Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 37 стр.

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,2)   
1
6
() 12 x
3
18 x
2
36 x ()ln 4 x
2 x
3
3
3 x
2
2
6 x
,,,3) 6
()arcctg 6 x4)  
2
1 x
5( )ln 1 x 4( )ln x 1
,5)  2( )ln x 34( )ln  x
2
2 x 56
§
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¨
¨
·
¹
¸
¸
arctg 
x
2
1
2
,6)  
 8 x
2
2 xx  8 x
2
2 x 9
§
©
¨
¨
·
¹
¸
¸
arcsin 
1
3
x
3
,7) ()  43x
2
x  9 x
2
10 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
5
4
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
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tg
x
2
32
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¸
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1
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ln 
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tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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·
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tg
x
2
4
2

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·
¹
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x
2
1
2
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ln 
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tg
x
2
1
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
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tg
x
2
26
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¹
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¸
ln  
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tg
x
2
2
4
§
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¨
·
¹
¸
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tg
x
2
13 6
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
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¨
¨
·
¹
¸
¸
tg
x
2
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 50
,1)  ()arcsin 3 x 6 x 2e
e
()4
x
,2)   
1
5
()ln 125x
2
1
50
()100 x 75 x
2
()arcctg 5 x
3
x
10
3
50
()arctg 5 x
,,,3) 8 ()cos 3 x4)  2( )ln 3 x 2( )ln x 42( )ln x 2
,5)  2( )ln  22xx
2
8()arctg 1 x ()ln 1 x
,6)   x
2
8 x 48 x 4  x
2
8 x 48 64 ( )ln  x 4  x
2
8 x 48
,7) 2( )ln  x 3
 x
2
6 x 10 ( ) x
2
5 x 4  x
2
6 x 10
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
2
1
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©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
2
2
,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
42
§
©
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¨
·
¹
¸
¸
ln 
§
©
¨
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·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
16
§
©
¨
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¨
·
¹
¸
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¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
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·
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tg
x
2
18 14
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 51
,1)  2()arctg 7 x 5()sin x 10 x
,2) () 76x 2 x
2
e
()2
x
,,,3) 8e
e
()arcctg 3 x
4)  
3
x 4
()ln x 32( )ln x 4
,5)  2( )ln  x
2
2 x 510
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
2
2( )ln 1 x
,6)  
x
2
4 xx 2 x
2
4 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
1
,7) ()  2 x
2
5 x   24 x
2
10 x ()arcsin x 5
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
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¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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·
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¸
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tg
x
2
2
,10)  
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
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¸
tg
x
2
10 8
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 52
,1)  5
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
3
4()ln x 5ee
()2 x
,2)
4
3
x
§
©
¨
¨
·
¹
¸
¸
  () x
2
3 x 6()ln 3 x
x
2
3
3 x
2
6
,,,3) 2ee
()arctg 5
x
4)  2( )ln x 6()ln 1 x 2( )ln x 1
,5)  ()ln 32x 12 ( )ln  x
2
6 x 18 32
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)   x
2
2 x 17  x
2
2 x 17 x 16
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
4
1
4
 x
2
2 x 17
4
,7) ()ln  x 4  x
2
8 x 15 ( )  3 x 33x
2
 x
2
8 x 15
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
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ln 
§
©
¨
¨
·
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x
2
32
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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
4
§
©
¨
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¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  8
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
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¸
¸
tg
x
2
824
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 53
,1)  4()arcsin x 5()cos 3 x 3
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
4
,2)   
1
2
()ln 19x
2
1
6
()9 x
2
18 x ()arcctg 3 x
x
2
1
6
()arctg 3 x
,,,3) 2( )ln ( )arctg 4 x4)  
4
x 5
3( )ln x 2()ln x 5
,5)  ()ln x 23( )ln  x
2
6 x 18 2
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)  
x
2
8 xx 4 x
2
8 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
4
1
,7) () 3 x 2 x
2
  12 x
2
8 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
2
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
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¨
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·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  12
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13 12
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 54
,1)


8 x 3()cos 4 x 4()sin 4 x
,2) e
()
8
x
()  78x 4 x
2
,,,3)
4 ()arcctg 4 x4)


3( )ln
x 33( )ln
x 23( )ln x 2
,5)  4( )ln  x
2
4 x 810
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
12( )ln x 3