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Is there a question in MSE with an answer containing the whole integration process for rational functions (on the reals)?

Questions on the topic appear frequently. Every time I try to find a link to the complete algorithm I can never find it; even elsewhere. Speaking of which; it would also work if someone knows another place in the Internet that has it.

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    $\begingroup$ Maybe this. $\endgroup$ – Will Orrick Feb 22 '15 at 6:24
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    $\begingroup$ @FamousBlueRaincoat: I can't seem to post this as an answer, even when I pad it with additional verbiage. Maybe I need more additional verbiage... $\endgroup$ – Will Orrick Feb 22 '15 at 6:37
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    $\begingroup$ See also Hermite reduction. and Bronstein's Symbolic integration tutorial. $\endgroup$ – Gone Feb 22 '15 at 6:43
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    $\begingroup$ @WillOrrick Okay, I posted it. For the future: you can put any amount of irrelevant verbiage (e.g., copying the whole question into answer box); if removed within 5 minutes of posting, it leaves no trace. $\endgroup$ – user147263 Feb 22 '15 at 6:44
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This answer by Arturo Magidin, found by Will Orrick, contains an extensive description of the integration of rational functions.

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    $\begingroup$ But that is far from the most efficient way to proceed. See the links in my comment. $\endgroup$ – Gone Feb 22 '15 at 6:44
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    $\begingroup$ Maybe it is worth mentioning that this answer is in the List of Generalizations of Common Questions. $\endgroup$ – Martin Sleziak Feb 22 '15 at 8:02

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