Question

$\int 5^{5^{5^x}}\cdot 5^{5^x}\cdot 5^{x}dx$.

Answer 1

$\int {5^5}^{5^x}.5^{5^x}{.5}^{x}dx$

Let $5^{5^x}=m$

$dm=5^{5^x}{.5}^x.l{n}^{2}5dx$

$\int \frac{5^{m}dm}{l{n}^{2}5}$

$\frac{5^m}{l{n}^{3}5}$

$\frac{{5^5}^{5^x}}{l{n}^{3}5}$