Formule 2

(1)

TABELLA INTEGRALI 0⋅ =

∫

dx c dx= +x c

∫

k f x⋅ ( )= ⋅k

∫

f x dx( ) 1 , ( 1) 1 n n x x dx c n n + = + ≠ − +

∫

[ ]

f x f x dx

[ ]

n f x c n n ( ) '( ) ( )

∫

⋅ = 1₊ + + 1 1

∫

dx= x +c x dx 2

∫

f x dx= f x +c x f ) ( ) ( 2 ) ( ' sin x dx= − x+c

∫

cos

∫

sen ( )f x ⋅f' ( )x dx= −cos ( )f x +c

cosx dx=senx+c

∫

cos ( )f x ⋅f'( )x dx=sen ( )f x +c

∫

dx =tgx+c x 2 cos 1 f x f x dx tg f x c ' ( ) cos2 ( ) ( )

∫

= +

∫

dx =−ctgx+c x 2 sen 1 f x f x dx ctg f x c ' ( ) sen2 ( ) = − ( )+

∫

dx x arc sin x c 1− 2 = +

∫

f

_{[ ]}

x f x dx arcsin f x c '( ) ( ) ( ) 1− 2 = +

∫

dx x x c 1+ 2 = +

∫

arctg

[ ]

f x f x dx f x c '( ) ( ) arctg ( ) 1+ 2 = +

∫

dx x = x +c

∫

ln f x f x dx f x c '( ) ( ) ln ( )

∫

= + e dxx =ex +c

∫

ef x( ) f'( )x dx=ef x( ) +c a dx a a c x x

∫

= + ln a f x dx a a c f x f x ( ) ( ) ' ( ) ln

∫

= + (x a) dx (x a) m c m m + = +₊ + +

∫

₁ 1 ( ) ( ) ( ) a bx dx a bx b n c n n + = + ₊ + +

∫

₁ 1 dx a x a x a c 2 2 1 + = +

∫

arctg dx a bx b a bx c ( + ) = − ( + )+

∫

2 1 ( ) ( ) ( ) a bx dx a bx b n c n n + = + ₊ + +

∫

₁ 1

∫

(a+dxbx)2 = −b a( +bx)+c 1 1 1 1 2 1 1 2 − = + − +

∫

_x dx x x c ln 1 1+ = 2 +

∫

_{cos x} tg x c

(2)

1 1− = − 2 +

∫

_{cos x}dx ctgx c

∫

tg x dx = −ln cosx+c ctg x dx= sin x +c

∫

ln dx sin x tg x c

∫

=ln + 2 dx x sinx sinx c cos ln

∫

= 1 +₋ + 2 1 1 arcsin x dx= x arcsin x+ −x +c

∫

1 2 arccosx dx xarccosx x c

∫

= − 1− 2 +

∫

_arctg_xdx ₌_x_arctg_x₋1_ln ₊ _x ₊_c 2 1 2 arcctgxdx = xarcctgx+ +x +c

∫

₂1ln1 2 dx a+bx = b a+bx +c

∫

1ln dx a bx ab b a x c + = ⋅       +

∫

2 1 arctg dx a bx dx ab ab bx ab bx c − = + − +

∫

2 1 2 ln a x dx x a x a arcsinx a c 2 2 2 2 2 2 2 − = − + +

∫

dx a x arcsinx a c 2 − 2 = +

∫

a2 x dx2 x a2 x2 a x a x c 2 2 2 2 2 + = + + + + +

∫

ln _a _{bx dx} b a bx c + = + +

∫

₃2 3 ( ) dx a x x a x c 2 2 2 2 ± = + ± +

∫

ln dx a+bx = b a+bx+c

∫

2 dx x x x c 2 1 1 2 1 1 − = − + +

∫

ln

∫

lnxdx= xlnx− +x c lnx ln x dx x x x c 2 1

∫

= − − + cos2 1( cos ) 2

∫

xdx= x+sinx x +c sin xdx2 1 x sinx x c 2 = − +

∫

( cos ) cos (2 ) 1( ( ) cos( )

2 x−a dx= x+sin x−a x−a +c

∫

dx sinx tg x c

∫

=ln + 2 dx x tg x c cos ln

∫

= − _π − _{ +} 4 2