Simple problems that Wolfram can't do

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SUMMARY

The forum discussion highlights the limitations of Wolfram Alpha in handling certain mathematical integrals, specifically the integral $$ \int_{0}^{\infty}e^{-x^p}dx=\frac{1}{p}\Gamma\left( \frac{1}{p} \right) $$, which fails to yield results. Users noted that Wolfram Mathematica successfully computes this integral, indicating that Wolfram Alpha may be a simplified version with resource constraints. Participants also shared alternative tools like https://www.integral-calculator.com/ that effectively solve such problems, emphasizing the need for precise input and alternative phrasing when using Wolfram Alpha.

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  • Understanding of integral calculus, specifically improper integrals.
  • Familiarity with Wolfram Alpha and Wolfram Mathematica functionalities.
  • Knowledge of the Gamma function and its applications in calculus.
  • Experience with online mathematical tools and calculators.
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  • Explore advanced features of Wolfram Mathematica for complex integrals.
  • Learn about the limitations and capabilities of Wolfram Alpha for mathematical queries.
  • Investigate alternative online calculators for solving integrals, such as https://www.integral-calculator.com/.
  • Research techniques for effectively inputting mathematical expressions in computational tools.
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Mathematicians, students studying calculus, educators teaching integral calculus, and anyone seeking efficient methods for solving complex integrals using computational tools.

Steve Zissou
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Hi everyone, I thought I would share a thought - apparently simple problems that Wolfram can't seem to handle. I'll go first:
$$ \int_{0}^{\infty}e^{-x^p}dx=\frac{1}{p}\Gamma\left( \frac{1}{p} \right) $$
Entering this into Wolfram alpha:
Integrate[Exp[-x^p],{x,0,\infty}]
Gets you nowhere. Ha!
Please share your own frustrations also. Thanks!
 
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But Wolfram Mathematica has no problem:
1746389059318.webp

I guess Alpha is a stripped-down Mathematica Lite!
 
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renormalize said:
But Wolfram Mathematica has no problem:
View attachment 360674
I guess Alpha is a stripped-down Mathematica Lite!
Well that's weird.
 
https://www.integral-calculator.com/ works.

Happily brought to you by our useful list of calculators:

1746390294240.webp
 
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Likes dextercioby, Steve Zissou, Lord Jestocost and 2 others
Cool!
 
Steve Zissou said:
Hi everyone, I thought I would share a thought - apparently simple problems that Wolfram can't seem to handle. I'll go first:
$$ \int_{0}^{\infty}e^{-x^p}dx=\frac{1}{p}\Gamma\left( \frac{1}{p} \right) $$
Entering this into Wolfram alpha:
Integrate[Exp[-x^p],{x,0,\infty}]
Gets you nowhere. Ha!
Please share your own frustrations also. Thanks!
I got Wolfram Alpha to give me the correct answer by submitting the problem again right after it failed the first time. I think you're just running into resource limits of the free version.
 
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FWIW ChatGPT got it

1746474166364.webp
 
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vela said:
I got Wolfram Alpha to give me the correct answer by submitting the problem again right after it failed the first time. I think you're just running into resource limits of the free version.
@vela Whoa that's unexpected. So it will do it, but there is some resource limits that I was unaware of?
 
BWV said:
FWIW ChatGPT got it

View attachment 360706
@BWV Ok that's unexpected. I've had AI give some wacky math answers so I haven't tried using that tech for a while for math.
 
  • #10
WolframAlpha cannot do simple contour integration. Can it?
 
  • #11
pines-demon said:
WolframAlpha cannot do simple contour integration. Can it?
I'm not sure how to tell WolframAlpha if certain variables are complex, real, or any sort of bounds on parameters.
 
  • #12
pines-demon said:
WolframAlpha cannot do simple contour integration. Can it?

You would have to tell it what the contour is; I'm not sure the UI is up to that.
 
  • #13
Ok I kid you not on this one:
Integrate[t^(z-1)*Exp[-t],{t,0,\infty}]
Yields the answer:

Try the following:​

  • Use different phrasing or notations
  • Enter whole words instead of abbreviations
  • Avoid mixing mathematical and other notations
  • Check your spelling
  • Give your input in English
 
  • #14
I remember wolframalpha as more capable in the past (at least for the no-account, no pay version which I used). Sadly, it appears not to be the case anymore. So we switch to https://www.integral-calculator.com/. For good.
 
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