jeszcze 2

TABLICE MATEMATYCZNE

1

POCHODNE FUNKCJI ELEMENTARNYCH

(c) =0    ceR .

(ax + b) = a

(a*² + bx + c) = 2ax + b

M    ae R\ {0,1}

&) =

2'fx

,v > 0

neN\ {0,1} *>0

*lna

Uwcsin*! =

1

VT7

la/rcos*) =

a>0, a ;*1,*>0 |*| <1 !*l<i

t i i

{arclgx) =--_r

1+*

(iarcctgx) =

i + *²

Jsin*r£c = -cos* + C j"cos*ć/* = sin* + C J/g*c/* = -ln|cos*j + C j" clgxdx = Injsin *| + C

[—dx = tgx + C ^J cos *

[—^—dx = -ctgx + C ^Jsin² *

I

cos*

sin*?*0

1    1    *

--dx =—arc Ig —+ C    0

+ a    a    a

CAŁKI FUNKCJI ELEMENTARNYCH ■

1 i . x -

fl*5		|"<iv = *-t-C	^JVa^2-*^2	a
	**0	Jarfv = a*+C	i u =r	*W*^2 ±a^2
			"a 1 -H ggl

+ C

MJg|gj = cos* (cos*) = — sin

fxⁿdx = —xⁿ"+C n*-1 J    /i + l

[(a* + b)ⁿ dx = —^—r(a* + Z))^,,+l+C n?*-l ^J    a{n + 1}

fsśm

Mm

COS X 1

MM =—|

(a*) =a^x • Ina

pp# i!

X 1

x* — + kn,keC 2

x*kn,keC a > 0

*>0

m ^J *

imiSmm

^J    Ina

J e^x dx = e* + C

J^£/* = |a/7+C

[-= rf* = 2-[x + C V*

</*

■ = — lna* + £ +C

a * 0

ⁱ ccc + b a BIOTECHNOLOGIA,. /l^ Kraków

ferii—-dx = — In ^a-*~ +C    a>0,l*l;*a

J n^l _ v²    In n - y    ¹¹

/a² -x²dx =—arcs\n-^7 + —^a² -*² +C 2    a 2

H +a² dx = —x-Jx² +a +— alnl* + V*² + al + C 2    2    !    I

_s

'o-

**0