Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 40 стр.

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,,,3) 4( )ln ( )arccos 9 x4)  2( )ln 3 x
4
3 x
5( )ln x 1
,5)  8( )ln  x
2
2 x 510
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
2
1
3
()ln 1 x
,6)  
 7 x
2
8 xx 4  7 x
2
8 x 9
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
4
3
,7) ()  2 x 33x
2
  12 x
2
8 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
2
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
46
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  10 6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
32
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 66
,1)  5()ln x 10 x e
()3
x
,2) () 82x 6 x
2
e
,,,3) 6( )ln ( )arcsin 4
x
4) 2( )ln 3
x
()ln 
x
4
,5)  8( )ln  x
2
4 x 812
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1( )ln 13x
,6)  x
2
2 x x
2
2 xx ()ln  x 1 x
2
2 x
,7) ()ln  1 x
 22xx
2
() 45x 5 x
2
 22xx
2
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
4

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
,10)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
312
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 4
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 67
,1)  3()arctg 2 x 6 x 5()ln x
,2)   
1
36
() 60 x
3
126 x
2
108 x ()ln 4 x
5 x
3
9
7 x
2
4
3 x
,,,3) 2( )ln ( )arctg 8 x4)  3( )ln 3 x
4
3 x
5( )ln x 2
,5)  
3
2
()ln 32x 3( )ln  x
2
6 x 18 4
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)  3
 56xx
2
 56xx
2
x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
3
2
x
2
,7) () 13x
2
x  7 x
2
8 x 2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
4
3
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
24
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  12
§
©
¨
¨
¨
·
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
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 68
,1)

3()ln x 8 x 5()sin x
,2)

()cos
x
()sin
x
x
()sin
x
,,,3) 4 ()sin 4 x4)


3( )ln
3 x 2( )ln
x 3()ln x 1
,5)  4( )ln  x
2
8 x 20 12
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
2
2
3
()ln 23x
,6)   x
2
2 x 65  x
2
2 x 65 x 64
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
x
8
1
8
 x
2
2 x 65
8
,7) 4( )ln  x 1
x
2
2 x ()  3 x 43x
2
x
2
2 x
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
34
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
4
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
3
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
32
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  22
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
arctg 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 69
,1)  2ee
()4
x
3()ln x ()arcsin 2 x
,2) ()  86x 4 x
2
e
()8
,,,3) 6( )ln ( )arcsin 5 x4)  ()ln 1 x
5
1 x
5( )ln x 1
,5)  8( )ln  x
2
8 x 20 36
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
2
1
2
()ln x 1
,6)  
 11 x
2
10 xx 5  11 x
2
10 x 36
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
6
5
6
,7) ()  22x
2
3 x   12 x
2
8 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
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
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
,10)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
4
§
©
¨
¨
·
¹
¸
¸
tg
x
2
13 8
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 70
,1)  4()cos 2 x ()sin 3 x 5
§
©
¨
¨
·
¹
¸
¸
arcsin
5
x
4
,2)   
1
36
()  84 x
3
162 x
2
216 x ()ln 8 x
7 x
3
9
9 x
2
4
6 x
,,,3) 2( )ln ( )cos 3
x
4)


()ln

x
53( )ln

x
13( )ln 
x
2
,5)

()ln 12x 4( )ln

x
2
8 x 17 30 ( )arctg x 4
,6)   x
2
2 x 48 x  x
2
2 x 48 49 ( )ln  x 1  x
2
2 x 48
,7) 5( )ln  x 5
 x
2
10 x 26 ( )  3 x 5 x
2
 x
2
10 x 26