Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 46 стр.

UptoLike

Составители: 

,2)
2
3
§
©
¨
¨
·
¹
¸
¸
  
§
©
¨
¨
·
¹
¸
¸
 6
21
4
xx
2
()ln 7 x 6
21 x
8
x
2
3
x
,,,3) 2
()arcctg 8 x4)  
4
x 2
2( )ln x 33( )ln x 2
,5)  ()ln  x
2
8 x 17 10 ( )arctg x 4()ln 1 x
,6)    9 x
2
10 xx 5  9 x
2
10 x 16
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
5
4
,7) () 4 x 13x
2
 7 x
2
6 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
3
4
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  10 6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
14
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 98
,1)  4
§
©
¨
¨
·
¹
¸
¸
arctg
7
x
3
2()sin 2 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin
7
x
3
,2)  
2
25
()sin 5 x
2
5
()cos 5 xx
2
5
()cos 5 x
,,,3) 6( )ln ( )arctg 8
x
4)  ()ln 
x
4()ln 
x
32( )ln 
x
2
,5)  4( )ln  10 6 xx
2
28 ( )arctg 3 x
3
2
()ln 32x
,6)   x
2
6 x 8 x 3  x
2
6 x 8( )ln  x 3  x
2
6 x 8
,7) ()ln  x 3
 x
2
6 x 8( ) x
2
4 x 4  x
2
6 x 8
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  13 6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
arctg 
3
2
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 99
,1)  4()sin 4 x 5
§
©
¨
¨
·
¹
¸
¸
arctg
4
x
3
4
x
,2) () 54x 9 x
2
e
()7
x
,,,3) 8 ()arctg 3 x4)  3( )ln x 2
5
1 x
2( )ln 1 x
,5)  
1
2
()ln 12x 4( )ln  x
2
4 x 812
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
,6)  
 21 x
2
4 xx 2  21 x
2
4 x 25
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
5
2
5
,7) ()  22x
2
3 x  7 x
2
8 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
4
3
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
x
x
©
¹
©
¹
©
¹
©
¹
©
¹
©
¹
©
¹
©
¹
©
¹
x
x

x
x
x
©
¹
x
©
¹
©
¹
x
©
¹
©
¹
x
©
¹
©
¹
x
©
¹
x
x
©
¹
©
¹
©
¹
©
¹
©
¹