14 (7)

Biblioteczka Opracowań Matematycznych

'2lnJ*—2|-JZ5+C

— f ^X~^l Jk-    »r *x-4    , I, <fr

^J4x²-4x + l    J

= -ln|4x² -4x + l|— f-8 ^{1 1}

_I ff* ₌I

4 V " 8

4x - 4x+ I

dx

-dx = -\ 8 J

8^J4x²-4x + l    2-Ux^ł-4x + l

¹ f dx    1,1^2    ,| 1

- h-rr = — ln 4x — 4x + l —

2ⁱ{2x-\\    8 ^1    1 2

ln|4x^! -4x + l|-

1

4(2x-l)

+ C

2x -1 = / 2 dx = dt

= -InUx² -8 ¹

4x + li

92/

SS

2x² -5x +1

x - 2x + x

<& = /

2x^;-5x+l _ 2x²-5x+l    2x²-5x+I .4 B C x²(a+B)+x(C- B-

x³-2x²+x x(x²-2x+l)    x(x-l)² x⁺x-I ⁺ (x-l)^{2 _}    x(x-i)²

2A)+A

4 + 5 = 2	[ 4 = 1
C-5-24 = -5	5 =^1
4 = 1 ]	C = -2
	cit
Jx^+Jx-1 ^2J(.	x-.)^2 '

93/

5x-1

f-T^-dx= f- .    -dx = I

^Jx³-3x-2    ^Jx-2x-x-2

5x —1    5x-I

___[__ _____A_ B C

(x³ -x)-2(x + l) x(x^J -l)-2(x+l) (x + l)^:(x-2)~ x + l ⁺ (x+l)²⁺x-2

_x^:(4 + C)+x(-4 + 5 + 2C)+(-24-25 + C)

(x+lf(x-2)

A + C = O -A+B+2C = 5 |-25-24 + C = -l

4    = -l

5    = 2 C = l

/= J—+    + f-^- = -ln|x + l| — + ln|x - 2j + C

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

\

5x + 2

x² + 2x+I0'

dx= fi

-(2x + 2)-3

2x + 2

+ 2x + 10    2 ^jx + 2x + 10

dx + 2jc + 10 x + \

= — Inbr + 2x +1 Ol - 3 [7—^-= — Inljr² - 2x + \o\-arctg + C

2 ^{1    1 J}(x + l)²+9    2 ^1    1    3

(Wykorzystano wzór (1.26)).

2£ _r x+₂

[—-——dx = I

x + 2	x+2
x^3-2x^2	*^2(	x-2)	X X
A+C = 0		/( = -l
II <N 1 02		5 = -l
-25 = 2		C = 1
r- dx	, f	- dx	f *
	^1 J	X- ^1	•>2x
96/	rx^2dx f.

²{x-2)

1 1

+ c

97/

^J.r+A^{2 J}

= y-*²x-*³c

+77e^)±,m	--*^2x 3
#^c

W+k² 3

i²

+1

98/

r 2x²+x+4    t 2x² + x+4 j    f 2x²+x + 4    ,

x³ + x² + 4x + 4    ■’x²(x + l)+4(x + l)    ³(x² + 4)(x+lj

(x^2 + 4Xx +	l) X + 1	x^2 + 4
A + B = 2	(A = \	[ -
B+C = 1	5 = 1 / =
4/< + C = 4	[c=o	X + 1

(x² +4X^ + 1)