Formulario sugli integrali indefiniti

Scritto da Gianluca il 31 dicembre 2018 Commenta (0) Vai ai commenti

FORMULARIO SUGLI INTEGRALI

Integrai fondamentali	Integrali notevoli
$\displaystyle \int k \,\text{d}x = k\,x +c$
$\displaystyle \int x^n \,\text{d}x = \frac{x^{n + 1}}{n + 1} +c$	$\displaystyle \int f(x)^n \cdot f'(x)\,\text{d}x = \frac{f(x)^{n + 1}}{n + 1} +c$
$\displaystyle \int \frac{1}{ x} \,\text{d}x = \ln \|x\| +c$	$\displaystyle \int \frac{1}{ f(x)}\cdot f'(x) \,\text{d}x = \ln \|f(x)\| +c$
$\displaystyle \int a^x \,\text{d}x =\frac{a^x }{\ln a}+c$	$\displaystyle \int a^{f(x)}\cdot f'(x)\,\text{d}x =\frac{a^{f(x)}}{\ln a}+c$
$\displaystyle \int e^x \,\text{d}x =e^x +c$	$\displaystyle \int e^{f(x)}\cdot f'(x)\,\text{d}x =e^{f(x)} +c$
$\displaystyle \int \cos x \,\text{d}x = \sin x +c$	$\displaystyle \int \cos f(x)\cdot f'(x) \,\text{d}x = \sin f(x) +c$
$\displaystyle \int \sin x \,\text{d}x = - \cos x +c$	$\displaystyle \int \sin f(x)\cdot f'(x)\,\text{d}x = - \cos f(x) +c$
$\displaystyle \int \frac{1}{\cos^2 x} \,\text{d}x = \tan x +c$	$\displaystyle \int \frac{1}{\cos^2 f(x)}\cdot f'(x) \,\text{d}x = \tan f(x) +c$
$\displaystyle \int \frac{1}{\sin^2 x} \,\text{d}x =-\cot x +c$	$\displaystyle \int \frac{1}{\sin^2 f(x)}\cdot f'(x) \,\text{d}x = -\cot f(x) +c$
$\displaystyle \int \frac{1}{\sqrt{1-x^2}}\,\text{d}x\,=\arcsin{x} +c$	$\displaystyle \int \frac{1}{\sqrt{1-f(x)^2}}\cdot f'(x)\,\text{d}x=\arcsin{f(x)} +c$
$\displaystyle \int \frac{1}{1+x^2}\,\text{d}x\,=\arctan{x} +c$	$\displaystyle \int \frac{1}{1+f(x)^2}\cdot f'(x)\,\text{d}x\,=\arctan{x} +c$