Integration by Parts: Solving ∫x*e^-x dx

[p.mather]

Homework Statement

∫ x * e^-x dx

Homework Equations

Integration by parts: Just wondering if below is correct. Not brilliant with Integration by parts and not sure if my +ve and -ve signs are correct. Some help to say if i am correct or where i have gone wrong would be brilliant.

The Attempt at a Solution

= x * ((e^-x)/(-1)) -∫ ((e^-x)/(-1)) * 1 dx

= -x * e^-x + ∫ e^-x dx

= -x * e^-x + ((e^-x)/(-1)) +c

= -x * e^-x - e^-x +c

 

[icystrike]

Yes.. That is right.. If u are not certain just differentiate your ans..