Jim Coroneos' 100 Integrals ~ 026 ~ ∫1/[x²(1+x²)].dx

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Partly to honour Jim, and partly to fulfil an international need, I have decided to produce 100 videos, showing how to solve his 100 integration 'problems.' I hope you find the videos useful!

This twenty-sixth problem is to evaluate ∫1/[x²(1+x²)].dx

Since we have a denominator that is the product of two polynomials, and since the numerator is a polynomial of lesser degree, you should automatically think "partial fractions." At least, I hope you would. By separating this expression into two, simpler, fractions we are able to reduce the expression to much smaller, and more manageable, expressions.

Once that step has been completed, the rest of the integration proceeds without incident.

We do rely on a "standard integral" but I declined to evaluate it "step-by-step" here in order to save time. I will devote a later series to deriving many of those standard integrals. If you have special requests, please let me know.

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Thank you.
  1. Crystal Clear Maths
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  3. Jim Coroneos
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Once you are versed in partial fractions this presentation is small and sweet. Otherwise, partial fractions deserve more time and space. Deriving table integrals is not an easy task. It is much easier just to remember them ;-)Thank you, Graeme, for continuing "Jim Coroneos' 100 Integrals" series (even though subtraction series was fun!)

MrVoayer