Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 34 стр.

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ȼɚɪɢɚɧɬ ʋ 33
,1)  3()cos x 3
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
2
2
x
,2) e
()2
x
()  27x 6 x
2
,,,3) 4 ()sin 8 x4)  2( )ln 3 x
2
3 x
3( )ln x 3
,5)  3( )ln  10 2 xx
2
4
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¨
¨
·
¹
¸
¸
arctg 
x
3
1
3
3( )ln 1 x
,6)    24 x
2
10 xx 5   24 x
2
10 x ()arcsin x 5
,7) () 5 x
2
4 x 1  86xx
2
2()arcsin 3 x
,8)  2
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·
¹
¸
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ln 
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tg
x
2
32
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ln 
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tg
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33
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ln 
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tg
x
2
1
,9)  2
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¨
¨
·
¹
¸
¸
ln 
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·
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tg
x
2
3
2

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·
¹
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tg
x
2
1
2
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ln 
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tg
x
2
1
,10)  8
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©
¨
¨
¨
·
¹
¸
¸
¸
ln  
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¹
¸
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tg
x
2
2
2
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tg
x
2
516
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arctg 
1
2
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·
¹
¸
¸
tg
x
2
1
2
3
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ln 
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tg
x
2
2
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ȼɚɪɢɚɧɬ ʋ 34
,1)  4()ln
x
()cos 2
x
4()arctg 4
x
,2)   
1
4
()  12 x
3
14 x
2
24 x ()ln 6 xx
3
7 x
2
4
6 x
,,,3) 4e
e
()cos 5
4)  2( )ln 3 x 3( )ln x 62( )ln x 1
,5) ()ln 12x 3( )ln  x
2
2 x 10
,6)   x
2
10 x 29 x 5  x
2
10 x 29 4
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©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
2
5
2
 x
2
10 x 29
2
,7) ()ln  x 5  x
2
10 x 26 ( )  3 x
2
5 x 3  x
2
10 x 26
,8)  2
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©
¨
¨
·
¹
¸
¸
ln 
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©
¨
¨
·
¹
¸
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tg
x
2
22
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·
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ln 
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tg
x
2
13
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¸
ln 
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¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
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¨
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·
¹
¸
¸
ln 
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tg
x
2
46
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ln 
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tg
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1
,10)  
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¨
·
¹
¸
¸
ln 
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tg
x
2
34
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ln  
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tg
x
2
2
4
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tg
x
2
58
§
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arctg 
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·
¹
¸
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tg
x
2
2
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ȼɚɪɢɚɧɬ ʋ 35
,1)  2()cos 3
x
4()sin 3
x
4()ln
x
,2) 
()x 4 1 x
2
4
1
2
()arcsin x
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¨
¨
·
¹
¸
¸
 x
2
2 x
1
2
,,,3) 2( )ln ( )arcctg 7 x4)  ()ln x 3
5
x 4
()ln x 4
,5)  
1
3
()ln 23x 3( )ln  x
2
8 x 25 4
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¨
·
¹
¸
¸
arctg 
x
3
4
3
,6)  
 60 x
2
4 xx 2  60 x
2
4 x 64
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¨
¨
·
¹
¸
¸
arcsin 
x
8
1
4
,7) () 24x
2
3 x  12 x
2
4 x
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¨
¨
·
¹
¸
¸
arcsin 
x
4
1
2
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
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x
2
1
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¹
¸
¸
ln 
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©
¨
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tg
x
2
2
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
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ln 
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x
2
26
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ln 
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tg
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2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  22
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
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·
¹
¸
¸
tg
x
2
2
6
§
©
¨
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·
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¸
¸
arctg 
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·
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¸
¸
tg
x
2
12
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ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
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ȼɚɪɢɚɧɬ ʋ 36
,1)  2
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
2
2()cos 4 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin
7
x
3
,2) ()  67x 6 x
2
e
()5
x
,,,3)
2 ()arccos 5 x4)


3( )ln
x 23( )ln
x 53( )ln x 2
,5)  12 ( )ln  18 6 xx
2
16
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1()ln x 2
,6)    63 2 xx
2
  63 2 xx
2
x 64 ( )ln  x 1  63 2 xx
2
,7) 2( )ln  1 x  22xx
2
()  x
2
x 4  22xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
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¨
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tg
x
2
33
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x
2
3
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ln 
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¨
¨
·
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¸
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tg
x
2
1
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
4
§
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¨
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·
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ln 
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x
2
46
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ln 
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2
1
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
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¸
¸
tg
x
2
2
4
§
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tg
x
2
518
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¸
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arctg 
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©
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tg
x
2
2
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ln 
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¨
¨
·
¹
¸
¸
tg
x
2
1
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ȼɚɪɢɚɧɬ ʋ 37
,1)  3()arctg x 3ee
()4
x
8 x
,2)


()

3 x
3
4 x
2
3 x ()ln 2 xx
3
2 x
2
3 x
,,,3) 4 ()sin 8 x4)  
5
1 x
3( )ln x 35( )ln 1 x
,5)  2( )ln x 28( )ln  x
2
4 x 88
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
,6)  
x
2
10 xx 5 x
2
10 x 25
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
5
1
,7) () 22x
2
x  5 x
2
4 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
2
3
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
26
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©
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·
¹
¸
¸
ln 
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¨
·
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¸
¸
tg
x
2
1
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
18
§
©
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¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
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¨
¨
·
¹
¸
¸
tg
x
2
516
§
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¨
¨
·
¹
¸
¸
arctg 
1
2
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 38
,1)


8 x 4()sin x 5()arctg 4 x
,2)  
3
10
()ln 125x
2
1
50
() 150 x 75 x
2
3()arctg 5 x
3
x
10
,,,3) 4( )ln ( )arcctg 5
x
4)
3( )ln ( )
1
x
()

x
4( )
x
3