Неопределенный интеграл. Варианты заданий для практических занятий. Сирота Ю.Н. - 41 стр.

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,8)  2
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2
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 71
,1)  5()ln x 4e
e
()
x
2()sin 4 x
,2)  
()3 x 12 19x
2
12
1
12
()36 x 18 x
2
()arccos 3 x
1
12
()arcsin 3 x
,,,3) 2e
e
()sin 2 x
4)  
5
x 5
2( )ln x 24( )ln x 5
,5)  4( )ln  13 6 xx
2
20
§
©
¨
¨
·
¹
¸
¸
arctg 
3
2
x
2
1
2
()ln 32x
,6)  3
 27 6 xx
2
 27 6 xx
2
x 36
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
6
1
2
,7) ()  14x
2
3 x   24 x
2
10 x ()arcsin x 5
,8)  2
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,9)  2
§
©
¨
¨
·
¹
¸
¸
ln 
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34
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4
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,10)  2
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ln 
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212
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13 14
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3
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2
2
3
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 72
,1)  ()arctg 2 x 6 x 3
§
©
¨
¨
·
¹
¸
¸
arcsin
7
x
4
,2) ()  59x 7 x
2
e
()6
x
,,,3) 8 ()sin 4 x4)  ()ln 3 x ()ln x 42( )ln x 2
,5)  
2
3
()ln 23x ()ln  10 6 xx
2
10 ( )arctg 3 x
,6)  
 x
2
10 x 16 x 5  x
2
10 x 16 9 ( )ln  x 5  x
2
10 x 16
,7) 5( )ln  1 x  22xx
2
()  4 xx
2
 22xx
2
,8)  
§
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¸
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3
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,9)  2
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6
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,10) 6
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______________________________________________________
ȼɚɪɢɚɧɬ ʋ 73
,1)  4()sin 3 x 6 x 2e
e
()
x
,2)   
1
36
()  84 x
3
126 x
2
72 x ()ln 2 x
7 x
3
9
7 x
2
4
2 x
,,,3) 6ee
()cos 9 x
4)  2( )ln x 25( )ln x 5
5
x 5
,5)  3( )ln x 312( )ln  x
2
2 x 10 12
§
©
¨
¨
·
¹
¸
¸
arctg 
1
3
x
3
,6)  
 24 x
2
10 xx 5  24 x
2
10 x 49
§
¨
¨
·
¸
¸
arcsin 
x
7
5
7
,7) ()  4 x 35x
2
6 xx
2
§
©
¨
¨
·
¹
¸
¸
arcsin 
x
3
1
,8)  2
§
©
¨
¨
·
¹
¸
¸
ln 
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©
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x
2
3
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32
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,9)  4
§
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·
¹
¸
¸
ln 
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4
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1
6
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,10)  2
§
©
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·
¹
¸
¸
ln 
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23
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2
6
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x
2
18 2
§
©
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¨
·
¹
¸
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arctg 
1
3
§
©
¨
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·
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¸
¸
tg
x
2
1
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 74
,1)  4 x 4
§
©
¨
¨
·
¹
¸
¸
arctg
5
x
3
3()sin x
,2)

()cos
x
()sin
x
x
2()sin
x
,,,3) 2ee
()arcctg 4
x
4)  2( )ln 3 x 3( )ln x 43( )ln x 3
,5)  ()ln x 13( )ln  x
2
6 x 18 4
§
©
¨
¨
·
¹
¸
¸
arctg 
x
3
1
,6)   x
2
8 x 9 x 4  x
2
8 x 925( )ln  x 4  x
2
8 x 9
,7) 2( )ln  x 5
 x
2
10 x 24 ( )  4 x 54x
2
 x
2
10 x 24
,8)  2
§
¨
¨
·
¸
¸
ln 
§
¨
¨
·
¸
¸
tg
x
2
23
§
¨
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·
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¸
ln 
§
¨
¨
·
¸
¸
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x
2
12
§
¨
¨
·
¸
¸
ln 
§
¨
¨
·
¸
¸
tg
x
2
2
,9)  
2

§
©
¨
¨
·
¹
¸
¸
tg
x
2
1
2
§
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·
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ln 
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26
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2
1
,10)  12
§
©
¨
¨
¨
·
¹
¸
¸
¸
ln  
§
©
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·
¹
¸
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tg
x
2
2
6
§
©
¨
¨
·
¹
¸
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x
2
18 26
§
©
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·
¹
¸
¸
arctg 
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
12
§
©
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tg
x
2
2
______________________________________________________
ȼɚɪɢɚɧɬ ʋ 75
,1)

3()sin 2 x 4 x 4()arcsin x
,2) e
()
7
x
() 42x 3 x
2
,,,3) 2ee
()cos 3 x
4)  4( )ln x 3
1
1 x
2( )ln 1 x
,5)

()ln 
22xx
2
10 ( )arctg
x 1()ln
1 x
,6)    24 x
2
10 xx 5   24 x
2
10 x ()arcsin x 5
,7) ()  2 x 33x
2
x
2
2 x 2()arcsin 1 x
,8)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
2
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©
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x
2
12
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·
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¸
¸
ln 
§
©
¨
¨
·
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¸
¸
tg
x
2
2
,9)  4
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
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x
2
4
2

§
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¹
¸
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x
2
1
2
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¸
ln 
§
©
¨
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·
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tg
x
2
1
,10)  
§
©
¨
¨
·
¹
¸
¸
ln 
§
©
¨
¨
·
¹
¸
¸
tg
x
2
16
§
©
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·
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¸
¸
¸
ln  
§
©
¨
¨
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¹
¸
¸
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x
2
2
2
§
©
¨
¨
·
¹
¸
¸
tg
x
2
10 2
§
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¨
¨
·
¹
¸
¸
arctg 
1
3
1
3
§
©
¨
¨
·
¹
¸
¸
tg
x
2
______________________________________________________