Question

What is $\int e^{e^x}{e}^{x}dx$ equal to?

• A. $e^{e^x}+c$
• B. $2e^{e^x}+c$
• C. $e^{e^x}{e}^x+c$
• D. $2e^{e^x}{e}^x+c$
  where $c$ is an arbitrary constant

Answer 1

The correct option is A $e^{e^x}+c$

Let $I=\int e^{e^x}{e}^{x}dx$

Take $e^x=y$

$\Rightarrow e^{x}dx=dy$

Putting in the above integral we have,

$I=\int e^{y}dy$

$=e^y+c$

$=e^{e^x}+c$

Hence, A is correct.