15 (7)

Biblioteczka Opracowań Matematycznych

99/ r dx _ r dx

Jx³ + 8 " J(x + 2Xx^J-2x + 4)“

1_ A ^ Bx + C _ x²(a + B)+x(-2A + 2B + C)+4A + 2C

(x + 2X*² -2x + 4) x + 2 x^J-2x + 4    (x + 2Xx²-2x+4)

A + B = O

1-2A + 2B+C = 0 4.4+ 2C = 1

-1 1

—x + -

I-±t*-+UZ    ³ <fr =—ln[* + 2|—L f—kii

l2^Jx+2 ^Jx²-2x + 4    12 ¹ ^ 24^Jx²-

2x + 4

<Lx = — ln|x + 2\ -

2x + A

ln|x+2j-—²--<fr=—ln(x-t-2|~—lnLr²-2x-t-4|₊—f-^-24^j*²-2*+4    12 ¹    ^ 24^Jjr-2x+4    12 ^ ^ 24 ¹    ’ 24^J.r-2*

I^+lt+l A B Cx+D _x^>(A+Ć)+x²(A+B+2C+D)+Ąa+C+2D)+A + B+D (x+l)²(r² + l) x+l (x+l)² r + 1    (x+l)²(x² + l)

A = -1 B = 1 C = 1 D = 1

/ł+C = 0

A + B + 2C + D = 3 A+C+2D=2 A+B+D=1

/ = f—— + f- ^    + f '^T,⁺¹ <fr = -ln|x + l|--— + — ln|x² +l| + arctgx +C

^J* + l ^J(x + l)^{2    J}x²+1    ^1    1 x + l 2    ^1    1

101/ c xdx r xdx

1 — x* ~ J(l-xXl+JtXl+x²)^-

_ x^,(A + C)+x^{1 2}(2A+ B-2C + D)+x(2A + 2B + 2C -2D)+2B + 2D

x⁴ + 4

4 = -I 8

B-i

4

c-I

8

o=i

4

NWR'i-**		l+x l+x^2 4 = 1 4 B~I 4 C = — 9
	A-B-C=0 A+B-D=0 A-B+C=1
	4+fl+D=0	0 = 0
J-I 4	f 1 r <&	+^1 f
	I — x 4->l + x	2 x^2 +1
102/	* -u II
1
x^4+4 (x^2-2x + 2		(x^2 + 2x +

Ax + B

MMRT

Cx + D

A+C = O

2A + B-2C + D = 0 2A + 2B + 2C-2D = 0 2B + 2D = \

1 I

—x + -

1 1

-x+—

I =    -^—dx + f-^8--—dx---\ ^X    +

'x² -2x +2    ^Jx* + 2x + 2    8^Jx³-2x + 2    8^j

x+2    ,    1.    1 .

—-dx = —/, + -I,

x³ + 2x + 2    8 '    8 *

= ->/ 3x²-2x + 1-

7^3

“łfH

+c

1

lf 2(x-2) ,    1 r2x-2-2 _ 1 r 2r-2, 1 f    _

2

8^/,_ 16-’x^J-2x+2    16V-2x+2 '    16V-2x+2    8V-2x+2

3

. . i 4,. _    2|♦ i    - - i ta|x’ - 2* - 2| * £-«*(* - O