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# Usuario:Rutrus/Proyecto en curso

## Reglas de integración

${\displaystyle {\mathfrak {Integrales\;inmeditas:}}}$

${\displaystyle \int x^{n}\,dx={\frac {x^{(n+1)}}{(n+1)}}+C\quad {\mbox{(Para todo }}n\neq -1)}$

• ${\displaystyle {\begin{matrix}{\mbox{Caso particular }}n=0:\;\int \,dx=\int \,1\,dx=\int x^{0}\,dx=x+C\end{matrix}}}$
• ${\displaystyle {\begin{matrix}{\mbox{En el caso }}n=-1:\;\int x^{-1}\,dx=\int {\frac {1}{x}}\,dx=\log x+C\end{matrix}}}$

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

${\displaystyle \int b^{x}={\frac {b^{x}}{\log b}}}$

${\displaystyle \int b^{x}\,dx={\frac {b^{x}}{\log x}}+C}$

${\displaystyle \mathrm {Integrales\;de\;funciones\;trigonom{\acute {e}}tricas:} \,\!}$

 ${\displaystyle \int \sin x\,dx=\cos x+C}$ ${\displaystyle \int \cos x\,dx=-\sin x+C}$ ${\displaystyle \int \tan x\,dx=\log |\cos x|+C}$
 ${\displaystyle \int \arcsin x\,dx={\frac {1}{\sqrt {1-x^{2}}}}+C}$ ${\displaystyle \int \arccos x\,dx={\frac {-1}{\sqrt {1-x^{2}}}}+C}$ ${\displaystyle \int \arctan x\,dx={\frac {1}{1+x^{2}}}+C}$

${\displaystyle \mathrm {Integrales\;de\;funciones\;hiperb{\acute {o}}licas:} \,\!}$

 ${\displaystyle \int \sinh x\,dx=\cosh x+C}$ ${\displaystyle \int \cosh x\,dx=\sinh x+C}$ ${\displaystyle \int \tanh x\,dx=\log |\cosh x|+C}$

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