Integrali indefiniti

Materie:	Appunti
Categoria:	Matematica
Download:	152
Data:	19.04.2001
Numero di pagine:	1
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INTEGRALI INDEFINITI

Proprietà degli Integrali:
D [D f(x) dx] = f(x)
d [d f(x) dx] = f(x) + k
d f(x) = f(x) + k
k f(x) dx = k f(x) dx k = costante
k [f1(x) + f2(x)] dx = ( f1(x) dx + ( f2(x) dx
( xn dx = [1/(n+1)] xn+1 + k (integrale di potenza) ==> [f(x)]n f’(x) dx = [1/(n+1)] [f(x)]n+1 + k
. n = 1 x dx = ½ x2 + k
. n= -1 (1/x) dx = ln |x| + k
. n = 0 1 dx = x + k
+ ( x) dx = (2/3) (/x3) + k (integrale di radice) ==> [f’(x)/f(x)] dx = ln |f(x)| + k

Integrali goniometrici:
r cos x dx = sen x + k sen x dx = -cos x +k
-sen x dx = cos x + k
cos f(x) f’(x) dx = sen f(x) + k
sen f(x) f’(x) dx = -cos f(x) + k
(1/cos2 x) dx = (1+tg2 x) dx = tg x + k ==> [f’(x)/cos2 f(x)] dx = tg f(x) + k
( (1/sen2 x) dx = (1+cotg2 x) dx = -cotg x + k ==> [f’(x)/sen2 f(x)] dx = -cotg f(x) + k
(1//1-x2) dx = arcsen x + k ==> [f’(x)/(1//1-[f(x)]2) dx = arcsen f(x) + k
) (1//1-x2) dx = -arccos x + k ==> [f’(x)/(1//1-[f(x)]2) dx = -arccos f(x) + k
) (1+x2) dx = arctg x + k ==> [f’(x)/(1+[f(x)]2) dx = arctg f(x) + k
) (1+x2) dx = -arccotg x + k ==> [f’(x)/(1+[f(x)]2) dx = -arccotg f(x) + k

Integrali esponenziali:
I ex dx = ex + k ==> ef(x) f’(x) dx = ef(x) + k
ax dx = ax (loga e) + k = (ax/ln a) + k ==> af(x) f’(x) dx = af(x) (loga e) + k = [af(x)/(ln a)] + k
/ ax (ln a) dx = ax + k ==> af(x) f’(x) (ln a) dx = af(x) + k

(1/x2+m2) dx = (1/m) arctg (x/m) + k
/ [1/(x+k)2+m2] dx = (1/m) arctg [(x+k)/m] + c c = costante