wzory pochodne i calki, Sem 1, Analiza I
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Wzorynapochodneicałki
(
c
)
0
=0
,c
–stałarzeczywista
Z
x
dx
=
x
+1
(
x
)
0
=
x
−
1
,
2
R
+1
+
C
6
=
−
1
(
a
x
)
0
=
a
x
ln
a,a>
0
,a
6
=1
Z
(
e
x
)
0
=
e
x
e
x
dx
=
e
x
+
C
Z
(sin
x
)
0
=cos
x
cos
xdx
=sin
x
+
C
Z
(cos
x
)
0
=
−
sin
x
sin
xdx
=
−
cos
x
+
C
(tg
x
)
0
=
1
cos
2
x
Z
1
sin
2
x
dx
=
−
ctg
x
+
C
(ctg
x
)
0
=
−
1
sin
2
x
(log
a
x
)
0
=
1
x
ln
a
,a>
0
,a
6
=1
(ln
x
)
0
=
1
x
,x>
0
Z
1
x
dx
=ln
|
x
|
+
C
Z
1
(arcsin
x
)
0
=
1
p
1
−
x
2
,
−
1
<x<
1
p
1
−
x
2
dx
=arcsin
x
+
C
(arccos
x
)
0
=
−
1
p
1
−
x
2
,
−
1
<x<
1
Z
1
x
2
+1
dx
=arctg
x
+
C
(arctg
x
)
0
=
1
x
2
+1
(arcctg
x
)
0
=
−
1
x
2
+1
(sh
x
)
0
=ch
x
Z
ch
xdx
=sh
x
+
C
Z
(ch
x
)
0
=sh
x
sh
xdx
=ch
x
+
C
Z
dx
p
x
2
+
K
=ln
|
x
+
p
x
2
+
K
|
+
C,K
2
R
Z
p
p
p
x
2
+
Kdx
=
K
x
2
+
K
|
+
x
2
2
ln
|
x
+
x
2
+
K
+
C,K
2
R
Z
dx
p
a
2
−
x
2
=arcsin
x
a
+
C,a>
0
Z
p
a
2
−
x
2
dx
=
a
2
2
arcsin
x
a
+
x
p
a
2
−
x
2
+
C,a>
0
2
Z
1
cos
2
x
dx
=tg
x
+
C
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