tabel derivate si integrale
2
Nr. Derivate 1 0 ' c 2 1 ' x 3 1 ' n n n x x 4 x x 2 1 ' 5 2 ' 1 1 x x 6 x x e e ' 7 a a a x x ln ' 8 x x 1 ln ' 9 a x x a 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 x x cos sin ' 15 x x sin cos ' 16 x x 2 ' cos 1 tg 17 x x 2 ' sin 1 ctg 18 2 2 ' 2 2 a x x a x 19 2 2 ' 2 2 a x x a x 20 2 2 ' 2 2 x a x x a www.mateinfo.ro Nr. Integrale nedefinite 1 C x dx 2 C x xdx 2 2 3 C n x dx x n n 1 1 4 C x x dx x 3 2 5 C e dx e x x 6 C a a dx a x x ln 7 C x dx x ln 1 8 C a x a x a dx a x ln 2 1 1 2 2 9 C x dx x arctg 1 1 2 10 C a x a dx a x arctg 1 1 2 2 11 C a x x dx a x 2 2 2 2 ln 1 12 C a x x dx a x 2 2 2 2 ln 1 13 C x dx x arcsin 1 1 2 14 C a x dx x a arcsin 1 2 2 15 C x dx x cos sin 16 C x dx x sin cos 17 C x xdx cos ln tg 18 C x xdx sin ln ctg 19 C x dx x tg cos 1 2 20 C x dx x ctg sin 1 2 21 C a x dx a x x 2 2 2 2 22 C a x dx a x x 2 2 2 2 23 C x a dx x a x 2 2 2 2
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Transcript of tabel derivate si integrale
Nr. Derivate1 0' c2 1'x
3 1'n nn xx
4 x
x2
1'
52
'11
xx
6 xx ee '
7 aaa xx ln'
8 x
x1
ln '
9 ax
xa ln
1log '
10 1
1arctg
2
'
xx
11 1
1arcctg
2
'
xx
12 2
'
1
1arcsin
xx
13 2
'
1
1arccos
xx
14 xx cossin '
15 xx sincos '
16
xx
2
'
cos
1tg
17
xx
2
'
sin
1ctg
18 22
'22
ax
xax
19 22
'22
ax
xax
20 22
'22
xa
xxa
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Nr. Integrale nedefinite
1 Cxdx
2 Cx
xdx2
2
3
Cn
xdxx
nn
1
1
4 Cxxdxx3
2
5 Cedxe xx
6 Ca
adxa
xx
ln
7 Cxdxx
ln1
8
Cax
ax
adx
axln
2
1122
9
Cxdxx
arctg1
12
10
Ca
x
adx
axarctg
1122
11 Caxxdxax
22
22ln
1
12 Caxxdxax
22
22ln
1
13 Cxdxx
arcsin1
12
14 Ca
xdx
xa
arcsin
122
15 Cxdxx cossin
16 Cxdxx sincos
17 Cxxdx coslntg
18 Cxxdx sinlnctg
19 Cxdxx
tgcos
12
20 Cxdxx
ctgsin
12
21 Caxdxax
x
22
22
22 Caxdxax
x
22
22
23 Cxadxxa
x
22
22
Nr.crt.
Operaţii Formule
1 gfgf
2 gfgfgf
3 fccf
Derivarea funcţiilor compuse ''' )()( uufuf
42g
gfgf
g
f
Derivata fucţiei inverse
)(,)(
1)(
'
'1 xfyundexf
yf
5 dxxgdxxfdxxgxf )()()()(
Formula Leibniz-Newton
fprimitivaoFaFbFxFdxxfb
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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