07 (4)

37/

Biblioteczka Opracowań Matematycznych

f 2cosxdx	sinx = /	-■>[ ^dt
Vl-sin’x	cosxc£v = di	‘W

■ = 2arcsin/ +C = 2arcsin(sinjr) + C

r -JS * 3 In t ^ r V5 + 3 In x

³ Jx ~    '

9    9

5 + 3 ln x = t¹

3 dx , ,

-= 2 tdt

x

dx    2 ,

-= — uh

x    3

/ = V5 + 3 ln

1    r 2/<*    ! r , ,

= — /-=—/-<*

2    ³    3    3 ³

38/ jV^l +c ') dx= |(e^2r +2e^Te~^jr +e~^2x)dx= je^2xdx+2je^xe ^Xdx+ je ^2xdx

= -e^u + 2 x--e-^2x+C

39/    , .

| x ax

cos^: x⁴

X⁴ = t 4x^}dx = dt

40/

I:

<£c

3 , dt x dx = — 4

x = t² dx = 2/<//

f 4    1 r dt    1    1    ₄

= —-*5— = — -5— = —tgt + C — —tgx + C

³cos~t 4 ^cos'/ 4    4

^J5 + /    ■'5 + /    ³ t + 5    ³

5 + V7

-loj—= 2/-l0ln|5 + /|+C = 2V*-I01n|5 + Vxj+C

41/

r x^}dx		.r + 1 = t x = t- 1	l 9-s 1 V«XV 1	(t^3 -3t^2 + 3t-l\/t
^J(x + 1)^10		*^3=('-iy dx = dt	J fio " J	t’°

=    J~- Jr⁷<*-3 JrV/ + 3jr⁹<*- Jr'°<* =

=    —+ c = -    ¹

6/^{6 +} lf $t* ⁺ 91^{9 +}

³    + . ¹ ,.+C

6(x + l)⁶ 7(jc -h 1 )⁷    8(.v + l)*    9{x +1)

Biblioteczka Opracowań Matematycznych

dt

3x* + 4x + 10 = t dt dt

m ,_r+2

J-———    ^dx = |(6x + 4)dx = dt

3x* + 4x +10

= ln|3x^: + \x +10| + C

(3*+ 2 )dx =

43/

/ =

1 +

dx

V6

= a/ó^/z

dt =

1    ^    1    x

= —arctgt + C = —7= arctg —f= + C

Vó    Vó Vó

44/

1 r -s/ó dt _ VćT r dt _

~ 6 ' i + /^J " "i^- J i +1¹ ~

dx .. r	dx	1 r 4x	X T “ * - dt	1 r 4<A
+ 16 ^J 16		^16 ur*'	4 dx = 4 dt	16 J /^J + 1

1 r dt 1    _    1 x ^

= — —— = —arct£t+C-—arctg—+C 4 V + 1    4    *    4    ⁵ 4

1 <•

V5 ^J TT^T⁷

Vs _r dr ⁼ V^^JVT7

arcsin t + C = arcsin -A=+ C V5

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