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Primitive

Tabloul primitivelor uzuale ale functiei f: I R f(x) dx)x(f I(intervalul de definitie) 0 Cdx0 I R 1 Cxdx1 I R x

C2x

xdx2

I R

x n

C1n

xdxx

1nn

I R

x ( 1 )

C1

xdxx

1n

I (0, )

x

1 Cx2x

dx

I (0, )

x

1 Cxlnx

dx

I R *

e x Cedxe xx I R a x , a > 0, a 0

Calna

dxax

x I R

sin x xdxsin = - cos x + C I R cos x xdxcos = sin x + C I R

xcos

12

xcosdx

2 = tg x + C I R-

Zz2

)1k2(

xsin

12

xsindx

2 = - ctg x + C

I R- Zzk

22 ax

1

, a > 0 22 ax

dx=

a2

1ln

ax

ax

+ C I R { a }

22 ax

1

, a 0 22 ax

dx=

a

1arctg

a

x+ C

I R

22 xa

1

, a > 0

22 xa

dx= arcsin

a

x+ C

I (-a, a)

22 ax

1

, a > 0

22 ax

dx=ln(x + 22 ax ) + C

I R

22 ax

1

, a > 0

22 ax

dx=ln 22 axx + C

I (- , -a) (a, )