18 (5)

Biblioteczka Opracowań Matematycznych

107/

\fxdx

idi

rfdt

r*6rdt _{e r} rat , _tcat , _t, . i „ ,

= —r—r ⁼ 6 Kr—t = 6 -=6 (/-1+—)di

^J/‘+/⁵    V(/+l)    ^J/ + l    J r+l

= 3/^: - 6/ + 61n|f + l| + C = 3VT - 6^/x + 6ln[>/7 + i| + C 108/

J—

x +

W

x = t dx=6t^f'dt

dx

2(*-i y

' W-

2

-*-¹ =/^j

x-2

1 -2r²

1 ~/²

2 tdt

(!-/*)•

f -2tdt (l-/²)²    _r-2<//

"^J $-<*/ '^J T^{5 =}

109/

ć£c

Vx²+3x+2 3

V

= In

110/

3

x+—=t

2

dx = dt

-f*

+c=

!_

4

+ C 6/

^X+2

x + — + Vx² + 3x + 2 2

-(₅o:-4)

^5jr"⁴    -._⁵f 5'    '

6x- —

6x-2

_rfy _ 3 f    _^₌₌₌^ ₌ _

V3x²-2x + 1    6•*V3jt² — 2jt +1    6 ^J V3x² - 2x +16 ^JV3x²-2x+l

<£r = —f-

A ■>

*dx-

dx

= -V3x²-2x + 1~- f-3    3 J

dx

x—

2 ³ 3

=- = -V3x² -2x+l -

x — = f 3

dx = dt

7V3 _r dt

9

f—^    =-V3x²-2x + l- —ln t + Jt²+-

³ /TT 3    9 V 9

+ C =

r + —

111/

Biblioteczka Opracowań Matematycznych

,    ~(5x+2 )dx c 4x+-

- ⁵ f ⁵    ₌ ⁵ f S

A J .    _2 . o_ i A J

_ 5 r (4x + 8)rfr

f (5x + 2)cbc j r 5'    ' J r    5    ^ 3 r

W2x²+8x-I    4 ^J V2jc² +8jc-I 4>j2x²+lx-\    4 J^jr+8.t-l

dx

-dx

--    —s-==-2V2x²+&r-l-8f-₇ f ^

4^JV2r²+&t-l 4    ■J2(x+2'f -9 2    Jl³ L₊₂y _

* i- _ -    < /- _    I V o

= — -J2x² +8j:-1 -4yfl f    =-yj2x²+8x-l-4V2lnt + Jt²--

2    ^J , 9    2    V 2

f- 2

9 2

+ C =

x + 2=t dx-d(

= — V2.r² + 8.v — 1 — 4 V2 in.r + 2 + J.r² + 4jr--2    V    2

+ C

112/

J

x-5

1 (■ -2(x-5)cfc    1 _f -2jt+4 I

V 5 + 4jt -

r4J-

6dx

2 ^Jy]9-(x-2f    2 ^V5 + 4x-jr^: 2 ^J^9_(^_₂)^:

= ^5 + 4x-4x² - 3 J , =

=* = -- f

J 2 J

= ——2-^5 + 4* - jc² - 3 f 2    J

C 3dt	»*• CO II <N 1 H
W9-9/^2	dx = 3t7/

113/

>/i^ż

= -j5 + 4x-x² -3 arcsin/ + C = ■j5 + 4x-x² -3arcsin ^X ^ ^ +C

f- ⁵^^r - f.

5</x

AT—1 =/

dx = dt

114/

J-

3xdx

1 r -6xdx _ i r

? J Ft ^ ńU ? J

= 5    = 5 arcsin/ + C = 5 arcsii^.r -1)+C

1 _f -6at-2+2 .    1 _r -6x-2

W 1-2jc-3jc²    2^SJ\-2x-3x²    2 ^J Vi-2jc-3a:

-Ir. ^2A 2 J

2^JVi-2a-3a^j

2 WI-2x-3a²

/

= -\l\-2x-3x² -1 + C = —J\-2x-3x² -—arcsin

3    2

f    f fifa    o 2.    ^    /3a + 0

tt-th-J

nTi) J

(1.36)

^całkach 110/- 7/2/ wykorzystano wzór (1.36).