Question

Evaluate $\int 2^{2^{2^x}}{.2}^{2^x}{.2}^{x}dx$

Answer 1

Let $2^x=t\Rightarrow 2^{x}dx=dt$

$\int 2^{2^{2^x}}{.2}^{2^x}{.2}^{x}dx=\int {2^2}^t{.2}^t.dt=\int 4^t{.2}^t.dt=\int 8^t.dt=\frac{8^t}{\log 8}+c=\frac{2^{3^t}}{\log 8}+c=\frac{2^{3^{2^x}}}{\log 8}+c$