How to integrate xex?
Integration is the inverse process of differentiation.
Answer: The integral of xe^x gives the result as xex - ex + c.
Go through the explanation to understand better.
To find ∫ xexdx
We can make use of integration by parts,
⇒ ∫ udv = uv - ∫ vdu ------(1)
Comparing the integration of xex with udv, we get:
x = u
⇒ dx = du
exdx = dv
⇒ ex = v
Putting the value of u and v in equation (1), we get:
∫ udv = uv - ∫ vdu
⇒ ∫ xexdx = xex - ∫ exdx
⇒ xex - ex + c
Thus, the integral of xe^x gives the result as xex - ex + c.