Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 35 стр.

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,5)  ()ln 12x ()ln  x
2
6 x 10 10 ( )arctg x 3
,6)   x
2
10 x 24 x 5  x
2
10 x 24 ( )ln  x 5  x
2
10 x 24
,7) ()ln  x 5
 x
2
10 x 24 ( )  3 x
2
x 1  x
2
10 x 24
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
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x
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32
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,9)  6
§
©
¨
¨
·
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ln 
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42
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4
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,10)  6
§
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¨
·
¹
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ln  
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4
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13 16
§
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arctg 
1
3
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2
2
3
2
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2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 39
,1)  ()sin 3 x 2e
e
()
x
4()arcsin x
,2) ()  65x 9 x
2
e
()8
x
,,,3) 6e
e
()arccos 8 x
4)  ()ln x 34( )ln x 5
4
x 5
,5)  4( )ln  x
2
8 x 20 12
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
2
1
2
()ln 32x
,6)  
  12 x
2
8 xx 4   12 x
2
8 x 4
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
2
,7) () 34x
2
2 x  12 x
2
4 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
4
1
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
32
§
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x
2
13
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ln 
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x
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2
,9)  6
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
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tg
x
2
32
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2
2
2

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·
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¸
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x
2
3
,10)  2
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
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·
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¸
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tg
x
2
2
4
§
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x
2
510
§
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¸
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arctg 
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tg
x
2
23
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tg
x
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 40
,1)  5e
e
()2 x
5
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
2
4()cos 2 x
,2)   
1
9
() 6 x
3
36 x
2
9 x ()ln 4 x
2 x
3
9
2 x
2
x
,,,3) 2
()arctg 2 x4)  2( )ln x 33( )ln x 63( )ln x 2
,5)  2( )ln  x
2
4 x 84
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
1
3
2
()ln 12x
,6)   x
2
4 x 32 x 2  x
2
4 x 32 36 ( )ln  x 2  x
2
4 x 32
,7) ()ln  x 2
 x
2
4 x 3( ) 5 x
2
2 x 3  x
2
4 x 3
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
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32
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2
,9)  
6

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
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1
,10)  
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  10 6
§
©
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¨
·
¹
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tg
x
2
§
©
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2
2
10
§
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arctg 
§
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tg
x
2
32
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x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 41
,1)

3()cos x 4()ln x 6 x
,2) 
()x 8 1 x
2
4
1
2
§
©
¨
¨
·
¹
¸
¸
 4 x
1
2
x
2
()arcsin x
,,,3) 6( )ln ( )cos 9 x4)  ()ln x 35( )ln x 4
1
x 4
,5)  
2
3
()ln 23x 8( )ln  x
2
8 x 20 36
§
©
¨
¨
·
¹
¸
¸
arctg 
x
2
2
,6)  
x
2
10 xx 5 x
2
10 x 25
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
5
1
,7) ()  25x
2
x   12 x
2
8 x
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
2
,8)  
§
¨
¨
·
¸
¸
ln 
§
¨
¨
·
¸
¸
tg
x
2
2
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x
2
13
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ln 
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tg
x
2
2
,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
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36
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x
2
3
6

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¨
·
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x
2
3
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
¨
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·
¹
¸
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x
2
2
4
§
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·
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x
2
812
§
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1
2
§
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·
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¸
¸
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x
2
13
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§
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tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 42
,1)

5()ln x 6 x 4()sin x
,2) ()  17x 9 x
2
e
()9
x
,,,3) 2ee
()arcsin 4
x
4)  ()ln x 32( )ln x 23( )ln 1 x
,5)  2( )ln  22xx
2
6()arctg 1 x
3
2
()ln 1 x
,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 4
 x
2
8 x 15 ( )  5 x
2
4 x 1  x
2
8 x 15
,8)  3
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
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tg
x
2
3
§
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ln 
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2
3
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¸
¸
ln 
§
©
¨
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·
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¸
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tg
x
2
1
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
6
§
©
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¸
¸
ln 
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44
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x
2
1
,10)  4
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  13 6
§
©
¨
¨
·
¹
¸
¸
tg
x
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
16
§
©
¨
¨
·
¹
¸
¸
arctg 
3
2
1
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
§
©
¨
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·
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¸
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§
©
¨
¨
·
¹
¸
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 43
,1)  3
§
©
¨
¨
·
¹
¸
¸
arcsin
5
x
3
4()ln x 4( )sin 3 x
,2)
1
3
x
§
©
¨
¨
·
¹
¸
¸
  () 12 12 xx
2
()ln 5 x 12 6 x
x
2
3
,,,3) 4ee
()cos 6 x
4)  
4
1 x
()ln x 33( )ln 1 x
,5)  6( )ln  x
2
4 x 13 4
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
2
3
2( )ln x 1
,6)  
 3 x
2
4 xx 2  3 x
2
4 x ()arcsin x 2
,7) () 2 x 4 x
2
  21 x
2
10 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
2
5
2
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
33
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¨
·
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¸
¸
ln 
§
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¨
¨
·
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¸
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x
2
22
§
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·
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ln 
§
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x
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1