Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 29 стр.

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,5)  8( )ln  13 6 xx
2
32
§
©
¨
¨
·
¹
¸
¸
arctg 
3
2
x
2
1
2
()ln 32x
,6)   x
2
8 x 20 x 4  x
2
8 x 20 36 ( )ln  x 4  x
2
8 x 20
,7) ()ln  x 3
 x
2
6 x 10 ( ) 2 x 42x
2
 x
2
6 x 10
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
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ln 
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x
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ln 
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tg
x
2
1
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
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·
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ln 
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·
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tg
x
2
26
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·
¹
¸
¸
ln 
§
©
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·
¹
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tg
x
2
1
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
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·
¹
¸
¸
tg
x
2
514
§
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¨
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·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
§
©
¨
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·
¹
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¸
ln 
§
©
¨
¨
·
¹
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tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 7
,1)  2()arctg 2 x 4()ln x 6 x
,2)   
1
36
()  24 x
3
126 x
2
180 x ()ln 9 x
2 x
3
9
7 x
2
4
5 x
,,,3) 8( )ln ( )arcsin 2 x4)  
3
x 4
()ln x 22( )ln x 4
,5)  ()ln 3 x 3( )ln  x
2
6 x 18 14
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)  
x
2
4 xx 2 x
2
4 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
1
,7) () 3 x
2
x 5 x
2
6 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
,10)  6
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
18 14
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
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·
¹
¸
¸
ln 
§
©
¨
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·
¹
¸
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 8
,1)  2()ln x 4()cos 3 x e
()4
x
,2)  
3
10
()ln 125x
2
1
50
()  25 x
2
150 x 1()arctg 5 x
x
10
,,,3) 2 ()arctg 9 x4)2( )ln ( )x 2( )x 1( )x 3
,5)  ()ln 1 x 4( )ln  x
2
6 x 13 10
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
3
2
,6)  3   40 6 xx
2
  40 6 xx
2
x 49 ( )ln  x 3   40 6 xx
2
,7) 5( )ln  1 x  22xx
2
()  13x 3 x
2
 22xx
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
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©
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tg
x
2
33
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
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·
¹
¸
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x
2
1
,10)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
56
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 9
,1)  2()cos 3 x
§
©
¨
¨
·
¹
¸
¸
arcsin
4
x
3
4()sin 4 x
,2) ()  83x 2 x
2
e
()
9
x
,,,3) 6ee
()arcctg 2 x
4)  
2
x 4
3( )ln x 15( )ln x 4
,5)  ()ln  x
2
6 x 10 2 ( )arctg x 3
1
3
()ln x 1
,6)  
  16 x
2
10 xx 5   16 x
2
10 x 9
§
©
¨
¨
·
¹
¸
¸
arcsin 
3
5
3
,7) ()  3 x 5 x
2
 82xx
2
4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
12
§
©
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  8
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
820
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 10
,1)  
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
4
5()sin 2 x ()cos 5 x
,2)   
1
4
() 12 x
3
6 x
2
4 x ()ln 5 xx
3
3 x
2
4
x
,,,3) 4( )ln ( )arcsin 8
x
4) ()ln ( )
1
x
()

x
4( )

x
3
,5)  
2
3
()ln 23x 6( )ln  x
2
2 x 10 8
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
x
3
,6)   x
2
8 x 15 x 4  x
2
8 x 15 ( )ln  x 4  x
2
8 x 15
,7) 2( )ln  x 2
 x
2
4 x 5( )  5 x
2
3 x 4  x
2
4 x 5
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 28
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 11
,1)  3ee
()
x
5()arctg 4 x 4( )sin 2 x
,2)  
2
9
()sin 3 x
2
3
()cos 3 xx
1
3
()cos 3 x
,,,3) 4
()sin 2 x4)  ()ln x 3
1
x 4
5( )ln x 4
,5)  ()ln 13x 8( )ln  x
2
6 x 13 20
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
3
2
,6)  
 7 x
2
6 xx 3  7 x
2
6 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
3
4
,7) () 23x
2
2 x  12 x
2
4 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
2