Tabla de integrales inmediatas

a, n son constantes.
f, g son funciones de x.

Reglas de integración:

\begin{array}{|c|c|c|}\hline\text{Suma y resta}&\displaystyle\int f+g=\int f+\int g&\displaystyle\int f-g=\int f-\int g\\\hline\text{Producto y cociente por una constante }a&\displaystyle\int af=a\int f&\displaystyle\int\frac fa=\frac1a\int f\\\hline\end{array}

Tabla de integrales inmediatas:

\begin{array}{|c|c|c|}\hline&\text{Simple}&\text{Compuesta}\\\hline\hline\text{Potencial }(n\neq-1)&\displaystyle\int x^n=\dfrac{x^{n+1}}{n+1}&\displaystyle\int f^n\cdot f'=\dfrac{f^{n+1}}{n+1}\\\hline\text{Logar\'itmica}&\displaystyle\int\dfrac1x=\ln|x|&\displaystyle\int\dfrac{f'}f=\ln|f|\\\hline\text{Exponencial}&\begin{array}{c}\displaystyle\int e^x=e^x\\\displaystyle\int a^x=\dfrac{a^x}{\ln(a)}\end{array}&\begin{array}{c}\displaystyle\int e^f\cdot f'=e^f\\\displaystyle\int a^ff'=\dfrac{a^f}{\ln(a)}\end{array}\\\hline\text{Seno}&\displaystyle\int\text{sen}(x)=-\cos(x)&\displaystyle\int\text{sen}(f)\cdot f'=-\cos(f)\\\hline\text{Coseno}&\displaystyle\int\cos(x)=\text{sen}(x)&\displaystyle\int\cos(f)\cdot f'=\text{sen}(f)\\\hline\text{Tangente}^*&\displaystyle\int\text{sec}^2(x)=\tan(x)&\displaystyle\int\text{sec}^2(f)\cdot f'=\tan(f)\\\hline\text{Arcoseno}(-\text{arcocoseno})&\displaystyle\int\dfrac1{\sqrt{1-x^2}}=\text{arcsen}(x)&\displaystyle\int\dfrac{f'}{\sqrt{1-f^2}}=\text{arcsen}(f)\\\hline\text{Arcotangente}&\displaystyle\int\dfrac1{1+x^2}=\text{arctan}(x)&\displaystyle\int\dfrac{f'}{1+f^2}=\text{arctan}(f)\\\hline\end{array}

(*) \text{sec}^2(x)=1+\text{tg}^2(x)=\dfrac1{\cos^2(x)}

Tabla para descargar

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