30

Biblioteczka Opracowań Matematycznych

= — + C

202/

|(6-2.v) dx -203/

6-2x = t 2

26

I_

26

e’ =1, 2xe'dx = dt, Ine‘=In/ x²lne=ln/, jc² = In /

= jx²xe^x dx = ^ jln/dt =

u = ln/ du--t

dv = dt v = t

= -/ ln|/| --1 + C = -e^,: ln e¹' -    + C = -e^ (x² -1)+ C

2 2 2 2 2 ^K '

204/

Jjr²V7*⁵+6<k =

205/

J(.v² + i)cos(at’+3j: + 5)dx =

sin t + C = sin (.t³ + 3.v + 5

206

'+⁺>l^+c

7.r³ + 6 = /\ *²rfr =

21

x*+3x + 5 = t

(3x² + 3 )dx = dt + C

= - ffdt = — + C = — V(7*³ + ó)⁷ +C

₇J 49    49^vv ’

= J3(a" + l)cos(.v³ + 3jf + 5)cZr = Jcos/cA =

x +1

207/

J

3dx

2 dt

3sinx+4cos.r + 5 2dt

ig— = t, dx = --sinx =

2/

cosx = -

1-/^J

1 + /■

= 3

208/

dt

r i+r    ₆r dt ₆|- ar ₌ o _{|C =}__o

Jfr+4(l-r)+5(l+/²)    V+6h-9    (/+3)² t+3    _/j?*

1+/

^Jl-sin⁴.t

igx = l, dir =

dt

1 + r

• 2 ' sin x = —

= J-

-+C

<*2⁺³

,2 V

i + r

Biblioteczka Opracowań Matematycznych

= f(^i+/:K fi±^_f= i

i 2t² +1 J 2r +1    J

I •>

2 2/ +1

i f, I r fll 1    lr

dt— c//+- ——=-/+- -

■y J    7

2 ^J2/ +1 2 2

1    1 r dt 1 VI 2/    1 VI i-

“ 2^,gX+4 JV—Y~2^{lgX +} ~A^arCtg~l7^{+C =} ^^:>^{tgX +} ~A~^arC'^g^^{2,gX + C}

209/

rsiruccosxćiv 1 +sin* x

r + -2

,    .    4 ^dt    -2    ¹

tgx=t, dx=-—sin x=

1 +r

t dt

sinxcosy=-

1+r

- f	1+r !
^_ J

+t

1+r

r tdt	t^2=z	1	r 1 r
+ 2t^2 + \ ~	2tdt = dz	~ 2	^J2r^J + 2r + l 2^J

= -arc/g(2r + l)+C = —arc/g(2/g²x +l)+C

_ l C dz    Ir dz

~7 J f I V . "li?

<-4)4 (-4)4

210/

k

sin’x + cos³x

a² -ab + b² = Jsinx<£t+ J*cosxdx - -cosx +sin x+C

sin * x - sin xcosx + cos* x

= a + b

= J(sinx+ cosx)dx =

-59-