Mathematics

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

##### SOLUTION
Given
$\int{e^xe^{e^x}e^{e^{e^x}}}dx$

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

Substitute $u=e^x$    $dx=e^{-x}du$

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

Substitute $v=e^u$    $du=e^{-u}dv$

$=\int{e^v}dv$

$=e^v$

$=e^{e^u}$

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

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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