13 (10)

Biblioteczka Opracowań Matematycznych

^J(x-2Xx-3) x-4    A

(x-2\x-3)    x-2    x-3

A = 2

B _x(A + B)-3A-2B

(x-2\x-3)

B = -1

/ = 2    - j~= -2 In|* -2|- ln|x-3| + C

f ^X ² >    f 2x +1 + 6    r 2.T + 1 , r

86/ Jx^J+x-2 ^T~ Jx² + x-2^i&_ Jx²+.v-2^⁺J

= ln|.v² + x-2| + /

6    ,4    5 x(A + B)-A + 2B

x² +x-2 x + 2 x-\    (x + 2){x -1)

.4 + 5 = 1 -3.4-25 =-4

dx r cLx x—2~ J jr^3 2x + 7

6cix

x²+x-2

A + B = O — .4 + 25 = 6 r-2dx

A =-2 5 = 2

^/= Jlff'⁺ lf^^=_21nl^Ar+2l⁺²¹ⁿl*-^,l^+c

J - ~^X + 7    = In|x² + x - 2| - 2 ln|x + 2| + 2 ln|x -1| + C

'x²+x-2

87/

I

3x² + 2x-3

3x² -l + 2x-2

2x-2

x(x-l)

Ax

= In|x³ - x| + 2 f——— = In|x³ - x| + / ^{1    1    J}x(x+1)    ^1    1

1__A_[ B x(A + B)+A

Ąx + i) x x + 1 x(x+l)

J/4+5 = 0 1 A-l

A = \ 5 = -I

^{/ = 2}J~~²J777 ^{= 21n}W^_2lnl^jr+1i

dx

x +1

j3x +2x—jnjjj.3 -x|₊2ln|x|-21n|x + l|+C

W    =    j(^x+4+^}*⁼T^+4j:+I^^A=y^+4t+/

7x + l 7x + l _A B x{A + B)-B x²-x x(x-l) X X — 1    x(x-l)

A+B-l    jA=8

. -s = *    U5 = -l

/= f---[-= 81n|x|-ln|x-l| + C

^J x ^Jx-1

f ^ ⁺ ^ dx = — + 4x - 8 ln|x| - ln|x -1| + C

J r² — r    9

82/ b

d&r

= /

r(x² -x +1

.4 + C = 0 -^+B+D=0 A-B = O fl = I

dr rdr

_*4 ^{+ J}B Cx + D    x^,(A + C)-x²(A-B-D)+x(A-B)+B

i}^_ x⁺x^J+x^J-x + l    x²(x^J-x + l)

.4=1 B =1

C = -l D = O

xdx

M-+R-

^J X ^Jx^{2 J}x²-x + l    ' x

_i i    n

/ = f ..?*- = f^X .2.12a₌1 fl_^i₊ij_^_=ii_IJx^J-x₊l)₊^ f—^

Jx²-x+l •’x^J-x+l 2V-x+l 2 V-x+l 2    2 Y O

1 . I 2 li ^3    2x— 1 _

= -ln|x² - x + \\ + —arctg —^-+C

1 = ln|x| - - - ^ ln|x² - x +1| - -y-arctg ^^4 + C

4)

x-2 = l dx-dt x=t+2

90/    _    .

f ^2X+5 dx= dx = dt

^]J^iT

-25-