Showing Page:
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Неопр. Интегралы (ЭОУСН) Вариант 4
1
1.4.
Cxxxdxxxxdx
x
xx
++=
+=
+
3
2
3
8
6
7
3
1
3
5
6
1
3
2
2
9
8
3
7
12
32
32
2.4.
=
+
+
+
=
+
+
4
3
4
2
2
1
4
3
222
x
dx
x
xdx
dx
x
x
( )
(
)
Cxxx
x
dx
x
xd
+++++=
+
+
+
+
=
4ln34
4
3
4
4
2
1
22
22
2
3.4.
( )
=
+
=
+
=
+
2
1
2
1
12
12
2
3
1212
6
12
16
2
2
2
222
x
dx
x
xd
x
dx
x
xdx
dx
x
x
C
x
x
xC
x
x
x +
+
+=+
+
+=
12
12
ln
4
2
12ln
2
3
2
1
2
1
ln
4
2
12ln
2
3
22
4.4.
( )
( )
=
+
+
+=
+
+=
+
12
12
124
12
2
124
12
18
22
3
x
xd
dxxxdx
x
xxdx
x
x
5.4.
( )
Cxxxdxdxx +==
5cos
20
1
5cos5cos
5
1
5sin5cos
433
6.4.
( )
Cxxxdxdxx +==
5cos
20
1
5cos5cos
5
1
5sin5cos
433
7.4.
( )
=
++
++
+
=
++
52
4
1
52
14
4
1
52
222
xx
dx
xx
dxx
dx
xx
x
( )
C
x
arctgxx
C
x
arctgxx
x
dx
xx
xxd
+
+
++=
=+
+
++=
+
+
++
++
=
39
14
392
1
52ln
4
1
4
39
4
1
39
4
8
1
52ln
4
1
16
39
4
1
8
1
52
52
4
1
2
2
22
2
8.4. Ответ не совпадает
( ) ( )
=
+
+
+
=
+
+
222
31
3
4
31
61
3
1
31
12
xx
dx
xx
dxx
dx
xx
dxx
( )
C
x
xx
C
x
xx
x
dx
xx
xxd
+
++=
=+
++=
+
+
+
=
13
16
arcsin
33
4
31
3
2
6
13
6
1
arcsin
33
4
31
3
2
6
1
36
13
33
4
31
31
3
1
2
2
22
2
9.4.
22
22
4 4 2 2 2
2
1
1
x sint
u ctgt
x cost cos t dt dt
dt
dx x cost costdt ctg t
du
x sin t sin t sin t sin t
dx costdt
sin t
=
=
= = = = = = =
=−
=
( )
2 2 2
3
2
2
33
2 2 2
2
12
2
3
11
1
1
33
3
cos t sin t x
ctg t
x
u ctg t
sin t sin t x
u du C C C
x
x
ctgt
x
−−
= = =
= = + = + = = +
=
Showing Page:
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Неопр. Интегралы (ЭОУСН) Вариант 4
2
10.4.
( ) ( ) ( )
=
+
+=
==
+
=+==+
2
2ln
;
2
;2ln
_
2ln
x
xdx
xx
xvdxdv
x
dx
duxu
частямпо
dxx
( ) ( )
Cxxxx
x
dx
dxxx ++++=
+
++=
2ln22ln
2
22ln
11.4.
=
+
+=
+=
+
=
===
+
22
1
1
2arcsin12
12
1
1
arcsin
_
1
arcsin
x
dxx
xx
xv
x
dx
dv
x
dx
duxu
частямпо
dx
x
x
Cxxx
x
dx
xx +++=
+=
14arcsin12
1
2arcsin12
12.4.
( )
=
==
====
xvxdxdv
xdxduxu
частямпо
dxxxdxxdxxx
2cos
2
1
2sin
2
_
32sin32sin
2222
Cxxx
x
x
x
dxxxdxx
x
x
x
xvxdxdv
dxduxu
частямпо
dxxxdxxx
x
+++=
=+=
=
==
===+=
3
2
2
2
2
2
2cos
4
1
2sin
2
2cos
2
32sin
2
1
2sin
2
2cos
2
2sin
2
1
2cos
_
32cos2cos
2
13.4.
( )
( )
( ) ( ) ( )
( )
( )
=
++
+++++++
=
++
++
dx
xxx
xxxxxxxxx
dx
xxx
xxx
32
75272622
32
7982
2
223234
2
234
( )( )( )
( )( )( )
( )( ) ( )( ) ( )( )
( )( )( )
Cxxxx
x
dx
x
dx
x
dx
xdx
x
dx
x
dx
x
dx
dx
x
x
C
B
A
Cxпри
Bxпри
Axпри
xxx
xxCxxBxxA
x
C
x
B
x
A
xxx
x
dx
xxx
x
dx
x
xx
++++++=
=
+
+
+
+
+=
+
+
+
+
+
+=
=
=
=
=
==
==
==
++
++++++
=
=
+
+
+
+
=
++
+
=
++
+
+
+
++
=
1ln2ln3ln5
123
52
123
2
3
7
2
1
1
2
12121_
332_
843_
123
231312
123123
75
123
75
3
762
2
2
14.4.
( )
( )
( )
( )
2
2 2 2
3 2 2
11
2
1
11
22
0 2 3
1
1 3 3
1 2 2 1 2
Ax Bx x C( x )
x A B С
xx
x x x x x
xx
dx dx
при _ x C A
x x x x
при _ x A B
при _ x A B C C
+ +
+
= + + =
−−
++
= = =
= = =

−−

= = =

= + = =



Cxx
x
x
dx
x
dx
x
dx
++=
=
1ln3ln3
2
23
1
3
2
Showing Page:
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Неопр. Интегралы (ЭОУСН) Вариант 4
3
15.4.
( )
( )
=
++
++
dx
xxx
xx
521
2022
2
2
( )
( )
( )
( )( )
( )
( )
=
=
=
=
=
=+
=+
++
++++
=
++
+
+
=
++
++
=
5
1
3
205
22
2
521
152
52
1
521
2022
2
2
22
2
C
B
A
CA
CBA
BA
xxx
xCBxxxA
xx
СBx
x
A
xxx
xx
( )
( )
( )
Cxxx
x
arctg
x
dx
xx
xxd
x
dx
xx
dx
xx
dxx
x
dx
xx
dxx
x
dx
++++
+
=
=
++
++
++
=
=
++
++
+
=
++
+
=
1ln352ln
2
1
2
1
2
41
4
52
52
2
1
1
3
52
4
52
22
2
1
1
3
52
)5(
1
3
2
22
2
222
16.4. Ответ не совпадает
( )
( )
=
+
+
=
+
=
=
=
+=
=
++
t
dtttt
t
tdtt
tdtdx
tx
xt
x
xdx
2
)2(2
2
2
24
2
4
4
42
2
2
( )
( ) ( )
1
23
232
424
3
2
2
3
2
22 CxxCttdttt +++=+==
17.4.
( )( )
( )( )
( )
=+++=
++
=
=
=
=
=
=
=
++
dttttdtt
t
tt
dttdx
tx
tx
tx
xt
dx
x
xx
166
11
6
11
2355
5
32
5
6
3
2
3
6
6
5
3
1
6
3
2346
62
2
3
62
2
3
CxxxxCtttt ++++=++++=
18.4.
( ) ( )
=
+
=
++
=
+
=
+
=
+
=
=
=
+
45101315
2
1
1
cos
1
2
sin
1
2
2
sin5cos35
222
2
2
2
2
tt
dt
ttt
dt
t
t
x
t
t
x
t
dt
dx
x
tgt
xx
dx
( )
( )
( )
1
12
42
ln
3
1
1
4
ln
3
1
1ln
3
1
4ln
3
1
13
1
43
1
4)1(
C
xtg
xtg
C
t
t
Ctt
t
dt
t
dt
tt
dt
+
=+
=
=+=
=
=
19.4.
( )
( )
( )
( )
2
2 2 2 2 2
22
2
2
2 3 2 3
23
3
2 2 2 2
2
t tgx
dt
tgx dx t dt
tgx dt
dx
dx
dt
sin x cos x t t t
tg x cos x
cos x
=
+
++
+
= = = = + =
=
+ + + +
+
22
1
33
22
2 2 2 2
t tgx
ln t arctg C ln tg x arctg C
= + + + = + + +
20.4 .
( )
( ) ( ) ( )
===
xxdxxdxdxxxdxx coscoscoscoscoscos1cossincos
462434
Cxx +=
57
cos
5
1
cos
7
1

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