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Standard mathematical integrals

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Integration

$\displaystyle \int_{}^{}\:x^n\:dx$	$\displaystyle =\; \frac{x^{n\,+\,1}}{n\:+\:1}$ for all values of n except n = - 1
$\displaystyle \int_{}^{}\frac{1}{x}\:dx$	$\displaystyle = \; Ln\:x$
$\displaystyle \int_{}^{}e^x\:dx$	$\displaystyle = e^x$
$\displaystyle \int_{}^{}sin\:x\:dx$	$\displaystyle = \;-\:cos\:x$
$\displaystyle \int_{}^{}cos\:x\:dx$	$\displaystyle = \;sin\:x$
$\displaystyle \int_{}^{}tan\:x\:dx$	$\displaystyle = \:-\:Ln\:cos\:x$
$\displaystyle \int_{}^{}sec^2\:x\:dx$	$\displaystyle = tan\:x$
$\displaystyle \int_{}^{}\frac{1}{a^2\:+\:x^2}\:dx$	$\displaystyle = \frac{1}{a}\:tan^{-1}\frac{x}{a}$
$\displaystyle \int_{}^{}\frac{1}{a^2\:-\:x^2}\:dx$	$\displaystyle = \frac{1}{2a}\:Ln\:\frac{a\:+\:x}{a\:-\:x} \frac{1}{a}\:tanh^{-1}\frac{x}{a}$
$\displaystyle \int_{}^{}\frac{1}{x^2\:-\:a^2}\:dx$	$\displaystyle =\;\frac{1}{2\,a}\:Ln\,\left(\frac{x-a}{x+a} \right)\;=\;-\:\frac{1}{a}\:coth^{-1}\frac{x}{a}$
$\displaystyle \int_{}^{}\frac{1}{\sqrt[]{(a^2}\:-\:x^2)}\:dx$	$\displaystyle = sin^{-1}\:\frac{x}{a}$
$\displaystyle \int_{}^{}\frac{1}{\sqrt[]{(a^2\:+\:x^2})}\:dx$	$\displaystyle = Ln\left(x\:+\:\sqrt{(x^2\:+\:a^2)} \right) = sinh^{-1}\:\frac{x}{a}$
$\displaystyle \int_{}^{}\frac{1}{\sqrt]{(x^2\:-\:a^2)}}\:dx$	$\displaystyle = Ln\left(x\:+\:\sqrt{(x^2\:-\:a^2}) \right)$

Integration Of The Squares Of The Circular Functions

$\displaystyle \int_{}^{}sin^2\:x\:dx$	$\displaystyle = \frac{1}{2}\:x\:-\:\frac{1}{4}\:sin\:2\,x$
$\displaystyle \int_{}^{}cos^2\:x\:dx$	$\displaystyle = \frac{1}{2}\:x\:+\:\frac{1}{4}\:sin\:2\,x$
$\displaystyle \int_{}^[]tan^2\:x\:dx$	$\displaystyle = (tan\:x)\:-\:x$
$\displaystyle \int_{}^{}cot^2\:x\:dx$	$\displaystyle = -\:(cot\:x)\:-\,x$
$\displaystyle \int_{}^{}cosec\:x\:dx$	$\displaystyle = -\:cot\:x$

Last Modified: 2008-01-02 12:15:58 Page Rendered: 2010-03-11 20:52:33

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