Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 44 стр.

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,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 4
 x
2
8 x 15 ( ) 4 x
2
2 x 3  x
2
8 x 15
,8)  2
§
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¨
·
¹
¸
¸
ln 
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33
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,9)  6
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6
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,10)  4
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ln  22
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6
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1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 87
,1)  4e
e
()3
x
5()sin 4 x 8 x
,2) ()  63x 7 x
2
e
()6
x
,,,3) 4e
e
()arccos 9 x
4)  
3
x 5
3( )ln x 5()ln x 1
,5)  4( )ln  x
2
4 x 512 ( )arctg x 2()ln 1 x
,6)    15 x
2
8 xx 4   15 x
2
8 x ()arcsin x 4
,7) ()  12x
2
3 x   16 x
2
10 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
5
3
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
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33
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23
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,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
4
§
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ln 
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2
42
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2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  10 6
§
©
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¹
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¸
tg
x
2
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2
2
16
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2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 88
,1)  5()arctg 2 x 6 x 5()sin x
,2)   
1
36
() 48 x
3
126 x
2
216 x ()ln 9 x
4 x
3
9
7 x
2
4
6 x
,,,3) 4e
e
()cos 9
x
4)  2( )ln 3 x 3( )ln x 43( )ln x 3
,5)  2( )ln  13 6 xx
2
14
§
©
¨
¨
·
¹
¸
¸
arctg 
3
2
x
2
2( )ln 1 x
,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 24 ( ) 4 x 33x
2
 x
2
10 x 24
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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x
2
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12
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,9)  6
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ln 
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,10)  4
§
©
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·
¹
¸
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¸
ln  
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2
2
2
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56
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1
2
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x
2
1
2
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 89
,1)  5()ln x 4()cos 3 x 10 x
,2)  
2
9
()cos 3 x
2
3
()sin 3 xx
2
3
()sin 3 x
,,,3) 6ee
()arccos 6 x
4)  4( )ln x 3
5
x 2
5( )ln x 2
,5)  8( )ln  x
2
8 x 20 36
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
2
3
2
()ln 32x
,6)    15 x
2
8 xx 4   15 x
2
8 x ()arcsin x 4
,7) () 2 x 33x
2
 3 x
2
4 x 5()arcsin x 2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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2
3
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x
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2
,9)  
2

§
©
¨
¨
·
¹
¸
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tg
x
2
1
4
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36
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,10)  4
§
©
¨
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¨
·
¹
¸
¸
¸
ln  
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x
2
2
6
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x
2
13 4
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1
2
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2
3
2
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 90
,1)  2
§
©
¨
¨
·
¹
¸
¸
arcsin
3
x
2
2()arctg 3 x ()cos 5 x
,2) ()  19x 3 x
2
e
()7
x
,,,3) 8ee
()cos 8
x
4)  2( )ln x 4()ln x 32( )ln 1 x
,5)  ()ln 3 x 8( )ln  x
2
6 x 13 20
§
©
¨
¨
·
¹
¸
¸
arctg 
2
3
2
,6)   x
2
4 x 20 x 2  x
2
4 x 20 16
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
4
1
2
 x
2
4 x 20
4
,7) 2( )ln  x 1
x
2
2 x () 4 x
2
3 x 4 x
2
2 x
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
32
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2
23
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x
2
1
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
32
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x
2
4
4

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x
2
3
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
32
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ln  22
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x
2
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2
2
8
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§
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·
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tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 91
,1)

3()ln
x
3()arcsin 7
x
3()sin
x
,2)   
1
36
() 84 x
3
162 x
2
36 x ()ln 6 x
7 x
3
9
9 x
2
4
x
,,,3) 2ee
()arccos 2 x
4)  3( )ln 3 x 2( )ln x 3
5
3 x
,5)

4( )ln 
x
2
8 x 17 34 ( )arctg
x 42( )ln 1 x
,6)   15 x
2
2 xx  15 x
2
2 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
4
,7) ()  5 x
2
4 x 4 x
2
4 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
1
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
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¨
·
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¸
ln 
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©
¨
¨
·
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¸
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x
2
13
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¸
¸
ln 
§
©
¨
¨
·
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¸
¸
tg
x
2
2
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
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x
2
3
4

§
©
¨
¨
·
¹
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x
2
1
4
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1