How to integrate xe^x?

Integration is the inverse process of differentiation.

Answer: The integral of xe^x gives the result xe^x - e^x + c.

Go through the explanation to understand better.

Explanation:

To find ∫ xe^xdx

We can make use of integration by parts,

⇒ ∫ udv = uv -  ∫ vdu ------(1)

Comparing the integration of xe^x with udv, we get:

x = u

⇒ dx = du

e^xdx = dv

⇒ e^x = v

Putting the value of u and v in equation (1), we get:

 ∫ udv = uv -  ∫ vdu

⇒ ∫ xe^xdx = xe^x -  ∫ e^xdx

⇒  xe^x - e^x + c

Thus, the integral of xe² gives the result xe^x - e^x + c.