Take the Fraction Apart First

You'll learnhow a fraction whose denominator factors comes apart into simple pieces that each integrate to a logarithm, and the fifteen-second check that catches a wrong constant before you integrate anything.

A fraction whose denominator factors can be split into simpler ones, and each simple piece integrates to a logarithm. The constants in that split are the whole of the method, and leaving them out gives a different function — which is something you can see, because both curves fit on one picture. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · PUT THE PIECES BACK AND COMPARE · v2

Split it, solve the constants, then add the pieces back and compare

Before you start

What you're looking at

One plot. The blue curve is the fraction being taken apart; pink and violet are its two pieces, and yellow is those pieces added back.

The question

What does a split actually claim, and how do you check yours in fifteen seconds?

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