Question

Find the integral, using techniques from this or the previous chapter. ∫xex dx.

Answer 1

Answer:

$xe^{x} - e^{x} +C$

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

∫$xe^{x}$

u=x ,

du= 1  

dv =$e^{x}$

v=∫dv= $e^{x}$

Substituting into  equ 1

∫udv = $xe^{x}$ - ∫$e^{x}dx$

∫udv = $xe^{x}- e^{x} + C$