Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

My calculus skills are pathetic. I haven't done the following integration exercise before, but this looks like it should easy to evaluate.

$$ \int x e^x\ \ \mathrm{dx} $$

I can probably guess-and-check my way to the solution. But I am looking for a more systematic, algorithmic method to doing this. The first thing I tried was

$$\mathrm{\frac{d}{dx}}(x e^x) = e^x + xe^x \implies xe^x =\mathrm{\frac{d}{dx}}(x e^x)-e^x $$

but how to go from here to $ \int x e^x\ \ \mathrm{dx} $, if that's even possible.

share|cite|improve this question
I like your method. Try $xe^x$. The derivative is $xe^x+e^x$, wrong. But if we subtract $e^x$, that will fix it. So use $xe^x-e^x$. – André Nicolas Nov 14 '13 at 0:33
Ah I see. Should have been totally obvious. – NaN Nov 14 '13 at 0:36
Integration by parts is the standard method here. But there is a lot to be said for more informal methods. – André Nicolas Nov 14 '13 at 0:40

Such a systematic method exists and it's called integration by parts.

share|cite|improve this answer
You beat me by < 1 minute! – Ahaan S. Rungta Nov 14 '13 at 0:29

Have you considered Integration by Parts?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.