$\int 5^{5^{5^x}}.5^{5^x}.5^x\,dx$ is equal to:

$\frac{5^{5^x}}{(\log 5)^3}+C$ $5^{5^{5^x}}(\log 5)^3+C$ $\frac{5^{5^{5^x}}}{(\log 5)^3}+C$ None of these

$\frac{5^{5^{5^x}}}{(\log 5)^3}+C$

Putting $5^{5^{5^x}}=t$ we have $5^{5^{5^x}}5^{5^x}5^x(\log 5)^3dx=dt$, we get: $\int 5^{5^{5^x}}.5^{5^x}.5^x\,dx=\frac{1}{(\log 5)^3}\int 1\,dt=\frac{t}{(\log 5)^3}+C=\frac{5^{5^{5^x}}}{(\log 5)^3}+C$