Home -> Solved problems -> Calculate the integral
Solution
\[\begin{aligned}
g(x)&=e^{x} \\\\
g(g(g(x)))&=e^{e^{e^{x}}} \\\\
(g(g(g(x))))^{\prime} &=g^{\prime}(g(g(x))) g^{\prime}(g(x)) g^{\prime}(x)\\\\&=e^{e^{e^{x}}} e^{e^{x}} e^{x} \\\\
\int_{0}^{1} e^{e^{e^{x}}} e^{e^{x}} e^{x} d x &=\int_{0}^{1}(g(g(g(x))))^{\prime} d x \\\\
&=[g(g(g(x)))]_{0}^{1} \\\\
&=\left[e^{e^{e^{x}}}\right]_{0}^{1} \\\\
&=e^{e^{e^{1}}}-e^{e^{e^{0}}}=e^{e^{e}}-e^{e} \approx 3.814 \times 10^{6}\\\\
\int_{0}^{1} e^{e^{e^{x}}} e^{e^{x}} e^{x} d x &\approx 3.814 \times 10^{6}
\end{aligned}\]
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Home -> Solved problems -> Calculate the integral
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Home -> Solved problems -> Calculate the integral