Answer:
[tex]xe^{x} - e^{x} +C[/tex]
Step-by-step explanation:
we will solve this using integration by parts as the problem is a product of two functions which none of them are constants.
∫udv = uv -∫vdu ..............equ 1
∫[tex]xe^{x}[/tex]
u=x ,
du= 1
dv =[tex]e^{x}[/tex]
v=∫dv= [tex]e^{x}[/tex]
Substituting into equ 1
∫udv = [tex]xe^{x}[/tex] - ∫[tex]e^{x}dx[/tex]
∫udv = [tex]xe^{x}- e^{x} + C[/tex]
