. . . .
F(x) f(x), , F(x) , : F(x) = f(x)
1. F(x) F(x), F(x)+C . , (x) y = f(x) (x) = F(x)+C, F(x) - , C - .
:
F(x) = f(x). , ,
(F(x)+C) = F(x)+C = F(x) = f(x). , F(x)+C y = f(x). , y = f(x) F(x) - , (x)
(x) = F(x)+C
,
Ԓ(x) = F(x)+C F(x) = f(x).
, , . , (x) = F(x)+C, .
.
y = f(x) ∫f(x)dx = F(x)+C
f(x) , f(x)*dx - .
: " " " ", : ,
1. (f(x)dx) = f(x)
2. ∫f′(x)dx = f(x) + c
3. ∫a ⋅ f(x)dx = a∫f(x)dx, a ≠ 0
4. ∫(f1(x) + f2(x))dx = ∫f1(x)dx + ∫f2(x)dx
.
(. . ). , ( ). .
pyc ∫f(x)dx. =φ(t), φ(t) - , . dx=φ'(t) dt peeoo poa caoo ∫f(x)dx = ∫f(φ(t)) * φ(t)dt eo . oe t .
u=u() ν=v() - , . d(uv)=udv+vdu.
, ∫d(uv) = ∫udv + ∫vdu
∫udv =uv - ∫vdu
. ∫udv ∫vdu, , .
, - pao dv (, , c); , ν du, . .