Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 42 стр.

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ȼɚɪɢɚɧɬ ʋ 76
,1)  4
§
©
¨
¨
·
¹
¸
¸
arcsin
5
x
3
2e
e
()5 x
3
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
4
,2)
8
3
§
©
¨
¨
·
¹
¸
¸
  
§
©
¨
¨
·
¹
¸
¸
 3
27
16
xx
2
()ln 9 x 3
27 x
32
x
2
3
x
,,,3) 8 ()arccos 5 x4)  3( )ln x 32( )ln x 23( )ln 1 x
,5)  2( )ln  x
2
4 x 812
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
13( )ln 1 x
,6)   x
2
10 x 61 x 5  x
2
10 x 61 36
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
6
5
6
 x
2
10 x 61
6
,7) 2( )ln  x 3
 86xx
2
() 55x 4 x
2
 86xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
36
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  22
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 77
,1)  3()arctg 3 x 10 x 2()sin x
,2)  ()sin
x
()cos
x
x
2()cos
x
,,,3) 8e
e
()arcctg 2 x
4)  3( )ln x 3
5
x 2
2( )ln x 2
,5)  4( )ln  22xx
2
16 ( )arctg 1 x
1
2
()ln 32x
,6)  
 35 2 xx
2
 35 2 xx
2
x 36
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
6
1
6
,7) ()  42x 2 x
2
 76xx
2
4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
3
4
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
26
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  6
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  18 6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
20
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 78
,1)  5e
e
()
x
3()sin 3 x 4()ln x
,2) ()  18x 2 x
2
e
x
,,,3) 8e
e
()sin 2
x
4)  2( )ln 3 x ()ln x 42( )ln x 1
,5)  3( )ln x 3( )ln  x
2
8 x 17 16 ( )arctg x 4
,6)   x
2
8 x 9 x 4  x
2
8 x 925( )ln  x 4  x
2
8 x 9
,7) 4( )ln  x 1
 22xx
2
() 4 x 2 x
2
 22xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
34
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
,10) 3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
312
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 79
,1)  ()sin 3 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin
7
x
3
6
x
,2)   
1
12
() 24 x
3
54 x
2
12 x ()ln 7 x
2 x
3
3
9 x
2
4
x
,,,3) 4ee
()arcsin 6 x
4)  2( )ln 3 x
4
3 x
4( )ln x 1
,5)  
1
3
()ln 13x 12 ( )ln  x
2
2 x 10 12
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
x
3
,6)  3
 56xx
2
 56xx
2
x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
3
2
x
2
,7) ()  35x
2
3 x   21 x
2
10 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
5
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
36
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 2
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 80
,1)  5ee
()
3
x
5()sin 2 x ()arctg 6 x
,2)  
()5 x 20 125x
2
100
1
100
()50 x
2
100 x ()arccos 5 x
1
100
()arcsin 5 x
,,,3) 4( )ln ( )arctg 6
x
4)

3( )ln
3
x
3( )ln

x
32( )ln 
x
5
,5)  ()ln x 33( )ln  x
2
6 x 18 2
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)   x
2
4 x 29 x 2  x
2
4 x 29 25
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
5
2
5
 x
2
4 x 29
5
,7) 5( )ln  x 1
 22xx
2
() 1 x 4 x
2
 22xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
36
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10) 2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
5
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 81
,1)

2()sin 4
x
3()cos 5
2()ln
x
,2) () 63x 8 x
2
e
()
x