$\int 5^{5^{5^x}}.5^{5^x}.5^x\,dx$ is equal to:
Answer & explanation
Correct answer: option 3
Putting $5^{5^{5^x}}=t$ we have
$5^{5^{5^x}}5^{5^x}5^x(\log 5)^3dx=dt$, we get: $\int 5^{5^{5^x}}.5^{5^x}.5^x\,dx=\frac{1}{(\log 5)^3}\int 1\,dt=\frac{t}{(\log 5)^3}+C=\frac{5^{5^{5^x}}}{(\log 5)^3}+C$