tabel derivate si integrale

1. Nr. Derivate
1 0'
c
2 1'x
3 1'
n nn
xx
4
x
x
2
1'
5 2
'
11
xx
6 xx
ee
'
7 aaa xx
ln
'
8
x
x
1
ln
'
9
ax
xa
ln
1
log
'
10
1
1
arctg 2
'
x
x
11
1
1
arcctg 2
'
x
x
12 2
'
1
1
arcsin
x
x
13 2
'
1
1
arccos
x
x
14 xx cossin
'
15 xx sincos
'
16 x
x 2
'
cos
1
tg
17 x
x 2
'
sin
1
ctg
18 22
'
22
ax
x
ax
19 22
'
22
ax
x
ax
20 22
'
22
xa
x
xa
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Nr. Integrale nedefinite
1 Cxdx
2 C
x
xdx
2
2
3 C
n
x
dxx
n
n
1
1
4 Cxxdxx
3
2
5 Cedxe xx
6 C
a
a
dxa
x
x
ln
7 Cxdx
x
ln
1
8 C
ax
ax
a
dx
ax
ln
2
11
22
9 Cxdx
x
arctg
1
1
2
10 C
a
x
a
dx
ax
arctg
11
22
11 Caxxdx
ax
22
22
ln
1
12 Caxxdx
ax
22
22
ln
1
13 Cxdx
x
arcsin
1
1
2
14 C
a
x
dx
xa
arcsin
1
22
15 Cxdxx cossin
16 Cxdxx sincos
17 Cxxdx coslntg
18 Cxxdx sinlnctg
19 Cxdx
x
tg
cos
1
2
20 Cxdx
x
ctg
sin
1
2
21 Caxdx
ax
x 22
22
22 Caxdx
ax
x 22
22
23 Cxadx
xa
x 22
22

2. Nr.
crt.
Operaţii Formule
1 gfgf
2 gfgfgf
3 fccf
Derivarea funcţiilor compuse
'''
)()( uufuf
4
2g
gfgf
g
f
Derivata fucţiei inverse
)(,
)(
1
)( '
'1
xfyunde
xf
yf
5 dxxgdxxfdxxgxf )()()()(
Formula Leibniz-Newton
fprimitivaoFaFbFxFdxxf
b
a
b
a
),()()()( |
6 dxxfdxxf )()(
Integrarea prin părţi
b
a
b
a
b
a
dxxgxfxgxfdxxgxf )()()()()()( ''
|
7 dxxgdxxfdxxgxf )()()()(
Prima schimbare de variabilă
)(
)(
'
)()()(
b
a
b
a
dttfdxxxf
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