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Integrate a rational function using partial fraction decomposition
ResourceFunction["IntegratePFD"][rat,x] gives the indefinite integral |
Perform a partial fraction decomposition:
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In this example we compute the partial fraction expansion prior to computing the integral with Integrate:
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IntegratePFD gives different results than Integrate:
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Another example:
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By default this integral produced an ArcTan, as expected:
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With the following extension we factor x2+1 into (x-I)(x+I) prior to computing the partial fraction decomposition:
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Compute the integral over different algebraic number fields until you find a solution which matched your homework problem:
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Integrate and IntegratePFD will both return valid antiderivatives, however the results will often look vastly different:
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The two results are equivalent:
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Sometimes Integrate will give a more concise answer than IntegratePFD:
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IntegratePFD may be used to generate many alternative forms of an integral by factoring the denominator over different algebraic number fields:
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Wolfram Language 13.0 (December 2021) or above
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