Tabla básica de integrales

  Cálculo, Integrales

Tabla de integrales para funciones elementales

 

$$\int x^n\, dx=\frac{x^{n+1}}{n+1} +C$$

$$\int \frac{dx}{x} =ln |x|+C$$

$$\int \sin{x} \,dx=-\cos{x}+C$$

$$\int \cos{x} \,dx=\sin{x}+C$$

$$\int \tan{x} \,dx=- \ln{|\cos{x}|}+C$$

$$\int \cot{x} \,dx=- \ln{|\sin{x}|}+C$$

$$\int \frac{dx}{\cos^2{x}} =\tan{x}+C$$

$$\int \frac{dx}{\sin^2{x}} =-\cot{x}+C$$

$$\int e^{x}\,dx=e^{x}+C$$

$$\int a^{x}\,dx=\frac{a^{x}}{\ln{a}}+C$$

$$\int \frac{dx}{1+x^2} =\arctan{x}+C$$

$$\int \frac{dx}{a^2+x^2} =\frac{1}{a}\arctan{\frac{x}{a}}+C$$

$$\int \frac{dx}{1+x^2} =\arctan{x}+C$$

$$\int \frac{dx}{a^2+x^2} =\frac{1}{a}\arctan{\frac{x}{a}}+C$$

$$\int \frac{dx}{a^2-x^2} =\frac{1}{2a}\ln{\left|\frac{a+x}{a-x}\right|}+C$$

$$\int \frac{dx}{\sqrt{1-x^2} }=\arcsin{x}+C$$

$$\int \frac{dx}{\sqrt{a^2-x^2} }=\arcsin{\frac{x}{a}}+C$$

$$\int \frac{dx}{\sqrt{x^2\pm a^2}} =\ln{\left|x+\sqrt{x^2\pm a^2}\right|}+C$$

 

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