Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 43 стр.

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,,,3) 6e
e
()arcsin 6 x
4)  
4
3 x
()ln 3 x 2( )ln x 2
,5)  4( )ln  22xx
2
16 ( )arctg 1 x
1
2
()ln 12x
,6)  
 45 x
2
4 xx 2  45 x
2
4 x 49
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
7
2
7
,7) () 3 x
2
x  5 x
2
4 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
2
3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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·
¹
¸
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tg
x
2
2
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ln 
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x
2
2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2
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ln 
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x
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ln 
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x
2
4
,10)  
§
©
¨
¨
·
¹
¸
¸
ln 
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©
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tg
x
2
38
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ln  
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©
¨
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x
2
2
6
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tg
x
2
13 16
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 82
,1)  3()ln x 3e
e
()5 x
4
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
2
,2)   
1
36
() 24 x
3
90 x
2
36 x ()ln 3 x
2 x
3
9
5 x
2
4
x
,,,3) 8( )ln ( )arcctg 9
x
4)  ()ln 
x
23( )ln 
x
5()ln 1
x
,5)  2( )ln x 34( )ln  x
2
6 x 13 4
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
3
2
,6)   x
2
10 x 89 x 5  x
2
10 x 89 64
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
8
5
8
 x
2
10 x 89
8
,7) 3( )ln  x 5
 x
2
10 x 26 ( ) 5 x
2
3 x 4  x
2
10 x 26
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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¸
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x
2
1
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¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
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ln 
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x
2
34
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¸
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ln 
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¨
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·
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¸
¸
tg
x
2
1
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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·
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tg
x
2
13
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ln  
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¸
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x
2
2
4
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¸
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tg
x
2
13 2
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 83
,1)  4()sin 3
x
3()ln
x
5()cos 2
x
,2)  
1
4
()ln 116x
2
1
32
()  16 x
2
64 x 1()arctg 4 x
x
8
,,,3) 4e
e
()arcsin 5 x
4)  
3
x 4
4( )ln x 13( )ln x 4
,5)  8( )ln  x
2
4 x 824
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
1
3
()ln x 1
,6)  
x
2
8 xx 4 x
2
8 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
,7) () 5 x
2
4 x  9 x
2
10 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
5
4
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
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tg
x
2
1
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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·
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¸
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tg
x
2
42
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·
¹
¸
¸
ln 
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tg
x
2
1
,10) 8
§
©
¨
¨
¨
·
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
52
§
©
¨
¨
·
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¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 84
,1)

2()cos 5
x
5()ln
x
5()arcsin 6
x
,2) e
()9
x
()  73x 3 x
2
,,,3) 8ee
()arctg 9
x
4)  3( )ln x 42( )ln x 6()ln x 2
,5)  ()ln 1 x 6( )ln  x
2
6 x 18 8
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)   x
2
10 x 61 x 5  x
2
10 x 61 36
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
6
5
6
 x
2
10 x 61
6
,7) 2( )ln  x 2
 x
2
4 x 5( ) 2 x
2
5 x 1  x
2
4 x 5
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
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x
2
1
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
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¹
¸
¸
ln 
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¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
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¸
¸
tg
x
2
10 20
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
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¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 85
,1)

()arcsin 7
x
()arctg
x
3()ln
x
,2)   
1
18
()  30 x
3
18 x
2
108 x ()ln 8 x
5 x
3
9
x
2
2
6 x
,,,3) 2ee
()arccos 9 x
4)  
1
x 2
()ln x 13( )ln x 2
,5)  12 ( )ln  x
2
4 x 13 18
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
2
3
1
2
()ln 32x
,6)  3
6 xx
2
6 xx
2
x 9
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
,7) ()  54x
2
x  8 x
2
6 x 5()arcsin x 3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
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©
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¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
§
©
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¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
54
§
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
§
©
¨
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 86
,1)  5ee
()3
x
4()cos 2 x 3()sin 4 x
,2)  
1
25
()cos 5 x
1
5
()sin 5 xx
3
5
()sin 5 x
,,,3) 8( )ln ( )sin 2
x
4)

3( )ln

x
3()ln

x
62( )ln 
x
2
,5)  
1
3
()ln 23x 12 ( )ln  x
2
4 x 13 8
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
2
3