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How should I integrate?

$\int_0^\infty e^{-x^{1/3}}dx$

I think this is a simple question for the experts. But a bit hard to tell Google what I want. So, thanks for your help! :)

And this looks terrifying to me.

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Hint: Try the change of variable $u=x^{\frac{1}{3}}$ (so $dx=3u^2du$).

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  • $\begingroup$ Incidentally, WolframAlpha is (IMO) more convenient to use. $\endgroup$ – Clement C. May 18 '13 at 0:23
  • $\begingroup$ wow, haven't done these since Freshman college, U-substitution? thanks for the hint. Still trying to remember why we do that. $\endgroup$ – user13985 May 18 '13 at 0:24
  • $\begingroup$ I was googling for that site, there it is! $\endgroup$ – user13985 May 18 '13 at 0:25
  • $\begingroup$ What do you mean by "U- substitution"? The reason for doing a change of variables like this is simply "the bit in the exponent looks tricky, let's simplify it by defining it to just be something new, like $u$". $\endgroup$ – Sharkos May 18 '13 at 0:44
  • $\begingroup$ wait, it's not u-sub? can you link to me where this technique is from? $\endgroup$ – user13985 May 18 '13 at 0:49

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