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#