$

Question

$(a)\;\frac{a^{\large a^{\Large a^{\Large a^{x}}}}}{(\log _e a)^4}+c\qquad(b)\;\frac{a^{\large a^{\Large a^{x}}}}{(\log _e a)^4}+c\qquad(c)\;\frac{a^{\large a^{\Large a^{\Large a^{x}}}}}{(\log _e a)^2}+c\qquad (d)\;None$