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TABELLA INTEGRALI
∫ 0 ⋅^ dx^ =c
∫ dx^ =^ x^ +c ∫ k^ ⋅^ f^ (^ x^ )^ =^ k^ ⋅^ ∫f^ (^ x dx)
1 , ( 1) 1
n x^ n x dx c n n
= + ≠ −
[ f^ x^ ] f^ x dx^ n [ f^ x^ ] c
n (^) n
∫ (^ )^ ⋅^ '(^ )^ =^ (^ )
1
∫ xdx=^ x+c
dx
2 ∫^
dx= f x +c f x
f x ( ) 2 ( )
∫ sinx dx^ = −^ cos^ x^ +c ∫sen^ f^ (^ x^ )^ ⋅^ f^ ' ( )x dx^ = −^ cos^ f^ ( )x^ +c
∫ cos^ x dx^ =^ senx^ +c ∫cos^ f^ (^ x^ )^ ⋅^ f^ '(^ x dx)^ =^ sen^ f^ (^ x^ )+c
∫ cos 2 xdx=^ tgx+c
1 f x f x
dx tg f x c
cos ( )
∫ 2 =^ ( )+
∫ sen 2 xdx=^ −ctgx+c
1 f x f x
' ( ) dx ctg f x c sen ( )
∫ 2 = −^ ( )+
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 =^ ln^ x^ +c
f x f x
'( )dx f x c ( )
∫ =^ ln^ (^ )+
∫ e dxx^ =^ e^ x+c ∫ e^ f^ (^ x^ )^ f^ '(^ x dx)^ =^ e^ f^ (^ x)+c
a dxx aa c
x
∫ =^ ln + a^ f^ x dx^
a a c
f x
f x ( )
( )
∫ ' ( )^ =^ ln +
x a dx
x a m c
1 1 (^ )^
a bx dx
a bx b n
n c n
1 1 dx a x a
x (^2 2) a c
∫ =^ arctg^ +
dx a bx b a bx
c ( + ) ( )
a bx dx
a bx b n
n c n
1 1
dx
∫ ( a + bx ) 2 = −^ b a( + bx )+c
− 2 =^1
∫ x dx^ − +
x ln (^) x c
∫ 1 + cos x =^ tg 2 +
x c
∫ 1 − cos x dx^ = −^ ctg 2 +
x c ∫ tg x dx = − ln cosx +c
∫ ctg x dx^ =^ ln^ sin x^ +c dx
sin x tg
x
∫ =^ ln^2 +c
dx x
sinx
∫ cos =^ ln sinx c
∫ arcsin x dx^ =^ x arcsin x^ +^1 −^ x^2 +c
∫ arccos^ x dx^ =^ x^ arccosx^ −^1 −^ x^2 +c ∫ arctg xdx = x arctg x − 1 ln + x +c
2
∫ arcctgxdx^ =^ xarcctgx^ +^21 ln^1 +^ x^2 +c ∫ a dx + bx =^ b^1 lna^ +^ bx^ +c
dx a bx (^) ab
b
∫ 2 1 arctg^ + dx
a bx dx^ ab
ab bx ab bx − =^ c
ln
a 2 x dx^2 x^ a 2 x 2 a^ arcsin xa c
2
∫ −^ =^2 −^ +^2 +
dx a x 2 2 arcsin ax c −
∫ =^ +
a 2 x dx^2 x^ a 2 x 2 a^ x a x c
(^22 )
∫ +^ =^2 +^ +^2 ln^ +^ +^ + ∫ a + bx dx = b a + bx +c
( )^3
dx a x 2 2 x^ a^2 x^2 c ±
∫ =^ ln^ +^ ±^ +
dx a bx b
a bx c
∫ =^ +^ +
dx x
x (^2 1) x c
− =^1
∫ ln^ + +
∫ln^ xdx^ =^ x^ lnx^ −^ x^ +c
ln x ln x
dx
x (^2) x x c
∫ = −^ −^ +^ cos^ (^ cos^ )
∫ xdx^ =^2 x^ +^ sinx^ x^ +c
∫ sin xdx^2 =^12 (^ x^ −^ sinx^ cos^ x^ )^ +c cos (^2 )^ (^ (^ ) cos(^ )
1 ∫^ x^ −^ a dx^ =^2 x^ +^ sin x^ −^ a^ x^ −^ a^ +c dx sinx tg
x
∫ =^ ln^2 +c^ dx
x
tg x^ c cos
∫ = −^ ln ^^ π − +
