Question

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

Answer 1

$\int 2^{2^{2^x}}\cdot 2^{2^x}\cdot 2^{x}dx$

$Applyu-substitution:u=2^{2^{2^x}}$

$=\int \frac{1}{{\ln }^3\left(2\right)}du$

$=\frac{1}{{\ln }^3\left(2\right)}u$

$=\frac{1}{{\ln }^3\left(2\right)}\cdot 2^{2^{2^x}}$

$=\frac{1}{{\ln }^3\left(2\right)}\cdot 2^{2^{2^x}}+C$