Question

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

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

Answer 1

Answer: (B)

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