how would i integrate 5xe^(-x)

Question

anonymous · Answer

Integration by parts

anonymous · Answer

how do you do that?

anonymous · Answer

$$
\int f\cdot g' = fg-\int f'\cdot g
$$

anonymous · Answer

In this example it's easiest to set $g'=e^{-x}, f=x$, you can just pull the 5 outside of the integral.

anonymous · Answer

what is the correct answer?

lgbasallote · Answer

in choosing f you follow this order of priority
1. logarithms
2. inverse trig functions
3. algebraic expressions
4. trig functions
5. exponential functions

anonymous · Answer

What are you getting as an answer? I'll let you know whether it's correct or not.

anonymous · Answer

i got -xe^(-x)+e^(-x)+c

anonymous · Answer

Don't forget about the 5 that you originally pulled out.

anonymous · Answer

is that right?

anonymous · Answer

Also, to verify an answer, just take the derivative and see if you get what you started with :)

anonymous · Answer

ok i will do that right now

anonymous · Answer

Put the 5 back in on each term, though, and yes that is correct. Still worth deriving to double-check though.

anonymous · Answer

yay thanks. so that means my answer should have been -5xe^(-x)+5e^(-x) right?

anonymous · Answer

Actually I think it's -5xe^(-x)-5e^(-x). Triple negative on the second term, one from the integration by parts formula, one from g, and one from integrating g. Sorry, doing this all in my head not with pen and paper.

anonymous · Answer

thank you