Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 38 стр.

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,6)   x
2
10 x 16 x 5  x
2
10 x 16 9 ( )ln  x 5  x
2
10 x 16
,7) 3( )ln  x 1
 22xx
2
() 43xx
2
 22xx
2
,8)  2
§
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ln 
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,9)  2
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4
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,10)  12
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ln  18 6
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32
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 55
,1)  5
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
4
2()arcsin 3 x 6
x
,2)   
1
4
() 12 x
3
14 x
2
4 x ()ln 3 xx
3
7 x
2
4
x
,,,3) 2 ()arccos 4 x4)  
3
1 x
4( )ln 1 x 3( )ln x 1
,5)  
3
2
()ln 12x 4( )ln  10 6 xx
2
20 ( )arctg 3 x
,6)  
 15 x
2
2 x  15 x
2
2 xx 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
4
,7) ()  32x
2
x  7 x
2
8 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
4
3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
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33
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22
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1
,9)  
2

§
©
¨
¨
·
¹
¸
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tg
x
2
1
4
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36
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1
,10)  8
§
©
¨
¨
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·
¹
¸
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¸
ln  
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2
2
4
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88
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1
2
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2
13
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x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 56
,1)  4()cos 3
x
2()ln
x
3()sin 3
x
,2)  
1
2
()ln 19x
2
1
18
()  9 x
2
54 x 1()arctg 3 x
x
6
,,,3) 2e
e
()sin 8
4)  ()ln x 33( )ln x 53( )ln 1 x
,5)  ()ln 13x 3( )ln  x
2
4 x 13 2
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
2
3
,6)   x
2
6 x 5 x 3  x
2
6 x 54( )ln  x 3  x
2
6 x 5
,7) 2( )ln  3 x
 10 6 xx
2
() 25x 5 x
2
 10 6 xx
2
,8)  3
§
©
¨
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·
¹
¸
¸
ln 
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33
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,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
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6
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2
6
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,10)  
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¸
ln 
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24
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2
32
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tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 57
,1)  4()cos 2 x 4
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
2
4ee
()5 x
,2) () 94x 3 x
2
e
()
2
x
,,,3) 8ee
()arcctg 5 x
4)  3( )ln x 5
1
x 5
3( )ln x 1
,5)  ()ln 32x 3( )ln  x
2
6 x 18 10
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)  3
 27 6 xx
2
 27 6 xx
2
x 36
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
6
1
2
,7) () 1 x
2
2 x x
2
8 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
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x
2
2
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2
,9)  
6

§
©
¨
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·
¹
¸
¸
tg
x
2
1
6
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46
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1
,10)  6
§
©
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¨
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·
¹
¸
¸
¸
ln  18 6
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x
2
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2
14
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1
3
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2
13
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x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 58
,1)

5()ln x 5ee
x
2()arcsin 2 x
,2)   
1
3
() 3 x
3
6 x
2
9 x ()ln 8 x
x
3
3
x
2
3 x
,,,3) 6ee
()cos 6
x
4)  2( )ln x 3()ln x 2()ln 1 x
,5)
3( )ln
3 x 2( )ln

22xx
2
,6)   x
2
8 x 20 x 4  x
2
8 x 20 36 ( )ln  x 4  x
2
8 x 20
,7) 5( )ln  x 1
x
2
2 x () 2 x
2
5 x 3 x
2
2 x
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
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x
2
12
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¸
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x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
36
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x
2
2
4

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¸
tg
x
2
3
,10)  8
§
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¨
·
¹
¸
¸
¸
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x
2
2
2
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¸
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x
2
512
§
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arctg 
1
2
1
2
§
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·
¹
¸
¸
tg
x
2
§
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¨
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 59
,1)  4()cos 4 x ()arcsin 5 x 3
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
4
,2)  
1
25
()cos 5 x
1
5
()sin 5 xx
3
5
()sin 5 x
,,,3) 6
()arccos 2 x4)  2( )ln x 2
2
1 x
5( )ln 1 x
,5)  2( )ln 3 x 8( )ln  x
2
2 x 510
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
2
,6)    15 x
2
8 xx 4   15 x
2
8 x ()arcsin x 4
,7) () 3 x
2
4 x 3  15 x
2
2 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
4
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
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2
33
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x
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1