Question

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

• A. $5^{5^{5^x}}{\left(log5\right)}^3+c$
• B. $\frac{5^{5^{5^x}}}{{\left(log5\right)}^3}+c$
• C. $\frac{5^{5^{5^x}}}{{\left(log5\right)}^2}+c$
• D. $5^{5^x}{\left(log5\right)}^3+c$

Answer 1

Answer: (B)

Let $I=\int 5^{5^{5^x}}{5}^{5^x}{5}^{x}dx$
Put $5^{5^x}=t$
$\Rightarrow 5^{5^{5^x}}{5}^{5^x}{5}^x(\log 5{)}^{3}dx=dt$
$\therefore I=\int \frac{dt}{(\log 5{)}^3}=\frac{t}{(\log 5{)}^3}+c$
$=\frac{5^{5^x}}{(\log 5{)}^3}+c$