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Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and ... Definite Integrals From Physics, Engineering,

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Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and ... Definite Integrals From Physics, Engineering,

4.85 84,600 ratings · 99,540 reviews
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Overview: Preface.- 1. Introduction.- 1.1 The Riemann Integral.- 1.2 An Example of Riemann Integration.- 1.3 The Lebesgue Integral.- 1.4 'Interesting' and 'Inside'.- 1.5 An Example of a Trick.- 1.6 Singularities.- 1.7 Dalzell's Integral.- 1.8 Where Integrals Come From.- 1.9 Last Words.- 1.10 Challenge Problems.- 2. 'Easy' Integrals.- 2.1 Six 'Easy' Warm-ups.- 2.2 A New Trick.- 2.3 Two Old Tricks, Plus a New One.- 2.4 Another Old Euler's Log-Sine Integral.- 2.5 Challenge Problems.- 3. Feynman's Favorite Trick.- 3.1 Leibniz's Formula.- 3.2 Dirichlet's Amazing Integral.- 3.3 Frullani's Integral.- 3.4 The Flip-Side of Feynman's Trick.- 3.5 Combining Two Tricks.- 3.6 Uhler's Integral and Symbolic Integration.- 3.7 The Probability Integral Revisited.- 3.8 Dini's Integral.- 3.9 Feynman's Favorite Trick Solves a Physics Equation .- 3.10 Challenge Problems.- 4. Gamma and Beta Function Integrals.- 4.1 Euler's Gamma Function.- 4.2 Wallis' Integral and the Beta Function.- 4.3 Double Integration Reversal.- 4.4 The Gamma Function Meets Physics.- 4.5 Challenge Problems.- 5. Using Power Series to Evaluate Integrals.- 5.1 Catalan's Constant.- 5.2 Power Series for the Log Function.- 5.3 Zeta Function Integrals.- 5.4 Euler's Constant and Related Integrals.- 5.5 Challenge Problems.- 6. Seven Not-So-Easy Integrals.- 6.1 Bernoulli's Integral .- 6.2 Ahmed's Integral.- 6.3 Coxeter's Integral.- 6.4 The Hardy-Schuster Optical Integral.- 6.5 The Watson/van Peype Triple Integrals.- 6.6 Elliptic Integrals in a Physical Problem.- 6.7 Challenge Problems.- 7. Using √(-1) to Evaluate Integrals.- 7.1 Euler's Formula.- 7.2 The Fresnel Integrals.- 7.3 (3) and More Log-Sine Integrals .- 7.4 (2), At Last!.- 7.5 The Probability Integral Again.- 7.6 Beyond Dirichlet's Integral.- 7.7 Dirichlet Meets the Gamma Function.- 7.8 Fourier Transforms and Energy Integrals.- 7.9 'Weird' Integrals from Radio Engineering.- 7.10 Causality and Hilbert Transform Integrals.- 7.11 Challenge Problems.- 8. Contour Integration.- 8.1 Prelude.- 8.2 Line Integrals.- 8.3 Functions of a Complex Variable.- 8.4 The Cauchy-Riemann Equations and Analytic Functions.- 8.5 Green's Integral Theorem.- 8.6 Cauchy's First Integral Theorem.- 8.7 Cauchy's Second Integral Theorem.- 8.8 Singularities and the Residue Theorem.- 8.9 Integrals with Multi-valued Integrands.- 8.10 Challenge Problems.- 9. Epilogue.- 9.1 Riemann, Prime Numbers, and the Zeta Function.- 9.2 Deriving the Functional Equation for (s).- 9.3 Challenge Questions.- Solutions to the Challenge Problems.

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Published August 27, 2014
ISBN 118098860
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Paul J. Nahin
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After spending years working in the corporate world, Paul J. Nahin finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Edward Diaz
Edward Diaz September 07, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Sharon Clark
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Michelle Rivera
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Joshua Gonzalez
Joshua Gonzalez June 05, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Donna Perez
Donna Perez March 27, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Jessica Harris
Jessica Harris November 17, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Laura Martinez
Laura Martinez April 09, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Betty Garcia
Betty Garcia January 23, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Kimberly Hernandez
Kimberly Hernandez February 07, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Carol Rodriguez
Carol Rodriguez February 17, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Paul Campbell
Paul Campbell March 05, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Robert Hill
Robert Hill July 17, 2025
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Eric Anderson
Eric Anderson March 21, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
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