6.3 Partial Fractions
Starde (Bot
2
(Q(1)
If day (P1 = de (Q), the Long Division
If de. :) <day (6), Partial Fantin
Stuck- (pardx
Tw
= (xx) + RN) dy
Quas
= 20 = 1, x + 2x²
(f(x)dx = ) 0.4x
Luse I: Q consists of distinct linew factors
Q(x) + (Ⓡ, x+h) (aqx+b₂)
х
Ex.
S'
x²-4x-10
x²-x-6
dx-
K +1
2+(
x²x6 √x²+0x² -4x-10
32
-x-x²-6x
0+x² +2x-10
2
-
کا
ROX) = 4,
2(x) (ectly) Pantor)
ясны
3x-4 AL + Aq
(x-3)(x+2)³ x-3
x+2
[](
3x-4
bx
(x-3)(x+2)
2. ( A + Az b
X-3
8+2
3=4₁+A₂
(-4=24-3A₂
7=3-4₂
-
0+3x-4
x
3x-4 = 4, (x+2) + A₂(x-3)
3x-4= x ( A + A₁₂) + 2A-342 -4=2(342)-SA₂
·
2 + ( x + 2 · dx = 2 + (x -31160 + 2/4/x+2116
x-)
6(313) - 2-1
x+2
་
+421-43 +213-(21)
+++47) 74(5)
fl
Starde (Bot
2
(Q(1)
If day (P1 = de (Q), the Long Division
If de. :) <day (6), Partial Fantin
Stuck- (pardx
Tw
= (xx) + RN) dy
Quas
= 20 = 1, x + 2x²
(f(x)dx = ) 0.4x
Luse I: Q consists of distinct linew factors
Q(x) + (Ⓡ, x+h) (aqx+b₂)
х
Ex.
S'
x²-4x-10
x²-x-6
dx-
K +1
2+(
x²x6 √x²+0x² -4x-10
32
-x-x²-6x
0+x² +2x-10
2
-
کا
ROX) = 4,
2(x) (ectly) Pantor)
ясны
3x-4 AL + Aq
(x-3)(x+2)³ x-3
x+2
[](
3x-4
bx
(x-3)(x+2)
2. ( A + Az b
X-3
8+2
3=4₁+A₂
(-4=24-3A₂
7=3-4₂
-
0+3x-4
x
3x-4 = 4, (x+2) + A₂(x-3)
3x-4= x ( A + A₁₂) + 2A-342 -4=2(342)-SA₂
·
2 + ( x + 2 · dx = 2 + (x -31160 + 2/4/x+2116
x-)
6(313) - 2-1
x+2
་
+421-43 +213-(21)
+++47) 74(5)
fl
