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Integrals

Overview

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This course covers a wide range of integrals and series, teaching various techniques and methods to solve complex mathematical problems. The learning outcomes include mastering integrals involving trigonometric functions, exponentials, and special functions like the Gaussian Integral. Students will learn skills such as tabular integration, substitution methods, and clever tricks for challenging integrals. The teaching method involves step-by-step explanations and demonstrations, with some integrals solved using multiple approaches. This course is intended for learners interested in advanced calculus, mathematical analysis, and problem-solving in mathematics.

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'HÃ´pital 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.

Dr Peyam