# How to integrate xe^{x}?

Integration is the inverse process of differentiation.

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

Go through the explanation to understand better.

**Explanation:**

To find ∫ xe^{x}dx

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^{x}dx = dv

⇒ e^{x} = v

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

∫ udv = uv - ∫ vdu

⇒ ∫ xe^{x}dx = xe^{x} - ∫ e^{x}dx

⇒ xe^{x} - e^{x} + c

### Thus, the integral of xe^x gives the result as xe^{x} - e^{x} + c.