Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 45 стр.

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,10)  3
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¹
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ln  18 6
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tg
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1
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2
1
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tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 92
,1)  3()cos 4 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin
3
x
2
e
x
,2)  
1
3
()cos 3 x ()sin 3 xx
1
3
()sin 3 x
,,,3) 4e
e
()arctg 3
x
4)  2( )ln x 3()ln x 12( )ln x 2
,5)  12 ( )ln  x
2
4 x 13 12
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
2
3
3
2
()ln x 1
,6)  
x
2
10 xx 5 x
2
10 x 25 ( )ln  x 5 x
2
10 x
,7) 2( )ln  x 5  x
2
10 x 26 ( ) 2 x
2
3 x 1  x
2
10 x 26
,8)  3
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©
¨
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·
¹
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ln 
§
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tg
x
2
33
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ln 
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33
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ln 
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,9)  6
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©
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ln 
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32
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,10)  6
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6
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18 8
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arctg 
1
3
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x
2
12
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 93
,1)  10 x 2e
e
()
x
2()ln x
,2) () 93x 8 x
2
e
()4
x
,,,3) 4e
e
()sin 3 x
4)  5( )ln 3 x
4
3 x
4( )ln x 1
,5)  4( )ln  10 6 xx
2
28 ( )arctg 3 x
1
2
()ln x 1
,6)  
 7 x
2
8 xx 4  7 x
2
8 x 9
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
4
3
,7) () 33x
2
x   16 x
2
10 x 3
§
¨
¨
·
¸
¸
arcsin 
x
3
5
3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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tg
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33
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ln 
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x
2
3
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,9)  4
§
©
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ln 
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32
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3
6
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,10)  
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ln  
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4
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58
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arctg 
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tg
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23
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tg
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2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 94
,1)  5()sin x 5e
e
()3
x
3()cos 3 x
,2)   
1
4
() 12 x
3
10 x
2
20 x ()ln 4 xx
3
5 x
2
4
5 x
,,,3) 6
()sin 4 x4)  ()ln x 33( )ln x 62( )ln 1 x
,5)  
3
2
()ln 1 x 3( )ln  x
2
6 x 18 2
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)  
 x
2
10 x 26 x 5  x
2
10 x 26 ( )ln  x 5  x
2
10 x 26
,7) 4( )ln  x 3  86xx
2
() 24x 2 x
2
 86xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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x
2
3
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1
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
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2
3
2
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,10)  12
§
©
¨
¨
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·
¹
¸
¸
¸
ln  
§
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tg
x
2
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4
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x
2
13 8
§
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¸
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arctg 
1
3
§
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¸
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tg
x
2
2
3
3
§
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ln 
§
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¨
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·
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¸
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 95
,1)  5()arcsin 4 x 4()cos 2 x
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
3
,2) 
()3 x 6 19x
2
18
§
©
¨
¨
·
¹
¸
¸
 x
1
18
x
2
()arcsin 3 x
,,,3) 6 ()sin 3 x4)  ()ln 3 x
4
3 x
3( )ln x 1
,5)  8( )ln  x
2
4 x 820
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
3
2
()ln 32x
,6)  
x
2
8 xx 4 x
2
8 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
,7) ()  x 3 x
2
 9 x
2
10 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
5
4
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
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tg
x
2
32
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2
13
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ln 
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tg
x
2
2
,9)  6
§
©
¨
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·
¹
¸
¸
ln 
§
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x
2
32
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x
2
4
6

§
©
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¨
·
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¸
tg
x
2
3
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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·
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tg
x
2
33
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¸
ln  
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x
2
2
6
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·
¹
¸
¸
tg
x
2
18 8
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 96
,1)

3()ln
x
2()cos
x
3()sin 3
x
,2) 3ee
()
4
x
()  3 xx
2
,,,3) 8ee
()arccos 7
x
4)  2( )ln x 5()ln x 1()ln x 2
,5)  6( )ln  18 6 xx
2
20
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
1
2
()ln 1 x
,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 3
 86xx
2
() 12x 5 x
2
 86xx
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
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x
2
22
§
©
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¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13 8
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 97
,1
)

2()arcsin 6
x
2()sin
x
2()cos 2
x