05 (6)

13/

Biblioteczka Opracowań Matematycznych

8.r-5 = t

J(8.r -5) dx= 8dr = dt

dx=* 8

³    8    8 ³    48    48

14/

r 4rdr J + 5

15/

3jc’ + 5 = i 6xdx = dl

.rdr=f*

dl

= ⁴    = f jf = f^lnkl + C = jln\3x^: + S| + C

(• 2e^udx ^ 2 + 5e^3r

2 + 5e^3x = / I5e^lxdx = dt

e^,rdx =

15

dr

= 2    f— = — ln|/| + C = — ln|2 + 5c³'| + C

³ l 15 ³ t 15 ¹¹    15 ^1    1

16/

cos* . sinx = /

\ctgxdx = ]««* = ^J    J sin x

17/

cos xdx = dt

= J— = ln|/| = Injsin at| + C

JV4r - ldt =

18/

jVlO-2*dr =

4 jr — 1 = / ²

4 dr = 2 tdt

. tdt dx = —

2

V4r- 1 = i

r tdt 1 r ₂    1 ,    ->/(4jr-1)

= / —=- [rdr = -/³+C = —-—+C

^J 2    2 ^J    fi    fi

10-2x = f⁴ -2dx = 4t^}dt dx = -2t'¹dt t = ViO-2a-

= Jr(- 2/³d/) = -2    =—+C

■

Biblioteczka Opracowań Matematycznych

19/

-X

je ⁴ dx =

-x

~

-dx

= t = dt

4

dx = -Adt

-X

= -4 je' dt = -4e' +C = -4e^T +C

20/
	-jr^3 =/
5 Je'^1 x^2dx =	-3x^2dx = dt
	x^2dx = —
	3
21/

⁼5j^e'(^]=y J^/=y«'+c=-

'TT

r_x=t

dx

2yfx

dx

= dt

= 2je^ ~=2je'dt = 2e^,+C = 2e'^iI +C

= 2 dt

221

j\l2x^s +\Qxⁱdx =

2x⁵ + 10 = /⁴ \0x^Ądx=4t^>dt

xⁱdx = —t³dt 10

r = V 2x⁵ + 10

= |j^=^/⁵+C=^^(2x^J+10)^S +C

25

25

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