... cos 3xdx = −
1
3
x
2
cos 3x +
2
3
I
1
.
Ta cˆa
`
n t´ınh I
1
.D˘a
.
t u = x, dv = cos 3xdx. Khi d´o du =1dx,
v =
1
3
sin 3x.T`u
.
d
´o
I = −
1
3
x
2
cos 3x +
2
3
1
3
x sin 3x −
1
3
sin 3xdx
= ... d
´o du =
1
1+x
·
dx
2
√
x
, v =
2
3
x
3
2
.Dod´o
I =
2
3
x
3
2
arctg
√
x −
1
3
x
1+x
dx
=
2
3
x
3
2
arctg
√
x −
1
3
1 −
1
1+x
dx
=
2
3
x
3
2
arctg
√
x −
1
3
(x −ln|1+x|)+C.
V´ı du
.
2. ... cu
’
a vi phˆan nhi
.
th ´u
.
c
23.
x
−
1
3
(1 −x
1/6
)
−1
dx.(DS. 6x
1
6
+3x
1
3
+2x
1
2
+6ln
x
1
6
− 1
)
24.
x
−
2
3
(1 + x
1
3
)
3
dx.(DS. −
3
2
(1 + x
1
3
)
−2
)
25.
x
−
1
2
(1 +...
... a
12
β + a
13
γ,
kβ = a
21
α + a
22
β + a
23
γ,
kγ = a
31
α + a
32
β + a
33
γ,
hay l`a
(a
11
−k)α + a
12
β + a
13
γ =0,
a
21
α +(a
22
− k)β + a
33
γ =0, (14.60)
a
31
α + a
32
β +(a
33
− k)γ =0.
Hˆe
.
(14.60) ... thuˆa
`
n nhˆa
´
t sau
13. y
(3)
+ y
(2)
= 1. (DS. y = C
1
+ C
2
x + C
3
e
−x
+
x
2
2
)
14. 3y
(4)
+ y
(3)
= 2. (DS. y = C
1
+ C
2
x + C
3
x
2
+ C
4
e
−
x
3
+
x
3
3
)
15. y
(4)
− 2y
(3)
+2y
(2)
−2y
+ ... C
3
x
3
,
y(t)=C
1
y
1
+ C
2
y
2
+ C
3
y
3
,
z(t)=C
1
z
1
+ C
2
z
2
+ C
3
z
3
,
hay l`a
x(t)=C
1
α
1
e
k
1
t
+ C
2
α
2
e
k
2
t
+ C
3
α
3
e
k
3
t
,
y(t)=C
1
β
1
e
k
1
t
+ C
2
β
2
e
k
2
t
+ C
3
β
3
e
k
3
t
,...