Question

Integrate x^2(e^-x/2)

Answer 1

Just to be certain that I'm interpreting your post correctly: Is the following what you meant?\[x ^{2e ^{\frac{ -x }{ 2 }}}?\] If not, please advise. Suggest you learn to use Equation Editor (blue button, below).

Answer 2

\[x ^{2}\exp ^{ \frac{ -x }{ 2 }}\]

Answer 3

Thanks hehe

Answer 4

I'm going to take your word that \(x ^{2}\exp ^{ \frac{ -x }{ 2 }}\) is correct.

Answer 5

And so you want \[\int\limits_{}^{}x ^{2}\exp ^{ \frac{ -x }{ 2 }}dx\]
What approach or approaches would you consider using here?

Answer 6

Product rule? :S

Answer 7

the product rule is for differentiation, not for integration. What about integration by parts?

Answer 8

Hint:\[\int\limits_{}^{}e ^{\frac{ -x }{ 2 }}dx=-2e ^{\frac{ -x }{ 2 }}+C\]

Answer 9

\[u=x ^{2}\] \[u'=2x\] \[v=\exp ^{\frac{ -x }{ 2 }}\]\[v'=2\exp ^{\frac{ -x }{ 2 }}\]

Answer 10

Your u and u' are fine, but it's v' that equals exp(-x/2) and it's v that equals -2exp(-x/2).

Answer 11

Although I'm going to get off the Internet now, others could continue helping you with this. If no one else has helped you to your satisfaction when I'm back on OpenStudy, I'd gladly continue. Good luck!

Answer 12

Okay, thanks! :)