1
00:00:00,613 --> 00:00:01,774
V tomto videu se ještě víc
procvičíme použití substituce,

2
00:00:01,774 --> 00:00:03,933


3
00:00:03,933 --> 00:00:07,509
kdy se hodí ji použít a jak
správně definovat proměnnou "u".

4
00:00:07,509 --> 00:00:09,343
Mějme neurčitý integrál (přirozeného
logaritmu z x) na desátou,

5
00:00:09,343 --> 00:00:12,014


6
00:00:12,014 --> 00:00:13,181


7
00:00:14,661 --> 00:00:15,494


8
00:00:17,842 --> 00:00:19,342


9
00:00:20,884 --> 00:00:22,967
to celé děleno x dx.

10
00:00:24,088 --> 00:00:25,481
Hodí se použít substituci a pokud ano,
tak jak definovat proměnnou "u"?

11
00:00:25,481 --> 00:00:28,639


12
00:00:28,639 --> 00:00:30,775
Klíč k úspěchu je vidět, jestli někde
ve výrazu mám funkci a také i její derivaci.

13
00:00:30,775 --> 00:00:34,583


14
00:00:34,583 --> 00:00:36,302
A možná jste rovnou poznali,

15
00:00:36,302 --> 00:00:38,020
že derivace přirozeného
logaritmu z x je 1 lomeno x.

16
00:00:38,020 --> 00:00:39,460


17
00:00:39,460 --> 00:00:40,501
Aby to bylo lépe,

18
00:00:40,501 --> 00:00:43,845
tak můžu tento integrál zapsat jako
(ln(x) na desátou) krát 1 lomeno x dx.

19
00:00:43,845 --> 00:00:47,375


20
00:00:47,375 --> 00:00:49,292


21
00:00:50,788 --> 00:00:52,012
Nyní to je vidět lépe.

22
00:00:52,012 --> 00:00:54,404
Máme funkci přirozený logaritmus z x
umocněnou na desátou,

23
00:00:54,404 --> 00:00:56,355


24
00:00:56,355 --> 00:00:58,212
ale taky tady máme
její derivaci, 1 lomeno x.

25
00:00:58,212 --> 00:00:59,512


26
00:00:59,512 --> 00:01:01,718
Takže můžeme použít substituci.

27
00:01:01,718 --> 00:01:03,301
Můžeme definovat "u" jako
přirozený logaritmus z x.

28
00:01:04,249 --> 00:01:06,455


29
00:01:06,455 --> 00:01:07,163
Důvod, proč jsem vybral
přirozený logaritmus z x, je ten,

30
00:01:07,163 --> 00:01:07,872


31
00:01:07,872 --> 00:01:09,126


32
00:01:09,126 --> 00:01:10,588
že vidím tady jeho derivaci.

33
00:01:10,588 --> 00:01:12,353


34
00:01:12,353 --> 00:01:13,700
A pak může říct, že
du lomeno dx je rovno 1 lomeno x.

35
00:01:13,700 --> 00:01:15,720


36
00:01:15,720 --> 00:01:16,553


37
00:01:17,508 --> 00:01:19,925
Což znamená, že du
je rovno 1 lomeno x dx.

38
00:01:21,432 --> 00:01:23,015


39
00:01:23,917 --> 00:01:26,334
A tady to máme.

40
00:01:27,655 --> 00:01:29,071
Toto je du, a toto je naše "u".

41
00:01:29,071 --> 00:01:31,858


42
00:01:31,858 --> 00:01:35,712
Krásně to zjednodušilo na
integrál z (u na desátou) du.

43
00:01:35,712 --> 00:01:38,290


44
00:01:38,290 --> 00:01:39,540


45
00:01:40,496 --> 00:01:42,163


46
00:01:44,606 --> 00:01:46,523


47
00:01:47,949 --> 00:01:49,946


48
00:01:49,946 --> 00:01:51,525


49
00:01:51,525 --> 00:01:54,358


50
00:01:54,358 --> 00:01:59,211


51
00:01:59,211 --> 00:02:00,720


52
00:02:00,720 --> 00:02:02,926


53
00:02:02,926 --> 00:02:04,259


54
00:02:06,223 --> 00:02:07,292


55
00:02:07,292 --> 00:02:10,287


56
00:02:10,287 --> 00:02:13,787


57
00:02:15,720 --> 00:02:18,739


58
00:02:18,739 --> 00:02:20,480


59
00:02:20,480 --> 00:02:22,570


60
00:02:22,570 --> 00:02:24,312


61
00:02:24,312 --> 00:02:27,354


62
00:02:27,354 --> 00:02:29,745


63
00:02:29,745 --> 00:02:30,578


64
00:02:31,789 --> 00:02:33,706


65
00:02:36,363 --> 00:02:37,361


66
00:02:37,361 --> 00:02:39,358


67
00:02:39,358 --> 00:02:41,843


68
00:02:41,843 --> 00:02:45,279


69
00:02:45,279 --> 00:02:46,835


70
00:02:46,835 --> 00:02:49,343


71
00:02:49,343 --> 00:02:50,759


72
00:02:50,759 --> 00:02:54,521


73
00:02:54,521 --> 00:02:56,166


74
00:02:56,166 --> 00:02:57,978


75
00:02:57,978 --> 00:03:00,741


76
00:03:00,741 --> 00:03:03,411


77
00:03:03,411 --> 00:03:05,640


78
00:03:05,640 --> 00:03:06,801


79
00:03:06,801 --> 00:03:09,100


80
00:03:09,100 --> 00:03:10,331


81
00:03:10,331 --> 00:03:11,677


82
00:03:11,677 --> 00:03:12,908


83
00:03:12,908 --> 00:03:15,950


84
00:03:15,950 --> 00:03:17,831


85
00:03:17,831 --> 00:03:19,131


86
00:03:19,131 --> 00:03:21,058


87
00:03:21,058 --> 00:03:23,311


88
00:03:23,311 --> 00:03:25,228


89
00:03:27,676 --> 00:03:30,259


90
00:03:33,690 --> 00:03:36,941


91
00:03:36,941 --> 00:03:39,448


92
00:03:39,448 --> 00:03:41,770


93
00:03:41,770 --> 00:03:45,462


94
00:03:45,462 --> 00:03:47,629


95
00:03:48,504 --> 00:03:49,671


96
00:03:51,848 --> 00:03:54,797


97
00:03:54,797 --> 00:03:56,399


98
00:03:56,399 --> 00:04:00,149


99
00:04:01,740 --> 00:04:04,823


100
00:04:05,687 --> 00:04:07,937


101
00:04:09,843 --> 00:04:12,189


102
00:04:12,189 --> 00:04:14,162


103
00:04:14,162 --> 00:04:15,162


104
00:04:16,461 --> 00:04:19,294


105
00:04:21,500 --> 00:04:22,667


106
00:04:25,215 --> 00:04:27,885


107
00:04:27,885 --> 00:04:29,186


108
00:04:29,186 --> 00:04:32,603