Overview

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Dive into an extensive 18-hour exploration of integrals and series, covering a wide range of advanced mathematical concepts. Master techniques for solving complex integrals, including Gaussian, tabular, and Cauchy integrals. Explore fascinating topics such as the Poisson Kernel, Kurzweil Henstock Integral, and Fourier series. Learn to tackle challenging problems involving trigonometric functions, logarithms, and exponentials. Discover clever substitution methods, integration by parts tricks, and approaches to solving seemingly impossible integrals. Engage with real-world applications of integral calculus, including Brownian motion and linear algebra. Enhance your problem-solving skills through a diverse array of exercises, from classic integrals to mind-bending challenges inspired by mathematical greats like Ramanujan. Perfect for advanced mathematics students and enthusiasts looking to deepen their understanding of integral calculus and its applications.

Syllabus

Integral x^x from 0 to 1.
Integral fractional part tan(x).
Gaussian Integral.
Integral sec(x)/sin^2(x) (feat. blackpenredpen).
Tabular Integration.
Integral sin(x^2) from 0 to infinity.
Integral of 1/x^4+1 from 0 to infinity.
Integral sqrt(1-x^2).
Integral 1/1-x^2 two ways.
Two limits with ln(x).
Integral of sqrt(x^2-1).
Integral arctan(sqrt(x)).
Cool sum with a cool method.
Integral sqrt(x^2+1).
A diagonally telescoping sum.
Integral 1/x^n + 1 from 0 to infinity.
Integral 1/x^n + 1 from 0 to infinity.
Integral of sin(x^2) from -infinity to infinity.
A linear algebra integral.
Integral of 1/x^4+1 from 0 to infinity.
Integral ln(sin x) from 0 to pi/2.
Sum of 1/n^2.
Integral of sec.
A multivariable integral.
A Cauchy integral.
A gamma zeta integral.
A golden integral.
Another golden integral.
Integral of the fractional part of 1/x.
Integral of sin^2.
A satisfying substitution.
A satisfying trig substitution.
Metal Integral.
Sum of 1/n^2+1.
Impossible integral?.
Reddit Integral.
Reddit Integral 2.
Ramanujan Integral.
Integral ln tan from 0 to pi/2.
Integral of e^-x ln(x) from 0 to infinity.
Vardi Integral.
Square rooty squared integral.
Poisson Kernel.
Integral square root dx.
Integral x^sqrt(x) from 0 to 1.
Product derivative.
Integral square root x to square root x from 0 to 1.
The Kurzweil Henstock Integral.
Fourier less series.
Integral ln cos squared from 0 to pi/2.
Malmsten Integral.
Integral sin x^n from 0 to infinity.
Integral sin sin x.
Integral ln gamma from 0 to 1.
Integral of Brownian motion.
Monster Integral.
Integral 1/x^2 + 1 two ways.
Sum 1/n^6.
Integral e^x cos x two ways.
FAST Integral x^3 sin x from 0 to pi.
Integral x^3 sin(x) in OVER 1 min (Peyam Classic).
Crazy hard or hardly crazy?.
Gauss cubed.
Integral e to arccos.
Integral with oscillation.
Odd sum two ways.
A neat limit with a clever trick.
A nice trig substitution.
Integral with a limit.
Geometric Integral.
Infinite geometric integral.
Integrating x^2 with my non dominant hand.
Limit with floor.
black integral red integral.
Nice L'Hôpital Problem.
riemann sum #shorts.
But I AM joking, Mr. Feynman!.
Clever substitution integral.
a limit from Italy.
Frullani Integral #shorts.
red integral black integral.
Integral 1/1-x^2 using complex numbers.
life changing integration by parts trick.