Tavola degli integrali indefiniti

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TAVOLA DEGLI 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

 

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