7/31/2019 matematika2_formule

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Integriranje

dx = x + C

xrdx= + C

xr+1

r+1

dxx

= ln|x| + C

exdx = e

x+ C

=

c 0

x 1

x2 2x

xn

ex ex

ax axlna

lnx1x

1

2 xx

nxn-1 n=0

logax

sinx cosx

cosx -sinx

tgx

ctgx

1

cos2x

-1

sin2x

arcsinx

arccosx

arctgx

arcctgx

1

1-x2

-11-x2

1

1+x2

-1

1+x2

logae

x

1

xlna=

Osnovne derivacije Svojstva deriviranja - pravila

(fg)=fg

(fg)=fg+fg

(cf)=cf

fg-fgg2

fg( )

[f(g(x))]=f(g(x))g(x)

f-1

(x)=1

f(f-1

(x))

axdx = + C

ax

lna

np

1 p>1

p 0, |x| < a

1

a2-x2= arctg + C

1

a

x

aa > 0