94
95
Demak,
ln
ln
.
x
xdx x
C
e
= ⋅
+
∫
Tekshirish:
( ln
) ( ln )
ln
(ln ) 0
1
ln
ln
1
1 1
.
x
x
x
x
x
C
x
C
x
x
e
e
e
e
x
e
x
lux
e
lux
lux
e
x e
′
′
′
′
′
+
=
+
= ⋅
+
+ =
=
+ ⋅ ⋅ =
−
+ =
− + =
1
ln
· ·
x
e
x
e
x e
=
+
⋅
1
ln
· ·
x
e
x
e
x e
=
+
⋅
1
ln
· ·
x
e
x
e
x e
=
+
=ln
x
– l n
e
+ 1 = l n
x
– 1 + 1 = l n
x .
Javob:
ln
.
x
x
C
e
⋅
+
∆
▲
3-misol.
cos
x
xdx
∫
integralni hisoblang.
Integralni hisoblash uchun
f
(
x
)
=x, g
′
(
x
)
=
cos
x
deyish qulay. U
holda
f
′
( )
,
df x
dx
=
1,
( )
cos
sin
g x
xdx
x
=
=
∫
(bu yerda boshlang‘ich funksiya -
lardan bittasini ol dik, shuning uchun o‘zgarmas son
C
ni yozma dik).
Bo‘laklab integrallash formulasiga muvofiq,
cos
x
xdx
∫
cos
sin
sin
sin
cos
.
x
xdx x
x
xdx x
x
x C
= ⋅
−
=
+
+
∫
Javob: x
sin
x+
cos
x+C
.
▲
Integrallarni hisoblang (
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