We will do 100 integrals in one take! These are Calculus 1 and Calculus 2 integrals, techniques include 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. And don't forget to check out the 2022 version here:
https://youtu.be/jQz1gQ24OHc)
😃 Lars has beaten cancer and he is doing well right now!! : )
👉 Integrals for you t-shirt:
https://amzn.to/3qBeuw6Try the problems first:
https://www.patreon.com/posts/files-to-my-100-95153770?Solutions by Jackw11111:
https://www.blackpenredpen.com/_files/ugd/287ba5_62e3789012b14a77ae31c0986f993ecc.pdfQ1 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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