Question

$\int 5^{5^{5^x}}\cdot 5^{5^x}\cdot 5^{x}dx$ is equal to

• A. $\frac{5^{5^x}}{(\ln 5{)}^3}+c$
• B. $5^{5^{5^x}}(\ell \ln 5{)}^3+c$
• C. $\frac{5^{5^{x^x}}}{(\ln 5{)}^3}+c$
• D. none of these

Answer 1

Answer: (C)

Let $5^{5^x}=t\Rightarrow 5^{5^x}\cdot \ln 5\cdot 5^x\cdot \ln 5dx=dt$
$I=\int \frac{5^{tdt}}{(\ln 5{)}^2}=\frac{5^t}{(\ln 5{)}^3}+c=\frac{5^{5^{3^x}}}{(\ln 5{)}^3}+c$