Wzory na pochodne i całki
(c) = 0 , c  stała rzeczywista

xą+1
(xą) = ąxą-1 , ą " R xądx = + C ą = -1

ą + 1
(ax) = ax ln a , a > 0, a = 1


(ex) = ex exdx = ex + C

(sin x) = cos x cos xdx = sin x + C

(cos x) = - sin x sin xdx = - cos x + C

1 1
(tg x) = dx = tg x + C
cos2 x cos2 x

1 1
(ctg x) = - dx = - ctg x + C
sin2 x sin2 x
1
(loga x) = , a > 0 , a = 1

x ln a

1 1
(ln x) = , x > 0 dx = ln |x| + C
x x

1 1
" "
(arcsin x) = , -1 < x < 1 dx = arcsin x + C
1 - x2 1 - x2
1
(arccos x) = -"
, -1 < x < 1
1 - x2

1 1
(arctg x) = dx = arctg x + C
x2 + 1 x2 + 1
1
(arcctg x) = -
x2 + 1

(sh x) = ch x ch xdx = sh x + C

(ch x) = sh x sh xdx = ch x + C

"
dx
"
= ln |x + x2 + K| + C , K " R
x2 + K

" "
K x"
x2 + Kdx = ln |x + x2 + K| + x2 + K + C , K " R
2 2

dx x
"
= arcsin + C , a > 0
a
a2 - x2

"
a2 x x"
a2 - x2dx = arcsin + a2 - x2 + C , a > 0
2 a 2