06 (4)

23/

Biblioteczka Opracowań Matematycznych

h

2x~ dx

3+x³=t⁵ 3x²dx = 5 t*dt    ł _t*jf

xrdx = - t*dt 3

=⁵VW

24/

r 12;xdx •J\-3x²

\-3x^z=t² - 6xdx = 2n//

*<& = —tdt 3

t = J\-3x²

cos2.v

-tdt

= 12 J—j—= -4 jdt = -4t +C = -4tJ\-3x² +C

25/

' sin* cos*

r cos2*

-c

'2 sin* cos*

(•2 cos2* , -dx =	sin 2x = t
^J sin 2*	2 cos 2xdx = dt

= jy- = ln|/j + C = ln|sin 2*| + C

26/

sin xdx 1 + 3 cos *

27/

J

1 + 3 cos * = t

- 3 sin dx = dt

, .    , dt

sin xdx =--

3

- dt

= J—y- = --jln|/| + C = - jln|l + 3 cos *|+C

J

dx

*(l + ln*)

28/

Jsin²* cos *<fc =

1 + ln* = / dx

— = dt x

⁼ J7ub⁼if⁼"^{łl+c=ln|l+ln}'l^+c

sin * = / cos .xy/v = dt

= Jrdf = —+C =

sin *

+ C

Biblioteczka Opracowań Matematycznych

29/ Jcos xsinxtir=

cos x=t -sinxdx=dt

= -\rdt=-—+C = --cos⁶x+C 6 6

30/    .    ^

pinxox

cos x

31/

cos x = t -s\nxdx = dt sin xdx = -dt

|2e^s,ni cos xdx =

x⁵ +1 = /

sin x = /

cos xdx = dt

r —dt    r -5 j / ^J    1

= —— = - / ⁵ dt=—+C = --t

J r ^J 4    4 cos

= 2j<?'<// = 2<?'+C = 2<?^s,ni + C

+ C

32[

JlO e^x'⁺'x^Adx = 33/

5x⁴c£x = dt

4 dt x dx - —

dx

= 10 Je' — = 2 \e'dt = 2e'+C = 2e'’*' + C

tgx=t

= 2    = f² + C = tg²x + C

r2tgxdx cos² x 34/

dx r dx r dx r <?*<& e' =t

cos² X

dx

— = dt

cos* x

C dx _ r dx _ r ć/x

J ^TT⁷ “ J    ^J ” ■>

e^2x +1

e’dx = dt

J/² + l

= arctgt + C = arctg (e^s) + C

35/

JlO + ln|x|^ i p/lO+lnH^_ J 2x    2^J x

^ ^/(l0+ ln|x[y

10 + ln|x| = t²

— = 2,dt

X

t = Vl0 + lnx

= 1J2/V/ = J/²dSf =

= —+c =

3

+ C

- 11 -