Question

Solve:
$\int 3^{3^{x^x}}{3}^{3^x}{3}^{x}dx=$

Answer 1

Put $t=3^{3^{3^x}}⟹dt=3^{3^{3^x}}{.3}^{3^x}{.3}^x\log 3dx$

$\int 3^{3^{3^x}}{.3}^{3^x}{.3}^{x}dx=\frac{1}{\log 3}\int dt=\frac{t}{\log 3}+C=\frac{3^{3^{3^x}}}{\log 3}+C$