Evaluate the integration of :( e^(x+e^x) )dx?

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Answer 1 · 2018-04-30T15:10:48

$I=e^(e^x)+c$

We know that,

$color(blue)((1)a^(m+n)=a^m*a^n$

Here,

$I=int( e^(x+e^x) )dx$

$=inte^x*e^(e^x)dx...tocolor(blue)(Apply(1)$

$=inte^(e^x)*e^xdx$

Let, $e^x=u=>e^xdx=du$

$I=inte^udu$

$=e^u+c$

Subst. back, $u=e^x$

$I=e^(e^x)+c$