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Integral x^x from 0 to 1
2
Integral fractional part tan(x)
3
Gaussian Integral
4
Integral sec(x)/sin^2(x) (feat. blackpenredpen)
5
Tabular Integration
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Integral sin(x^2) from 0 to infinity
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Integral of 1/x^4+1 from 0 to infinity
8
Integral sqrt(1-x^2)
9
Integral 1/1-x^2 two ways
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Two limits with ln(x)
11
Integral of sqrt(x^2-1)
12
Integral arctan(sqrt(x))
13
Cool sum with a cool method
14
Integral sqrt(x^2+1)
15
A diagonally telescoping sum
16
Integral 1/x^n + 1 from 0 to infinity
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Integral 1/x^n + 1 from 0 to infinity
18
Integral of sin(x^2) from -infinity to infinity
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A linear algebra integral
20
Integral of 1/x^4+1 from 0 to infinity
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Integral ln(sin x) from 0 to pi/2
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Sum of 1/n^2
23
Integral of sec
24
A multivariable integral
25
A Cauchy integral
26
A gamma zeta integral
27
A golden integral
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Another golden integral
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Integral of the fractional part of 1/x
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Integral of sin^2
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A satisfying substitution
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A satisfying trig substitution
33
Metal Integral
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Sum of 1/n^2+1
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Impossible integral?
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Reddit Integral
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Reddit Integral 2
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Ramanujan Integral
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Integral ln tan from 0 to pi/2
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Integral of e^-x ln(x) from 0 to infinity
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Vardi Integral
42
Square rooty squared integral
43
Poisson Kernel
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Integral square root dx
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Integral x^sqrt(x) from 0 to 1
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Product derivative
47
Integral square root x to square root x from 0 to 1
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The Kurzweil Henstock Integral
49
Fourier less series
50
Integral ln cos squared from 0 to pi/2
51
Malmsten Integral
52
Integral sin x^n from 0 to infinity
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Integral sin sin x
54
Integral ln gamma from 0 to 1
55
Integral of Brownian motion
56
Monster Integral
57
Integral 1/x^2 + 1 two ways
58
Sum 1/n^6
59
Integral e^x cos x two ways
60
FAST Integral x^3 sin x from 0 to pi
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Integral x^3 sin(x) in OVER 1 min (Peyam Classic)
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Crazy hard or hardly crazy?
63
Gauss cubed
64
Integral e to arccos
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Integral with oscillation
66
Odd sum two ways
67
A neat limit with a clever trick
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A nice trig substitution
69
Integral with a limit
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Geometric Integral
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Infinite geometric integral
72
Integrating x^2 with my non dominant hand
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Limit with floor
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black integral red integral
75
Nice L'Hôpital Problem
76
riemann sum #shorts
77
But I AM joking, Mr. Feynman!
78
Clever substitution integral
79
a limit from Italy
80
Frullani Integral #shorts
81
red integral black integral
82
Integral 1/1-x^2 using complex numbers
83
life changing integration by parts trick
Description:
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.

Integrals

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Integral x^x from 0 to 1