. .
. . = j(t), φ(t) , , .
(4.10)
(4.10) . , , , ( 4.5, 4.6)
, .
. x = j(t), t, , , .
. .
.
. f (ax + b)
. (4.11)
(4.11)
.
.
1. .
.
.
.
2. .
.
.
.
(4.12)
.. , x = f 1(t) , dt, dx.
3. .
. , arctg x. :
t = arctg x.
dt = d (arctg(x)) = e arctg x = et.
,
= e arctg x + C.
4. .
.
t = cos x,
.. dt = - sin x d x, sin3 x d x = sin2 x sin x d x = (1 cos2(x)) sin xdx.
. u (x) v (x) .
|
|
, ,
(4.13)
. , , .
. u (x) v (x),
.
, , (4.7)
.
.
(4.13).
5. .
. sin x. , .
= - x ∙cos(x) + =
= - x ∙ cos(x) + sin(x)+ C.
u (x) :
ln(x), arsin(x), arcos(x), artg(x), arctg(x)
v(x) , sin(x), cos(x).
n, n , .
. R (x) ()
(4.14)
.
, , .
n , (, .. , ) , ( ).
1. ,
,
2. , k ,
, k ,
3. , , .. ,
,
4. , k ,
, k .
,
1. . (4.15)
2. . (4.16)
3. . (4.17)
6. .
. (4.15)
.
7. .
. (4.16)
.
8. .
. , (4.17)
, :
,
k k -1 ,
.
9. .
. : 1 = -1 , 2 = 0 2.
|
|
.
, , 1 2 ,
.
.
( - , , ).
.
.
10. .
. : 1=0 ,
.
, , D ,
.
.
.
9 10, (4.15-4.17)
,
.
. , .
, r m / n, k / s
. .
. ¼ 12. ,
=
.
.
. : t 1= 1, t 2= -1 , t 2+ 1.
.
.