Integrate e^x * (x-2)

We have to integrate e^x / (x –
2)

We use integration by parts
here:

The general formula is Int [ u dv] = u*v – Int [ v
du]

let u = (x – 2) , du =
dx

dv = e^x , v =
e^x

=> Int [ (x – 2) * e^x dx] = (x – 2)* e^x – Int
[ e^x dx]

=> Int [ e^x  * ( x – 2) dx] = (x – 2) e^x
– e^x

=> Int [ e^x * ( x - 2) dx] = e^x ( x – 3) +
C

The integral of e^x / (x-2) is e^x ( x – 3)
+ C