# Fun with exponents

Calculus Level 4

$\Large\int_0^1 \exp({x+e^x+e^{e^x}+e^{e^{e^x}}}) \, dx$

If the above integral can be expressed as

$^Ae - ^B e$

for positive integers $$A$$ and $$B$$, find $$A+B$$.

Notations:

• $$\exp(x)$$ denotes the exponential function, $$\exp(x) = e^x$$.

• $$^na$$ denotes the Tetration function, $$\Large ^n a = \underbrace{a^{a^{a^{\cdot^{\cdot^a}}}}}_{n\text{ number of } a\text{'s}}$$.

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