Jim Coroneos' 100 Integrals ~ 025 ~ ∫1/[x²(1-x)].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-fifth problem is to evaluate ∫1/[x²(1-x)].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.

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This is an integral of simple enough rational function so that your explanation of partial fractions is as sufficient as it is correct. But there is more to "Integration by partial fractions" than this particular example shows. Nevertheless, your workout and final solution are both quick and nice. Thank you, Greame.

MrVoayer