Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 31 стр.

UptoLike

Составители: 

,1)  3()ln x ()sin 2 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin
7
x
3
,2)  
1
6
()ln 19x
2
1
18
()  18 x 18 x
2
2()arctg 3 x
x
3
,,,3) 4e
e
()arccos 2 x
4)  
1
x 4
5( )ln x 12( )ln x 4
,5)  
3
2
()ln x 112( )ln  x
2
2 x 10 6
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
x
3
,6)  
 5 x
2
6 xx 3  5 x
2
6 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
3
2
,7) () 4 x 15x
2
6 xx
2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
22
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
46
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
18
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
512
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 18
,1)  e
()4
x
2()sin 4 x 2 x
,2) e
()5
x
()  47x 7 x
2
,,,3) 2e
e
()sin 6
x
4)  3( )ln x 42( )ln x 53( )ln x 2
,5)  2( )ln  x
2
8 x 17 8 ( )arctg x 4
1
3
()ln 13x
,6)   x
2
4 x 53 x 2  x
2
4 x 53 49
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
7
2
7
 x
2
4 x 53
7
,7) 2( )ln  x 5  x
2
10 x 26 ( ) 5 x
2
2 x 1  x
2
10 x 26
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
34
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
¨
¨
¨
·
¸
¸
¸
ln  
§
¨
¨
·
¸
¸
tg
x
2
2
2
§
¨
¨
·
¸
¸
tg
x
2
56
§
¨
¨
·
¸
¸
arctg 
1
2
§
¨
¨
·
¸
¸
tg
x
2
1
2
2
§
¨
¨
·
¸
¸
ln 
§
¨
¨
·
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 19
,1)  5()arctg 2 x 3()ln x 4 x
,2)
§
©
¨
¨
·
¹
¸
¸
  () 6 xx
2
()ln 8 x 6
x
2
x
2
3
x
,,,3) 8e
e
()arctg 3 x
4)  
4
x 4
4( )ln x 12( )ln x 4
,5)  
1
3
()ln 13x ()ln  x
2
4 x 512 ( )arctg x 2
,6)  
 35 2 xx
2
 35 2 xx
2
x 36
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
6
1
6
,7) ()  2 x
2
5 x 5 x
2
2 x 2()arcsin 1 x
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
23
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
36
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 22
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 20
,1)

2()ln
x
4()arctg 6
x
()arcsin 2
x
,2)  
1
8
()cos 4 x
1
2
()sin 4 xx
1
4
()sin 4 x
,,,3
)
6( )ln ( )arctg 3
x
4
)

()ln
3
x
3( )ln

x
52( )ln 
x
1
,5)  6( )ln  10 2 xx
2
12
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
3
3
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 8( ) 5 x
2
4 x 4  x
2
6 x 8
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
52
§
©
¨
¨
·
¹
¸
¸
arctg 
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 21
,1)  5()arcsin 3 x 4ee
()5
x
5()cos 4 x
,2) e
()
7
x
()  87x 9 x
2
,,,3) 6ee
()arctg 5 x
4)  
2
x 5
4( )ln x 23( )ln x 5
,5)  12 ( )ln  x
2
8 x 25 34
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
4
3
()ln 32x
,6)  
 12 x
2
4 xx 2  12 x
2
4 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
2
,7) ()  35x 4 x
2
 82xx
2
3
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
3
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  6
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 6
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
3
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 22
,1)  2()sin 4 x e
()4
x
3()ln x
,2)   
1
9
() 12 x
3
18 x
2
9 x ()ln 8 x
4 x
3
9
x
2
x
,,,3) 4 ()sin 4 x4)


()ln
x 3()ln
x 22( )ln x 2