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Integral of 1/x^4+1 from 0 to infinity

In this video (another Peyam Classic), I calculate the integral of 1/(x^4 + 1) using complex analysis, enjoy!

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Integral ln(sin x) from 0 to pi/2
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Integral ln(sin x) from 0 to pi/2

An integral solved by Residue Theorem
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An integral solved by Residue Theorem

Integral of 1/(x^2+1) from -inf to inf, Contour Integral
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Integral of 1/(x^2+1) from -inf to inf, Contour Integral

2026 Fields Medal: Hong Wang
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2026 Fields Medal: Hong Wang

ONE OF THE COOLEST INTEGRALS EVER!!! int ln(x)/(1+e^x) from 0 to infty
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ONE OF THE COOLEST INTEGRALS EVER!!! int ln(x)/(1+e^x) from 0 to infty

Using Feynman's technique TWICE! (the integral of sin^3(x)/x^3 from 0 to inf)
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Using Feynman's technique TWICE! (the integral of sin^3(x)/x^3 from 0 to inf)

This integral looks crazy
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This integral looks crazy

Supreme Integral with Feynman's Trick
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Supreme Integral with Feynman's Trick

integral of sin(x)/x from 0 to inf by Feynman's Technique
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integral of sin(x)/x from 0 to inf by Feynman's Technique

Complex Analysis: Integral of 1/(x^4+1) using Contour Integration
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Complex Analysis: Integral of 1/(x^4+1) using Contour Integration

How 𝑒 Was Discovered
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How 𝑒 Was Discovered

2 ridiculously awesome log integrals solved using contour integration
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2 ridiculously awesome log integrals solved using contour integration

Destroying the Gaussian Integral using Papa Leibniz and Feynman
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Destroying the Gaussian Integral using Papa Leibniz and Feynman

the quantum integral
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the quantum integral

2026 Fields Medal: Yu Deng
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2026 Fields Medal: Yu Deng

Complex Analysis: Integral of 1/(x^n+1) feat. pizza contour
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Complex Analysis: Integral of 1/(x^n+1) feat. pizza contour

Integral 1/x^n + 1 from 0 to infinity
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Integral 1/x^n + 1 from 0 to infinity

Cauchy Residue Theorem, Introduction
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Cauchy Residue Theorem, Introduction

Feynman Technique: Int( ln(x+1)/(x^2+1) )dx. Putnam Exam. Differentiating under the integral.
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Feynman Technique: Int( ln(x+1)/(x^2+1) )dx. Putnam Exam. Differentiating under the integral.

Integral of 1/(x^4+1) from 1 to inf
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Integral of 1/(x^4+1) from 1 to inf

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