Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 30 стр.

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,8)  3
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ȼɚɪɢɚɧɬ ʋ 12
,1)  2
§
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arctg
5
x
4
()arcsin 2 x 8
x
,2) e
()
x
()  95x 2 x
2
,,,3) 8e
e
()sin 4
x
4)  2( )ln x 42( )ln 1 x ()ln x 1
,5)  ()ln  x
2
8 x 17 10 ( )arctg x 42( )ln x 2
,6)  x
2
8 xx 4 x
2
8 x 16 ( )ln  x 4 x
2
8 x
,7) 5( )ln  1 x  22xx
2
()  12x 4 x
2
 22xx
2
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ȼɚɪɢɚɧɬ ʋ 13
,1)  2e
e
()4 x
3
§
©
¨
¨
·
¹
¸
¸
arcsin
4
x
3
4()cos 4 x
,2)   
1
9
()  12 x
3
18 x
2
36 x ()ln 7 x
4 x
3
9
x
2
4 x
,,,3) 6( )ln ( )sin 6 x4)  
4
x 4
()ln x 25( )ln x 4
,5)  
3
2
()ln 12x 4( )ln  13 6 xx
2
14
§
©
¨
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¹
¸
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arctg 
3
2
x
2
,6)  3
 16 6 xx
2
 16 6 xx
2
x 25
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arcsin 
x
5
3
5
,7) ()x 2
2
x
2
4 x 3
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arcsin 
x
2
1
,8)  3
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 14
,1)  4()arctg 2
x
3()arcsin
x
2()ln
x
,2)  
1
2
()sin 2 x
3
4
()cos 2 x
3
2
()sin 2 xx
,,,3) 2( )ln ( )arcctg 5
x
4)

3( )ln
3
x
2( )ln

x
4()ln 
x
2
,5) 3( )ln ( )
x 2( )

10 2 xx
2
,6)    24 2 xx
2
  24 2 xx
2
x 25 ( )ln  x 1   24 2 xx
2
,7) 4( )ln  x 2  x
2
4 x 3( )  x
2
3 x 3  x
2
4 x 3
,8)  
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1
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x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 15
,1)  e
()3 x
2
§
¨
¨
·
¸
¸
arcsin
7
x
3
5()arctg 2 x
,2) ()  24x 5 x
2
e
()
8
x
,,,3) 4ee
()cos 5 x
4)  
4
x 4
3( )ln x 34( )ln x 4
,5)  4( )ln  x
2
8 x 17 24 ( )arctg x 4
1
2
()ln x 1
,6)  x
2
2 x x
2
2 xx ()arcsin 1 x
,7) () 5 x
2
x  5 x
2
4 x 3
§
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¨
¨
·
¹
¸
¸
arcsin 
x
3
2
3
,8)  3
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·
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¸
¸
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,9)  6
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,10)  
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6
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1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 16
,1)  4ee
()5
x
()arcsin 4 x 2()cos x
,2)   
1
12
() 24 x
3
54 x
2
84 x ()ln 5 x
2 x
3
3
9 x
2
4
7 x
,,,3)
2( )ln ( )arcsin 7
x
4)


2( )ln

x
4()ln

x
33( )ln 1
x
,5)  2( )ln 1 x 12 ( )ln  x
2
8 x 25 40
§
©
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¨
·
¹
¸
¸
arctg 
x
3
4
3
,6)  3 6 xx
2
6 xx
2
x 9( )ln  x 3 6 xx
2
,7) ()ln  x 5  x
2
10 x 26 ( ) 4 x
2
5 x 4  x
2
10 x 26
,8)  2
§
©
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·
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¸
¸
ln 
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,9)  4
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,10)  12
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·
¹
¸
¸
¸
ln  
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x
2
2
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x
2
10 16
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1
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 17