INTEGRALI INDEFINITI - Proprietà degli Integrali

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INTEGRALI INDEFINITI

Proprietà degli Integrali:

D [ f(x) dx] = f(x)

d [ f(x) dx] = f(x) + k

d f(x) = f(x) + k

k f(x) dx = k f(x) dx  k = costante

[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 x³) + k  (integrale di radice) [f'(x)/f(x)] dx = ln |f(x)| + k

Integrali goniometrici:

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-x²) dx = arcsen x + k [f'(x)/(1/ 1-[f(x)]²) dx = arcsen f(x) + k

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:

e^x dx = e^x + k e^f(x) f'(x) dx = e^f(x) + k

a^x dx = a^x (log_a e) + k = (a^x/ln a) + k a^f(x) f'(x) dx = a^f(x) (log_a e) + k = [a^f(x)/(ln a)] + k

a^x (ln a) dx = a^x + k a^f(x) f'(x) (ln a) dx = a^f(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