Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 33 стр.

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,9)  6
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 28
,1)  3e
e
()5 x
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·
¹
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arctg
3
x
2
3()arcsin x
,2)   
1
4
()  12 x
3
10 x
2
24 x ()ln 2 xx
3
5 x
2
4
6 x
,,,3) 8
()arcctg 2 x4)  3( )ln x 32( )ln x 23( )ln 1 x
,5)  4( )ln  13 6 xx
2
16
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arctg 
3
2
x
2
()ln 23x
,6)   x
2
6 x 27 x 3  x
2
6 x 27 36 ( )ln  x 3  x
2
6 x 27
,7) ()ln  x 3
 x
2
6 x 8( ) 4 x
2
x 4  x
2
6 x 8
,8)  2
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33
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,9)  4
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,10)  3
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 29
,1)  10 x 5()cos 5 x ()sin 2 x
,2)   
3
8
()ln 116x
2
1
32
()16 x
2
96 x ()arcctg 4 x
x
8
1
32
()arctg 4 x
,,,3) 6
()arctg 5 x4)  
3
x 5
()ln x 5()ln x 1
,5)  3( )ln  10 2 xx
2
6
§
©
¨
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·
¹
¸
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arctg 
x
3
1
3
1
2
()ln 1 x
,6)  
 32 x
2
4 xx 2  32 x
2
4 x 36
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·
¹
¸
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arcsin 
x
6
1
3
,7) () x 3 x
2
  16 x
2
10 x 3
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·
¹
¸
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arcsin 
x
3
5
3
,8)  3
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,9)  4
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,10)  3
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 30
,1)  4()ln
x
3()cos
x
()arcsin 7
x
,2) 3e
e
()5
()  22xx
2
,,,3) 4e
e
()arctg 3
x
4)  2( )ln x 2()ln x 63( )ln 1 x
,5)  6( )ln  x
2
8 x 25 8
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arctg 
x
3
4
3
2
3
()ln x 1
,6)  3   55 6 xx
2
  55 6 xx
2
x 64 ( )ln  x 3   55 6 xx
2
,7) 3( )ln  x 5  x
2
10 x 26 ( ) 5 x
2
2 x 4  x
2
10 x 26
,8)  3
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,9)  2
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ln 
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,10)  
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x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 31
,1)

5()arctg 7 x 6 x 2()cos 2 x
,2)   
1
4
() 12 x
3
18 x
2
32 x ()ln 3 xx
3
9 x
2
4
8 x
,,,3) 6
()arccos 9 x4)  
3
x 4
3( )ln x 22( )ln x 4
,5)  ()ln x 312( )ln  x
2
4 x 13 18
§
©
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¨
·
¹
¸
¸
arctg 
x
3
2
3
,6)  
 63 2 xx
2
 63 2 xx
2
x 64
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
8
1
8
,7) ()  2 x 3 x
2
x
2
4 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
1
,8)  
§
©
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·
¹
¸
¸
ln 
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2
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,9)  2
§
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6
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2
3
,10)  
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2
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32
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x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 32
,1)

4()ln
x
4()arcsin 4
x
()cos 2
x
,2)  
()6 x 16 14x
2
16
1
16
()24 x
2
32 x ()arccos 2 x
3
16
()arcsin 2 x
,,,3) 4( )ln ( )arcsin 7
x
4)

2( )ln
3
x
2( )ln

x
33( )ln 
x
5
,5)  6( )ln  x
2
2 x 10 4
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
x
3
2( )ln x 2
,6)  
 x
2
4 x 13 x 2  x
2
4 x 13 9
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
3
2
3
 x
2
4 x 13
3
,7) 2( )ln  1 x  22xx
2
() 44x 5 x
2
 22xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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x
2
2
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12
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x
2
2
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
3
2
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2
3
6
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2
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,10)  8
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  13 6
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x
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x
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32
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2
1
2
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