100 integrals (world record?)

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We will do 100 integrals in one take! These are the integrals you will encounter in your calculus 1 and calculus 2 classes. We will cover all integration techniques including u-substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fraction decomposition, integrals with hyperbolic functions, integrals with inverse functions, and more! This ultimate calculus tutorial will help you become an integration master and excel in further calculus and differential equations studies.

😃 Lars has beaten cancer and he is doing well right now!! : )

Q1 to Q25, myself
0:00 100 integrals in one take!
1, Integral of tan^5(x)*sec^3(x), 2:19
2, Integral of cos(2x)/(sin(x)+cos(x)), 5:58
3, Integral of (x^2+1)/(x^4-x^2+1), 8:00
4, Integral of (x+e^x)^2, 12:00
5, Integral of csc^3(x)*sec(x), 14:00
6, Integral of cos(x)/(sin^2(x)-5sin(x)-6), 20:00
7, Integral of 1/sqrt(e^x), 23:38
8, Integral of e^x*sqrt(e^x-1)/(e^x+3), 25:51
9, Integral of 1/(x+sqrt(x)), 32:04
10, Integral of abs(x-3) from -1 to 5, 34:39
11, Integral of sin(x)/sec^2019(x), 37:19
12, Integral of x*sin^-1(x)/sqrt(1-x^2), 39:00
13, Integral of 2sin(x)/sin(2x), 43:06
14, Integral of cos^2(2x), 45:36
15, Integral of 1/(x^3+1), 47:55
16, Integral of x*sin^2(x), 1:01:07
17, Integral of (x+1/x)^2, 1:04:45
18, Integral of 3/(x^2+4x+29), 1:06:00
19, Integral of cot^5(x), 1:08:08
20, 1:12:06
21, 1:13:43
22, 1:16:16
23, 1:20:15
24, 1:21:30
25, 1:25:30

Thanks to GaMeR 123
26. 1:29:48 integral of cos(sqrt x)
27. 1:31:35 integral of cosec x
28. 1:34:09 integral of sqrt(x^2+4x+13)
29. 1:43:26 integral of e^2x*cosx
30. 1:46:43 integral of (x-3)^9 from 3 to 5
31. 1:49:32 integral of (x-x^(3/2))^-1/2
32. 1:52:37 integral of (x-x^2)^-1/2
33. 1:56:03 integral of e^(2lnx)
34. 1:56:57 integral of lnx/sqrt x
35. 2:00:32 integral of 1/e^x+e^-x
36. 2:01:57 integral of log(x) base 2
37. 2:05:15 integral of x^3*sin2x
38. 2:08:32 integral of x^2[1+x^3]^1/3
39. 2:12:30
40. 2:19: 38
41. 2:27:29
42. 2:28:50 integral of (sinhx)^2
43. 2:32:53 integral of (sinhx)^3
44. 2:35:03 integral of 1/sqrt(x^2 + 1)
45. 2:36:34 integral of ln(x + sqrt(x^2 + 1)
46. 2:39:23 integral of tanh(x)
47. 2:40:59 integral of sech(x)
48. 2:48:37 integral of tanh inverse of x
49. 2:43:15 integral of sqrt(tanhx)
50. 2:51:20 integral of [x] from 0 to 5
51. 2:53:40 integral of (secx)^6

BIG thanks to Angel Mendez-Rivera
52, Integral of 1/(5x-2)^4, 2:55:51
53, Integral of ln(1+x^2), 2:57:18
54, Integral of 1/(x^4+x), 3:00:42
55, Integral of (1-tan(x))/(1 + tan(x)), 3:03:09
56, Integral of x·sec(x)·tan(x), 3:05:08
57, Integral of arcsec(x), 3:06:45
58, Integral of (1-cos(x))/(1+cos(x)), 3:11:20
59, Integral of (x^2)sqrt(x+4), 3:14:46
60, Integral of sqrt(4-x^2) from -1 to 1, 3:18:38
61, Integral of sqrt(x^2+4x), 3:25:10
62, Integral of (x^2)e^(x^3), 3:36:48
63, Integral of (x^3)e^(x^2), 3:37:27
64, Integral of tan(x)ln(cos(x)), 3:39:55
65, Integral of 1/(x^3-4x^2), 3:42:11
66, Integral of sin(x)cos(2x), 3:50:00
67, Integral of 2^ln(x), 3:58:06
68, Integral of sqrt(1+cos(2x)), 4:01:21
69, Integral of 1/(1+tan(x)), 4:02:40
70, Integral of sqrt(1- ln(x)^2)/x from 1/e to e, 4:07:13
71-72, Integral of 1/(cbrt(x)+1) & Integral of 1/cbrt(x + 1), 4:10:30
73, Integral of (sin(x)+cos(x))^2, 4:14:10
74, Integral of 2xln(1-x), 4:16:00
75, Integral of 1/(x(1+sin(ln(x))^2)), 4:19:34
76, Integral of sqrt((1-x)/(1+x)), 4:25:48
77, Integral of x^(x/ln(x)), 4:27:52
78, Integral of arcsin(sqrt(x)), 4:29:12
79, Integral of arctan(x), 4:39:16
80, Integral of f(x) from 0 to 5, f(x) is a piecewise function, 4:41:32
81, Integral of sin(1/x)/x^3, 4:44:11
82, Integral of (x-1)/(x^4-1), 4:47:18
83, Integral of sqrt(1+(x-1/(4x))^2), 4:52:49
84, Integral of e^tan(x)/(1-sin(x)^2), 4:55:17
85, Integral of arctan(x)/x^2, 4:56:12
86, Integral of arctan(x)/(1+x^2), 5:00:28
87, Integral of ln(x)^2, 5:02:32
88, Integral of sqrt(x^2+4)/x^2, 5:06:39
89, Integral of sqrt(x + 4)/x, 5:13:46
90, Integral of sin(x)^3/(cos(x)^3 + sin(x)^3), 5:18:03
91, Integral of x/(1 + x^4), 5:19:13
92, Integral of e^sqrt(x), 5:20:07
93, Integral of 1/csc(x)^3, 5:21:37
94, Integral of arcsin/sqrt(1-x^2), 5:24:16
95, Integral of sqrt(1+sin(2x)), 5:24:58
96, Integral of x^(1/4), 5:26:22
97, Integral of 1/(1+e^x), 5:27:47
98, Integral of sqrt(1+e^x), 5:29:13
99, Integral of sqrt(tan(x))/sin(2x), 5:34:43
100, Integral of 1/(1+sin(x)), 5:39:16
101, Integral of sin(x)/x + ln(x)cos(x), 5:45:39

Mistakes
33:39 should be a du, NOT dx
1:52:05 -2 times 2 equals -4, NOT -1
3:32:30 2*(1/2)*(1/2) = 1/2, NOT 1
5:16:56 MUST use absolute value since sqrt(x+4)-2 could be neg

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Комментарии

WOW... hope this record gets acknowledged and you get an entry in the guiness book of world record. And the person Lars mentioned in the video is me, so thank you so much bprp, and thanks to all others wishing me well. I finished the first of 3 chemo rounds, and apart from about 2-3 days, I did quite well on it. If things go well with chemo, I could be free from cancer by the end of April.

LS-Moto

Fun fact: the uploading time for this was 12 hours.

blackpenredpen

If you watch the video reverse, you learn the derivative.

canerylmaz

Please, differentiate all the results in one take to check

rosroblechannel

I love that you didn't just solve them, you also explained everything!

AlineMayne

1, Integral of tan^5(x)*sec^3(x), 2:19
2, Integral of cos(2x)/(sin(x)+cos(x)), 5:58
3, Integral of (x^2+1)/(x^4-x^2+1), 8:00
4, Integral of (x+e^x)^2, 12:00
5, Integral of csc^3(x)*sec(x), 14:00
6, Integral of cos(x)/(sin^2(x)-5sin(x)-6), 20:00
7, Integral of 1/sqrt(e^x), 23:38
8, Integral of e^x*sqrt(e^x-1)/(e^x+3), 25:51
9, Integral of 1/(x+sqrt(x)), 32:04
10, Integral of abs(x-3) from -1 to 5, 34:39
11, Integral of sin(x)/sec^2019(x), 37:19
12, Integral of x*sin^-1(x)/sqrt(1-x^2), 39:00
13, Integral of 2sin(x)/sin(2x), 43:06
14, Integral of cos^2(2x), 45:36
15, Integral of 1/(x^3+1), 47:55
16, Integral of x*sin^2(x), 1:01:07
17, Integral of (x+1/x)^2, 1:04:45
18, Integral of 3/(x^2+4x+29), 1:06:00
19, Integral of cot^5(x), 1:08:08
20, Integral of tan(x)/(x^4-x^2+1) from -1 to 1, 1:12:06
21, Integral of sin^3(x)*cos^2(x), 1:13:43
22, Integral of 1/(x^2*sqrt(x^2+1)), 1:16:16
23, Integral of sin(x)*sec(x)*tan(x), 1:20:15
24, Integral of sec^3(x), 1:21:30
25, Integral of 1/(x*sqrt(9x^2-1)), 1:25:30
Thanks to GaMeR 123
26. 1:29:48 integral of cos(sqrt x)
27. 1:31:35 integral of cosec x
28. 1:34:09 integral of sqrt(x^2+4x+13)
29. 1:43:26 integral of e^2x*cosx
30. 1:46:43 integral of (x-3)^9 from 3 to 5
31. 1:49:32 integral of (x-x^(3/2))^-1/2
32. 1:52:37 integral of (x-x^2)^-1/2
33. 1:56:03 integral of e^(2lnx)
34. 1:56:57 integral of lnx/sqrt x
35. 2:00:32 integral of 1/e^x+e^-x
36. 2:01:57 integral of log(x) base 2
37. 2:05:15 integral of x^3*sin2x
38. 2:08:32 integral of x^2[1+x^3]^1/3
39. 2:12:30
40. 2:19:38 integral of sqrt(x^2-1) from 1 to 2
41. 2:27:29 integral of sinh(x)
42. 2:28:50 integral of (sinhx)^2
43. 2:32:53 integral of (sinhx)^3
44. 2:35:03 integral of 1/sqrt(x^2 + 1)
45. 2:36:34 integral of ln(x + sqrt(x^2 + 1)
46. 2:39:23 integral of tanh(x) 47. 2:40:59 integral of sech(x)
48. 2:48:37 integral of tanh inverse of x
49. 2:43:15 integral of sqrt(tanhx)
50. 2:51:20 integral of [x] from 0 to 5
51. 2:53:40 integral of (secx)^6
BIG thanks to Angel Mendez-Rivera
52, Integral of 1/(5x - 2)^4, 2:55:51
53, Integral of ln(1 + x^2), 2:57:18
54, Integral of 1/(x^4 + x), 3:00:42
55, Integral of (1 - tan(x))/(1 + tan(x)), 3:03:09
56, Integral of x·sec(x)·tan(x), 3:05:08
57, Integral of arcsec(x), 3:06:45
58, Integral of (1 - cos(x))/(1 + cos(x)), 3:11:20
59, Integral of (x^2)sqrt(x + 4), 3:14:46
60, Integral of sqrt(4 - x^2) from -1 to 1, 3:18:38
61, Integral of sqrt(x^2 + 4x), 3:25:10
62, Integral of (x^2)e^(x^3), 3:36:48
63, Integral of (x^3)e^(x^2), 3:37:27
64, Integral of tan(x)ln(cos(x)), 3:39:55
65, Integral of 1/(x^3 - 4x^2), 3:42:11
66, Integral of sin(x)cos(2x), 3:50:00
67, Integral of 2^ln(x), 3:58:06
68, Integral of sqrt(1+cos(2x)), 4:01:21
69, Integral of 1/(1+tan(x)), 4:02:40
70, Integral of sqrt(1- ln(x)^2)/x from 1/e to e, 4:07:13
71-72, Integral of 1/(cbrt(x)+1) & Integral of 1/cbrt(x + 1), 4:10:30
73, Integral of (sin(x)+cos(x))^2, 4:14:10
74, Integral of 2xln(1 x), 4:16:00
75, Integral of 1/(x(1+sin(ln(x))^2)), 4:19:34
76, Integral of sqrt((1-x)/(1+x)), 4:25:48
77, Integral of x^(x/ln(x)), 4:27:52
78, Integral of arcsin(sqrt(x)), 4:29:12
79, Integral of arctan(x), 4:39:16
80, Integral of f(x) from 0 to 5, f(x) is a piecewise function, 4:41:32
81, Integral of sin(1/x)/x^3, 4:44:11
82, Integral of (x-1)/(x^4-1), 4:47:18
83, Integral of sqrt(1+(x-1/(4x))^2), 4:52:49
84, Integral of e^tan(x)/(1-sin(x)^2), 4:55:17
85, Integral of arctan(x)/x^2, 4:56:12
86, Integral of arctan(x)/(1+x^2), 5:00:28
87, Integral of ln(x)^2, 5:02:32
88, Integral of sqrt(x^2+4)/x^2, 5:06:39
89, Integral of sqrt(x + 4)/x, 5:13:46
90, Integral of sin(x)^3/(cos(x)^3 + sin(x)^3) from 0 to π/2, 5:18:03
91, Integral of x/(1 + x^4), 5:19:13
92, Integral of e^sqrt(x), 5:20:07
93, Integral of 1/csc(x)^3, 5:21:37
94, Integral of arcsin/sqrt(1 - x^2), 5:24:16
95, Integral of sqrt(1 + sin(2x)), 5:24:58
96, Integral of x^(1/4), 5:26:22
97, Integral of 1/(1 + e^x), 5:27:47
98, Integral of sqrt(1 + e^x), 5:29:13
99, Integral of sqrt(tan(x))/sin(2x), 5:34:43
100, Integral of 1/(1 + sin(x) from 0 to π/2, 5:39:16
101, Integral of sin(x)/x + ln(x)cos(x), 5:45:39

I only copied from the description of the video, for easy access. Thanks for the likes, they were not necessary. 👋

eddyfer.Y

My man never forgotten to put the “dx” and “+C”

cristobalperezperez

Time stamps!
Here are the time stamps:
[Q1 to Q25, myself]
Q1 Integral of tan^5(x)*sec^3(x), 2:19
Q2 Integral of cos(2x)/(sin(x)+cos(x)), 5:58
Q3 Integral of (x^2+1)/(x^4-x^2+1), 8:00
Q4 Integral of (x+e^x)^2, 12:00
Q5 Integral of csc^3(x)*sec(x), 14:00
Q6 Integral of cos(x)/(sin^2(x)-5sin(x)-6), 20:00
Q7 Integral of 1/sqrt(e^x), 23:38
Q8 Integral of e^x*sqrt(e^x-1)/(e^x+3), 25:51
Q9 Integral of 1/(x+sqrt(x)), 32:04
Q10 Integral of abs(x-3) from -1 to 5, 34:39
Q11 Integral of sin(x)/sec^2019(x), 37:19
Q12 Integral of x*sin^-1(x)/sqrt(1-x^2), 39:00
Q13 Integral of 2sin(x)/sin(2x), 43:06
Q14 Integral of cos^2(2x), 45:36
Q15 Integral of 1/(x^3+1), 47:55
Q16 Integral of x*sin^2(x), 1:01:07
Q17 Integral of (x+1/x)^2, 1:04:45
Q18 Integral of 3/(x^2+4x+29), 1:06:00
Q19 Integral of cot^5(x), 1:08:08
Q20 Integral of tan(x)/(x^4-x^2+1) from -1 to 1, 1:12:06
Q21 Integral of sin^3(x)*cos^2(x), 1:13:43
Q22 Integral of 1/(x^2*sqrt(x^2+1)), 1:16:16
Q23 Integral of sin(x)*sec(x)*tan(x), 1:20:15
Q24 Integral of sec^3(x), 1:21:30
Q25 Integral of 1/(x*sqrt(9x^2-1)), 1:25:30

[26 to 51, thanks to GaMeR 123]
26. 1:29:48 integral of cos(sqrt x)
27. 1:31:35 integral of cosec x
28. 1:34:09 integral of sqrt(x^2+4x+13)
29. 1:43:26 integral of e^2x*cosx
30. 1:46:43 integral of (x-3)^9 from 3 to 5
31. 1:49:32 integral of (x-x^(3/2))^-1/2
32. 1:52:37 integral of (x-x^2)^-1/2
33. 1:56:03 integral of e^(2lnx)
34. 1:56:57 integral of lnx/sqrt x
35. 2:00:32 integral of 1/e^x+e^-x
36. 2:01:57 integral of logx base 2
37. 2:05:15 integral of x^3*sin2x
38. 2:08:32 integral of x^2[1+x^3]^1/3
39. 2:12:30 integral of 1/(x^2 + 4)^2
40. 2:19:38 integral of sqrt(x^2-1) from 1 to 2
41. 2:27:29 integral of sinh(x)
42. 2:28:50 integral of (sinhx)^2
43. 2:32:53 integral of (sinhx)^3
44. 2:35:03 integral of 1/sqrt(x^2 + 1)
45. 2:36:34 integral of ln(x + sqrt(x^2 + 1)
46. 2:39:23 integral of tanhx
47. 2:40:59 integral of sechx
48. 2:48:37 integral of tanh inverse of x
49. 2:43:15 integral of sqrt(tanhx)
50. 2:51:20 integral of [x] from 0 to 5
51. 2:53:40 integral of (secx)^6

[Q52 to Q101, BIG thanks to Angel Mendez-Rivera]
Q52, Integral of 1/(5x - 2)^4, 2:55:51
Q53, Integral of ln(1 + x^2), 2:57:18
Q54, Integral of 1/(x^4 + x), 3:00:42
Q55, Integral of (1 - tan(x))/(1 + tan(x)), 3:03:09
Q56, Integral of x·sec(x)·tan(x), 3:05:08
Q57, Integral of arcsec(x), 3:06:45
Q58, Integral of (1 - cos(x))/(1 + cos(x)), 3:11:20
Q59, Integral of (x^2)sqrt(x + 4), 3:14:46
Q60, Integral of sqrt(4 - x^2) from -1 to 1, 3:18:38
Q61, Integral of sqrt(x^2 + 4x), 3:25:10
Q62, Integral of (x^2)e^(x^3), 3:36:48
Q63, Integral of (x^3)e^(x^2), 3:37:27
Q64, Integral of tan(x)ln(cos(x)), 3:39:55
Q65, Integral of 1/(x^3 - 4x^2), 3:42:11
Q66, Integral of sin(x)cos(2x), 3:50:00
Q67, Integral of 2^ln(x), 3:58:06
Q68, Integral of sqrt(1 + cos(2x)), 4:01:21
Q69, Integral of 1/(1 + tan(x)), 4:02:40
Q70, Integral of sqrt(1 - ln(x)^2)/x from 1/e to e, 4:07:13
Q71-72, Integral of 1/(cbrt(x) + 1) & Integral of 1/cbrt(x + 1), 4:10:30
Q73, Integral of (sin(x) + cos(x))^2, 4:14:10
Q74, Integral of 2xln(1 + x), 4:16:00
Q75, Integral of 1/(x(1 + sin(ln(x))^2)), 4:19:34
Q76, Integral of sqrt((1 - x)/(1 + x)), 4:25:48
Q77, Integral of x^(x/ln(x)), 4:27:52
Q78, Integral of arcsin(sqrt(x)), 4:29:12
Q79, Integral of arctan(x), 4:39:16
Q80, Integral of f(x) from 0 to 5, f(x) = 10 if x < 2 or x = 2, f(x) = 3x^2 - 2 if x > 2, 4:41:32
Q81, Integral of sin(1/x)/x^3, 4:44:11
Q82, Integral of (x - 1)/(x^4 - 1), 4:47:18
Q83, Integral of sqrt(1 + (x - 1/(4x))^2), 4:52:49
Q84, Integral of e^tan(x)/(1 - sin(x)^2), 4:55:17
Q85, Integral of arctan(x)/x^2, 4:56:12
Q86, Integral of arctan(x)/(1 + x^2), 5:00:28
Q87, Integral of ln(x)^2, 5:02:32
Q88, Integral of sqrt(x^2 + 4)/x^2, 5:06:39
Q89, Integral of sqrt(x + 4)/x, 5:13:46
Q90, Integral of sin(x)^3/(cos(x)^3 + sin(x)^3) from 0 to π/2, 5:18:03
Q91, Integral of x/(1 + x^4), 5:19:13
Q92, Integral of e^sqrt(x), 5:20:07
Q93, Integral of 1/csc(x)^3, 5:21:37
Q94, Integral of arcsin/sqrt(1 - x^2), 5:24:16
Q95, Integral of sqrt(1 + sin(2x)), 5:24:58
Q96, Integral of x^(1/4), 5:26:22
Q97, Integral of 1/(1 + e^x), 5:27:47
Q98, Integral of sqrt(1 + e^x), 5:29:13
Q99, Integral of sqrt(tan(x))/sin(2x), 5:34:43
Q100, Integral of 1/(1 + sin(x) from 0 to π/2, 5:39:16
Q101, Integral of sin(x)/x + ln(x)cos(x), 5:45:39

bprptw

it's MY sleepover and I get to choose the movie

hlhlgd

*finally finishes*

'press "start" to begin recording'

Potatoverynice

I, on the other hand, can do 1 integral in 100 takes!

snakesocks

He explained each and every integral with immense subtleness till the end hats off 👏👏👏 wasnt expecting that

jyotipawar

wtf.. he also explain his steps for every question...

kallzvx

prof: "this exam is designed to only take 1 hour"
the exam:

shulamitp

My man did *Math* for close to 6hrs straight.

*RESPECT **_100_*

nischay

the way he switches between the black and red marker while solving is impressive

fedalhanoun

Other time stamps (26-61)[1-25 are in description]
26. 1:29:48 integral of cos(sqrt x)
27. 1:31:35 integral of cosec x
28. 1:34:09 integral of sqrt(x^2+4x+13)
29. 1:43:26 integral of e^2x*cosx
30. 1:46:43 integral of (x-3)^9 from 3 to 5
31. 1:49:32 integral of (x-x^(3/2))^-1/2
32. 1:52:37 integral of (x-x^2)^-1/2
33. 1:56:03 integral of e^(2lnx)
34. 1:56:57 integral of lnx/sqrt x
35. 2:00:32 integral of 1/e^x+e^-x
36. 2:01:57 integral of logx base 2
37. 2:05:15 integral of x^3*sin2x
38. 2:08:32 integral of x^2[1+x^3]^1/3
39. 2:12:30 integral of 1/(x^2 + 4)^2
40. 2:19:38 integral of sqrt(x^2-1) from 1 to 2
41. 2:27:29 integral of sinhx
42. 2:28:50 integral of (sinhx)^2
43. 2:32:53 integral of (sinhx)^3
44. 2:35:03 integral of 1/sqrt(x^2 + 1)
45. 2:36:34 integral of ln(x + sqrt(x^2 + 1)
46. 2:39:23 integral of tanhx
47. 2:40:59 integral of sechx
48. 2:48:37 integral of tanh inverse of x
49. 2:43:15 integral of sqrt(tanhx)
50. 2:51:20 integral of [x] from 0 to 5
51. 2:53:40 integral of (secx)^6
52. 2:55:39 integral of 1/(5x-2)^4
53. 2:57:11 integral of ln(1+x^2)
54. 3:00:38 integral of 1/x^4+x
55. 3:02:59 integral of (1-tanx)/1+tanx
56. 3:04:54 integral of xsecxtanx
57. 3:06:32 integral of sec inverse of x
58. 3:11:13 integral of (1-cosx)/1+cosx
59. 3:14:38 integral of x^2*sqrt(x+4)
60. 3:18:18 integral of sqrt(4-x^2) from -1 to 1
61. 3:24:57 integral of sqrt(x^2 + 4x)

archithtelukunta

When mom says you can watch one more video before going to bed

non-inertialobserver

"As we all know"

no, i didnt

pikanoob

If I ever did this much math I would probably ascend to astral dimension

CloroxBleach-gdbz

100 integrals (world record?)

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i did another 100 integrals!

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Integral of ln(x) fast!

How calculus teachers create integrals

How calculus teachers create integrals for your test!

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100 Integrals Solved Part 2 | Breaking The World Record | 100 Subscriber Special

What my calculus 2 students did to this integral!

One weird integral trick

Integral of abs(x) in 44 seconds!

integration by parts, the life changing way!!