100 integrals part 2 (this is passion!)

100 integrals, part 2! This video features calculus 3 integrals and non-elementary integrals with special functions. We use a variety of integration techniques, including integration by parts, u-substitution, trig substitution, partial fraction decomposition, reverse power rule, integral reduction formulas, Weierstrass substitution, improper integrals, Feynman's technique, power series, the Gaussian Integral, double integrals, Jacobian, polar coordinates, and more! Join us in this nonstop calculus adventure and boost your integration skills. #calculus #integration #mathchallenge #nonstop #specialfunctions #techniques #improperintegrals #polarcoordinates #powerseries #feynmantechnique

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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S.
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Thanks to Nathaniel Barnett for the time stamps!
0:00 100 integrals part 2!
Q1, 0:00:46 integral of 2022
Q2, 0:03:03 integral by trig identities and u-sub
Q3, 0:08:23 integral by trig sub
Q4, 0:12:34 integral by u-sub and integration by parts
Q5, 0:17:02
Q6, 0:19:42
Q7, 0:30:07
Q8, 0:33:45
Q9, 0:37:58
Q10, 0:45:16
Q11, 0:48:30
Q12, 0:53:16
Q13, 0:59:06
Q14, 0:58:34
Q15, 1:00:41
Q16, 1:04:56
Q17, 1:07:27
Q18, 1:12:27
Q19, 1:14:42
Q20, 1:18:50
Q21, 1:22:30 integral of x^n*e^x
Q22, 1:25:14 integral of (ln(x))^n
Q23, 1:27:40 integral of sin^n(x)
Q24, 1:37:44 integral of tan^n(x)
Q25, 1:42:58 integral of sec^n(x)
Q26, 1:52:14
Q27, 1:54:45
Q28, 1:57:45
Q29, 2:01:49
Q30, 2:04:49
Q31, 2:24:38 integral of sec(x) by Weierstrass Substitution
Q32, 2:27:17
Q33, 2:31:25
Q34, 2:35:00
Q35, 2:37:20
Q36, 2:42:02
Q37, 2:44:24
Q38, 2:50:18
Q39, 2:51:53
Q40, 2:56:12
Q41, 3:00:21
Q42, 3:04:07
Q43, 3:06:45
Q44, 3:11:58
Q45, 3:19:02
Q46, 3:24:19
Q47, 3:28:36
Q48, 3:31:54
Q49, 3:33:44
Q50, 3:43:40
Q51, 3:49:16
Q52, 3:55:44
Q53, 3:59:50
Q54, 4:03:18 integral of x/(1+e^x)
Q55, 4:08:21 integral of e^x/(1+x)
Q56, 4:09:21 integral of e^e^x
Q57, 4:10:27 integral of ln(ln(x))
Q58, 4:12:40
Q59, 4:14:28
Q60, 4:19:48 integral of the Lambert W function
Q61, 4:25:39 improper integral of 1/x^p from 1 to inf
Q62, 4:28:52
Q63, 4:29:32
Q64, 4:32:55
Q65, 4:35:29 the Gaussian Integral
Q66, 4:50:04
Q67, 4:55:42
Q68, 4:58:36 integral of ln(x) from 0 to 1
Q69, 5:02:56
Q70, 5:10:32
Q71, 5:13:24 integral of ln(x)/(x-1) from 0 to 1
Q72, 5:21:08 integral of (x-1)/ln(x) from 0 to 1
Q73, 5:28:08 integral by symmetry
Q74, 5:34:14 integral by even and odd function properties
Q75, 5:43:16
Q76, 5:51:17
Q77, 5:52:58
Q78, 6:00:28 the Dirichlet integral, the integral of sin(x)/x from 0 to inf
Q79, 6:08:10
Q80, 6:13:28
Q81, 6:37:48 double integral & change the order of integration
Q82, 6:45:45
Q83, 6:49:24
Q84, 6:54:00
Q85, 6:57:25
Q86, 7:03:50
Q87, 7:07:33
Q88, 7:11:11
Q89, 7:17:27
Q90, 7:21:37
Q91, 7:28:52
Q92, 7:37:47
Q93, 7:55:15
Q94, 8:07:00
Q95, 8:10:24
Q96, 8:21:05
Q97, 8:22:55
Q98, 8:26: 30
Q99, 8:29: 59
Q100, 8:33:33
Q101, 8:38:32 the BIG integral from the Berkeley Math Tournament

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[nathanielbarnett]

Timestamps below, all errors are my own :) the times below cut off some of bprp's best jokes/explanations/tired monologues, so watch those too!

Q1, 0:00:46
Q2, 0:03:03
Q3, 0:08:23
Q4, 0:12:34
Q5, 0:17:02
Q6, 0:19:42
Q7, 0:30:07
Q8, 0:33:45
Q9, 0:37:58
Q10, 0:45:16
Q11, 0:48:30
Q12, 0:53:16
Q13, 0:59:06
Q14, 0:58:34
Q15, 1:00:41
Q16, 1:04:56
Q17, 1:07:27
Q18, 1:12:27
Q19, 1:14:42
Q20, 1:18:50
Q21, 1:22:30
Q22, 1:25:14
Q23, 1:27:40
Q24, 1:37:44
Q25, 1:42:58
Q26, 1:52:14
Q27, 1:54:45
Q28, 1:57:45
Q29, 2:01:49
Q30, 2:04:49
Q31, 2:24:38
Q32, 2:27:17
Q33, 2:31:25
Q34, 2:35:00
Q35, 2:37:20
Q36, 2:42:02
Q37, 2:44:24
Q38, 2:50:18
Q39, 2:51:53
Q40, 2:56:12
Q41, 3:00:21
Q42, 3:04:07
Q43, 3:06:45
Q44, 3:11:58
Q45, 3:19:02
Q46, 3:24:19
Q47, 3:28:36
Q48, 3:31:54
Q49, 3:33:44
Q50, 3:43:40
Q51, 3:49:16
Q52, 3:55:44
Q53, 3:59:50
Q54, 4:03:18
Q55, 4:08:21
Q56, 4:09:21
Q57, 4:10:27
Q58, 4:12:40
Q59, 4:14:28
Q60, 4:19:48
Q61, 4:25:39
Q62, 4:28:52
Q63, 4:29:32
Q64, 4:32:55
Q65, 4:35:29
Q66, 4:50:04
Q67, 4:55:42
Q68, 4:58:36
Q69, 5:02:56
Q70, 5:10:32
Q71, 5:13:24
Q72, 5:21:08
Q73, 5:28:08
Q74, 5:34:14
Q75, 5:43:16
Q76, 5:51:17
Q77, 5:52:58
Q78, 6:00:28
Q79, 6:08:10
Q80, 6:13:28
Q81, 6:37:48
Q82, 6:45:45
Q83, 6:49:24
Q84, 6:54:00
Q85, 6:57:25
Q86, 7:03:50
Q87, 7:07:33
Q88, 7:11:11
Q89, 7:17:27
Q90, 7:21:37
Q91, 7:28:52
Q92, 7:37:47
Q93, 7:55:15
Q94, 8:07:00
Q95, 8:10:24
Q96, 8:21:05
Q97, 8:22:55
Q98, 8:26:30
Q99, 8:29:59
Q100, 8:33:33

Q101, 8:38:32

[anakinhavadayuruyen]

This might be the mathematics equivalent of David Goggins doing 4030 pull-ups in 17 hours.

[lgoleml]

Most impressive is that the kept holding the mic for 9 hours instead of putting it on his collar

[harmane]

Q1, 0:00:46 (u-sub)
Q2, 0:03:03 (trig identities + u-sub)
Q3, 0:08:23 (trig sub)
Q4, 0:12:34 (u-sub + IBP)
Q5, 0:17:02 (u-sub + trig sub)
Q6, 0:19:42 (u-sub)
Q7, 0:30:07 (u-sub)
Q8, 0:33:45 (linearity of integration)
Q9, 0:37:58 (trig identities)
Q10, 0:45:16 (partial fractions)
Q11, 0:48:30 (polynomial special products + u-sub + formula)
Q12, 0:53:16 (trig identities)
Q13, 0:59:06 (expansion)
Q14, 0:58:34 (u-sub)
Q15, 1:00:41 (u-sub)
Q16, 1:04:56 (trig identities + u-sub)
Q17, 1:07:27 (trig sub)
Q18, 1:12:27 (trig identities + u-sub)
Q19, 1:14:42 (trig sub)
Q20, 1:18:50 (u-sub)
Q21, 1:22:30 (proof of a reduction formula + IBP)
Q22, 1:25:14 (proof of a reduction formula + IBP)
Q23, 1:27:40 (proof of a reduction formula + IBP)
Q24, 1:37:44 (proof of a reduction formula + IBP + u-sub)
Q25, 1:42:58 (proof of a reduction formula + IBP)
Q26, 1:52:14 (box method)
Q27, 1:54:45 (u-sub)
Q28, 1:57:45 (algebra manoeuvres)
Q29, 2:01:49 (u-sub)
Q30, 2:04:49 (trig identities)
Q31, 2:24:38 (trig identities + Weierstrass substitution + partial fractions)
Q32, 2:27:17 (trig identities + Weierstrass substitution + formula)
Q33, 2:31:25 (trig identities + Weierstrass substitution)
Q34, 2:35:00 (Weierstrass substitution)
Q35, 2:37:20 (trig identities + Weierstrass substitution)
Q36, 2:42:02 (multiplication by the conjugate)
Q37, 2:44:24 (trig substitution)
Q38, 2:50:18 (algebra manoeuvres)
Q39, 2:51:53 (relation between e^x, f(x) and f'(x))
Q40, 2:56:12 (IBP)
Q41, 3:00:21 (u-sub + trigonometric integral)
Q42, 3:04:07 (trig identities + trigonometric integral)
Q43, 3:06:45 (trig sub + elliptic integral of the first kind)
Q44, 3:11:58 (u-sub + error function)
Q45, 3:19:02 (IBP)
Q46, 3:24:19 (IBP + Fresnel integral)
Q47, 3:28:36 (trig identities + trigonometric integral)
Q48, 3:31:54 (IBP + trigonometric integral)
Q49, 3:33:44 (u-sub + IBP + exponential integral)
Q50, 3:43:40 (u-sub + IBP + trigonometric integral)
Q51, 3:49:16 (trig identities + u-sub + elliptic integral of the second kind)
Q52, 3:55:44 (u-sub + IBP + Fresnel integral)
Q53, 3:59:50 (exponential integral + IBP + imaginary error function)
Q54, 4:03:18 (IBP + offset (or Eulerian) logarithmic integral)
Q55, 4:08:21 (exponential integral)
Q56, 4:09:21 (u-sub + exponential integral)
Q57, 4:10:27 (IBP + logarithmic integral)
Q58, 4:12:40 (trigonometric integral + IBP)
Q59, 4:14:28 (Fresnel integral + IBP)
Q60, 4:19:48 (Lambert W function + u-sub + IBP)
Q61, 4:25:39 (improper integral)
Q62, 4:28:52 (improper integral)
Q63, 4:29:32 (improper integral)
Q64, 4:32:55 (improper integral)
Q65, 4:35:29 (Gaussian integral + double integrals + Jacobian)
Q66, 4:50:04 (improper integral)
Q67, 4:55:42 (improper integral)
Q68, 4:58:36 (improper integral)
Q69, 5:02:56 (improper integral)
Q70, 5:10:32 (improper integral + partial fractions)
Q71, 5:13:24 (improper integral + u-sub + power series)
Q72, 5:21:08 (improper integral + Feynman's technique)
Q73, 5:28:08 (improper integral + u-sub)
Q74, 5:34:14 (improper integral + u-sub)
Q75, 5:43:16 (improper integral + u-sub)
Q76, 5:51:17 (odd improper integral)
Q77, 5:52:58 (improper integral)
Q78, 6:00:28 (Dirichlet integral + Laplace transform)
Q79, 6:08:10 (a variant of Dirichlet integral + IBP)
Q80, 6:13:28 (another variant of Dirichlet integral + Feynman's technique)
Q81, 6:37:48 (double integral)
Q82, 6:45:45 (double integral)
Q83, 6:49:24 (double integral)
Q84, 6:54:00 (double integral)
Q85, 6:57:25 (double integral)
Q86, 7:03:50 (double integral)
Q87, 7:07:33 (double integral)
Q88, 7:11:11 (double integral)
Q89, 7:17:27 (double integral)
Q90, 7:21:37 (double integral)
Q91, 7:28:52 (double integral over a given region)
Q92, 7:37:47 (double integral over a given region)
Q93, 7:55:15 (double integral over a given region)
Q94, 8:07:00 (double integral over a given region)
Q95, 8:10:24 (double integral over a given region)
Q96, 8:21:05 (double integral over a given region)
Q97, 8:22:55 (double integral over a given region)
Q98, 8:26:30 (double integral over a given region)
Q99, 8:29:59 (double integral over a given region)
Q100, 8:33:33 (double integral over a given region)
Q101, 8:38:32 (infinitely nested square root integral + power series)

[sylvainhellegouarch]

Somebody give this man a medal. Though I think I'm equally amazed that you carried that mic for 9 hours straight.

[Anna.Bystrik]

It is very refreshing to see the presenter to do things live, in real-time, with small typos corrected and elements of improvisation : that is exactly how these topics must be taught to any student body, not via a power point presentation :)

[GlortMusic]

Can we all stand up together for a moment and appreciate how much hard work and effort bprp is putting into the hard and intricate mathematical theorems to make them easier?

Cheers Steve, you're making my approach to calculus and maths for university exams easier! :)

[JRLeeman]

I skipped ahead to see how badly your cheerful demeanour would be eroded after 9 hours of integrals, but you seem to be in great spirits throughout! Amazing! Also, you helped me remember how to do chain rule integration which I haven’t had to do in years, so thanks!

[theshyamgadhiya]

The dedication this man has inspires me to very greater extent

[hunterkiller]

I have absolutely 0 idea whats going on in the video, but its still impressive!

[Sanidhya_]

must say he is one of the best mathematics teacher i have ever seen [ he gives better pov to understand the question and solve it ] ...love from india 🇮🇳

[Ahmed_Asif]

You are a very good human being for giving free education. 🙏🏼.
Love and respect from India 🇮🇳

[sky-zgvb]

This guy is just insane
The efforts and dedication this guy has is really priceless

[ceb]

oh wow.. i havent even come close to learning calculus in my school and yet i still enjoy and somehow understand these videos. congrats man

[tambuwalmathsclass]

Incredible, you are indeed the GOAT of all Math content creators. 👍

[BrijeshsChannel]

your way of explanation is so amazing!!, even though i didn't learn power series, i was able to understand the last question. your students are really lucky to have you as their teacher!

[wowshdheusjjsjejwksjxj]

Teachnology is amazing, It can show the talents of talented and hardworking teachers like you

[coachingeducativomafisqui]

I really enjoy mathematics when I see the explanations so perfect that you do, thank you professor for teaching us and showing us your passion for this beautiful science!!!!

[blackpenredpen]

Could anyone please do the timestamps for this (in the format of "Q1, time")
Thank you very much!

[uebtonoliveira]

Hello Mr. BPRP! I'm a 16 year old guy from Brazil and I love your videos, they helped me a lot to learn calculus. Thank you for making me love math!