06 (4)

23/

Biblioteczka Opracowań Matematycznych

C lx²dx

'WT7

3+*³=/⁵ 3x²dx = 5t^Adt

x^:dx = -tⁱdt 3

⁵

-tdt

24/

f 12xdx

'7TP

1 - 3x² = /² - 6.irc/v = 2tdi

xdx = - — tdt 3

=

cos2.v

-tdt

~3~

=¹2 j—^—= “4 p/=-4_f + c =-4    + C

25/ ■'siiiacosa:

= J— = lnj/| + C = ln|sin 2xj + C 26/ ‘

1 + 3 cos x = t - 3 sin dx = dt

3*²

r ^cos2y -fr-	f2cos2x .	sin2x = /
•'2sin.vcosx	r~r—av = ^1 sin 2*	2 cos 2xdx = dt

i

sin xdx 1 + 3 cos x

, .    , dt

sin xdx ---

3

-dt

r 3 i

J / ~~ 3^ⁿ|ł|+C = --ln|l + 3cos^| + C

27/

J

dx

28/

Jsin \r cos xdx =

1 + lnx = f

dx

—=dt x

= f——L—= r<*

Jxl + Inx J7 = H/|+C = i^ + ^|n.xj+C

suu = / cos xdx = dt

_{+ r}> sin x ^ 3 ^c =—r-+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

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