Question

xᵉ+eˣ+eᵉ,Integrate the given function w.r.t. x considering them well defined and integrable over proper domain.

Answer 1

In the attachment I have answered this problem.   The solution is simple and easy to understand.   See the attachment for detailed solution.

Answer 2

Dear Student,

Solution:

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

apply linearity

$\int {x}^{e} \: dx +\int {e}^{x} dx +\int{e}^{e} dx$
for 1st function apply
power rule of Integration

$\int{x}^{e} dx \: = \frac{ {x}^{e + 1} }{e + 1} + c$

second function is a direct formula So,

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

as third function is a constant So,

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

$\int{x}^{e} + {e}^{x} + {e}^{e} dx \: = \frac{ {x}^{e + 1} }{e + 1} + {e}^{x} + x \: {e}^{e} + c$

Hope it helps you.