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List of integrals of rational functions : ウィキペディア英語版
List of integrals of rational functions
The following is a list of integrals (antiderivative functions) of rational functions.
For other types of functions, see lists of integrals.

== Miscellaneous integrands ==

:\int\frac \, dx= \ln\left|f(x)\right| + C
:\int\frac \, dx = \frac\arctan\frac\,\! + C
:\int\frac \, dx = \begin \displaystyle -\frac\,\operatorname\frac = \frac\ln\frac + C & \text|x| < |a|\mbox \\() \displaystyle -\frac\,\operatorname\frac = \frac\ln\frac + C & \text|x| > |a| \mbox \end
: \int \frac = \sum_^ \left (\cos \left(\frac \right) \ln \left | x^2 - 2 x \cos \left(\frac \right) + 1 \right | \right ) \right \} + C


Any rational function can be integrated using partial fractions in integration, by decomposing the rational function into a sum of functions of the form:
: \frac, and \frac.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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