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The Most Satisfying Integral

We evaluate the integral from 0 to 1 of 1/(1-x) + 1/ln(x). 00:00 Substitution 02:06 Geometric series 04:00 Adding in another term 07:17 Exchanging orders 09:53 Frullani integrals 13:10 Evaluating 15:59 Conclusion

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A Beautiful Proof of a Beautiful Inequality
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A Beautiful Proof of a Beautiful Inequality

the famous goat problem
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the famous goat problem

3 Proofs of Vandermonde's Identity
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3 Proofs of Vandermonde's Identity

This trick from Euler was ingenious
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This trick from Euler was ingenious

Bigger than Graham's Number?  The innocent-looking n(k) function
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Bigger than Graham's Number? The innocent-looking n(k) function

The Obsessive Engineering of Precision Linear Motion
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The Obsessive Engineering of Precision Linear Motion

Extending the Riemann Zeta Function with Fractional Sums
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Extending the Riemann Zeta Function with Fractional Sums

A unique approach to the half-derivative.
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A unique approach to the half-derivative.

The meme hiding surprisingly advanced math
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The meme hiding surprisingly advanced math

This Calculus Problem Looks Impossible
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This Calculus Problem Looks Impossible

How Many Real Solutions Problem (Plus a Proof of Descartes' Rule of Signs)
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How Many Real Solutions Problem (Plus a Proof of Descartes' Rule of Signs)

The Fixed Point Theorem - Numberphile
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The Fixed Point Theorem - Numberphile

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A periodically perturbed harmonic series... does it converge???

How to Apply Feynman Technique Integration
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How to Apply Feynman Technique Integration

You Know You're An Engineer If... (Part 2) | Don McMillan Comedy
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You Know You're An Engineer If... (Part 2) | Don McMillan Comedy

Solving the Most Ridiculous Systems of Equations (ft. a cool theorem) #some3
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Solving the Most Ridiculous Systems of Equations (ft. a cool theorem) #some3

We can't invent a robot better than these ferrets
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We can't invent a robot better than these ferrets

A Fun Golden Ratio Limit
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A Fun Golden Ratio Limit

Another Surprising Integral That Seems Impossible
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Another Surprising Integral That Seems Impossible

William Dunham, A tribute to Euler
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William Dunham, A tribute to Euler

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