Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 36 стр.

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,9)  
6
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ȼɚɪɢɚɧɬ ʋ 44
,1)  4
§
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·
¹
¸
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arcsin
4
x
3
5()cos x 2()ln x
,2)  ()sin
x
2()cos
x
2()sin
x
x
,,,3) 4 ()sin 4 x4)  2( )ln 3 x 2( )ln x 43( )ln x 2
,5)  12 ( )ln  10 2 xx
2
16
§
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¹
¸
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arctg 
x
3
1
3
()ln 12x
,6)   x
2
10 x 11 x 5  x
2
10 x 11 36 ( )ln  x 5  x
2
10 x 11
,7) 4( )ln  x 4
 x
2
8 x 15 ( ) 4 x
2
x 4  x
2
8 x 15
,8)  
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,9)  6
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,10)  
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2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 45
,1)  ()sin 4 x 3()ln x 8 x
,2) () 93x 5 x
2
e
()9
x
,,,3) 8 ()arccos 9 x4)  5( )ln x 3
1
x 4
()ln x 4
,5)  4( )ln  x
2
8 x 17 28 ( )arctg x 4
2
3
()ln x 1
,6)  
x
2
4 xx 2 x
2
4 x 4
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©
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¨
·
¹
¸
¸
arcsin 
x
2
1
,7) () 4 x 23x
2
  21 x
2
10 x 5
§
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¨
¨
·
¹
¸
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arcsin 
x
2
5
2
,8)  2
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,9)  
2
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 46
,1)  3()sin x 2 x 3e
e
()4
x
,2)   
1
36
() 12 x
3
126 x
2
252 x ()ln 5 x
x
3
9
7 x
2
4
7 x
,,,3) 6 ()cos 5 x4)  3( )ln 3 x ()ln x 52( )ln x 1
,5) ()ln ( )12x () x
2
4 x 5
,6)   x
2
6 x 10 x 3  x
2
6 x 10 ( )ln  x 3  x
2
6 x 10
,7) 4( )ln  x 3  86xx
2
() 35x 4 x
2
 86xx
2
,8)  3
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,9)  2
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,10) 6
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2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 47
,1)  5()arcsin x 6 x 5ee
()
x
,2)  
1
25
()sin 5 x
1
5
()cos 5 xx
2
5
()cos 5 x
,,,3) 6
()arctg 8 x4)  
3
x 4
4( )ln x 32( )ln x 4
,5) 2( )ln  22xx
2
1
3
()ln 13x
,6)  
  21 x
2
10 xx 5   21 x
2
10 x 4
§
¨
¨
·
¸
¸
arcsin 
x
2
5
2
,7) () 14x 3 x
2
 86xx
2
2()arcsin 3 x
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
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2
32
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,9)  6
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,10)  
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10 8
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1
3
1
3
§
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¸
tg
x
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 48
,1)  4()cos 2 x 3()arcsin 6 x
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
2
,2) () 56x 9 x
2
e
()
4
x
,,,3) 8( )ln ( )arcctg 8
x
4)


2( )ln
3
x
()ln

x
53( )ln 
x
1
,5)  
3
2
()ln 12x 3( )ln  x
2
4 x 13 12
§
©
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¨
·
¹
¸
¸
arctg 
x
3
2
3
,6)  
 x
2
8 x 32 x 4  x
2
8 x 32 16
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
4
1
 x
2
8 x 32
4
,7) 3( )ln  3 x  10 6 xx
2
() 42x 2 x
2
 10 6 xx
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
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x
2
3
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x
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33
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x
2
1
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
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x
2
3
6
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x
2
1
4
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¸
ln 
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x
2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
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·
¹
¸
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tg
x
2
2
4
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·
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x
2
54
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x
2
22
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·
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¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 49
,1)

4()ln x 3()cos 5 x 6 x