Question

Solve :
$\int e^x{e}^{e^x}{e}^{e^{e^x}}dx$

Answer 1

Given

$\int e^x{e}^{e^x}{e}^{e^{e^x}}dx$

$=\int e^{e^{e^x}+e^x+x}dx$

Substitute $u=e^x$ $dx=e^{-x}du$

$=\int e^{e^u+u}du$

Substitute $v=e^u$ $du=e^{-u}dv$

$=\int e^{v}dv$

$=e^v$

$=e^{e^u}$

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