PF Integral Bee: Share Interesting/Quirky Integrals!

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SUMMARY

The forum discussion centers around the concept of sharing interesting and quirky integrals, specifically highlighting the integral ##\displaystyle{\int_0^1} \dfrac{\ln{(x+1)}}{x^2+1} dx##. Participants express enthusiasm for exploring integrals, with one user noting the connection between this integral and the derivative of the natural logarithm function, ##\dfrac{d}{dx}\ln x=\dfrac{1}{x}##. The discussion encourages users to contribute their own unique integrals, fostering a collaborative learning environment.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with logarithmic functions
  • Knowledge of the fundamental theorem of calculus
  • Basic skills in mathematical notation and expressions
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  • Research advanced techniques in integral calculus
  • Explore the properties of logarithmic integrals
  • Study the applications of the fundamental theorem of calculus
  • Investigate quirky integrals in mathematical literature
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Mathematics enthusiasts, students studying calculus, educators looking for engaging examples, and anyone interested in exploring unique integrals.

ergospherical
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Thought it could be fun to have a sort of "PF Integral Bee"... if you know some interesting/quirky/etc. integrals then post them here! 🤓

To get the ball rolling...
1. ##\displaystyle{\int_0^1} \dfrac{\ln{(x+1)}}{x^2+1} dx##
 
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Not studied integrals seriously, but for me it has been really fascinating to understand ##\dfrac{d}{dx}\ln x=\dfrac{1}{x}##. The demonstration is similar to the demonstration of fundamental theorem of calculus.
 

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