30839

Wzory na pochodne i całki

9-9' ‘ f

.9* 0

(c)' = 0 ,c - stała rzeczywista (i^a)' = ax^a~^l , a <E R (a^x)' = a¹ Ina , a > 0,a ^ 1 (c*)^# = e*

(ani/ = cosi (cosi)' = — sini (tg i)' =    ¹

(ctgi)' =

(log_ai)' =

COS^- X 1

/i^Q+ł

X°dx=^— + C Q#-l

a + 1

J c^xdx = c^x + C J cos xdx = sini + C J sin idi = — cos i + C

/—-5— dx = tg i + C

J COS^xX

—5—dx = — ctgi + C sin i

x ln a (ln i)' = - , x > 0

(arcsin i)' — (arccos i)' =

>/n^

1 <I< 1 -1 < X < 1

/tt

f -dx = ln |i| + C 7 i

:di = arcsin x + C

(arctg*)' =

(arcctgi)' =

i² +1

(sli i)' = cłi i (ch xY = słi x

dx

I    = arctg x + C

j cłi xdx = sh i + C J słi idi = ch i + C

_

J V s¹ + /\

J y/x² + Kdx = ^ ln |i + y/x- + I<\ + ^ y/x² + K + C , K € IR

/dx y/a² — i²

y \/o² -

ln|i+ v/x2 + A:| + C\ /CeR K

arcsin —I-C ,a>0

x*dx = — arcsin — -f ^ \/a² — i² -f C , a > 0

wzory trygonometryczne

sin (a + /?) = sin a cos + sin /? cos a, cos(a + ,d) = cosa cos ,3 — sin a sin 3