How to integrate $5^{5^{5^x}}5^{5^x}5^x$? How to integrate $5^{5^{5^x}}5^{5^x}5^x$ ?
I guess it's simple but can't figure it out !

Let $u=5^{5^x}$, then $x = \frac{\frac{\ln(u)}{\ln(5)}}{\ln{5}}$ and $du = 5^{x+5^x}\ln^2(5)\hspace{.1cm} dx \implies dx = \frac{5^{-x-5^x}}{\ln^2(5)} \hspace{.1cm} du$. Thus we transform
$ \begin{align}
\int 5^{5^{5^x}} 5^{5^x} 5^x \hspace{.1cm} dx &= \int 5^uu5^x \frac{5^{-x-5^x}}{\ln^2(5)} \hspace{.1cm} du \\
&= \int \frac{u5^{u-5\frac{\frac{\ln(u)}{\ln(5)}}{\ln{5}}}}{\ln^2(5)} \hspace{.1cm} du \\
&= \frac{1}{\ln^2(5)} \int u5^{u-5\frac{\frac{\ln(u)}{\ln(5)}}{\ln{5}}} \hspace{.1cm} du \\
&= \frac{1}{\ln^2(5)} \int 5^u \hspace{.1cm} du \\
&= \frac{1}{\ln^2(5)} \frac{5^u}{\ln(5)} \\
&= \frac{1}{\ln^2(5)} \frac{5^{5^{5^x}}}{\ln(5)} \\
&= \frac{5^{5^{5^x}}}{\ln^3(5)}
\end{align}$
