Unknown process in integrationFor the integrand 1 y ( 1 − y L ) , cancel common terms in the numerator and denominator: = ∫ − L y ( y − L ) d yThis is part of WolframAlpha’s calculations before creating partial fractions. What exactly is this method/theorem? And how does it work?

Question

Unknown process in integrationFor the integrand       1          y      (      1      −              y        L            )      , cancel common terms in the numerator and denominator:  =  ∫  −      L          y      (      y      −      L      )        d  yThis is part of WolframAlpha’s calculations before creating partial fractions. What exactly is this method/theorem? And how does it work?

faliryr · Accepted Answer

It’s not a method, it simply do this:  ∫      1          y      (      1      −              y        L            )        d  x  =  ∫      1          y              (                              L            −            y                    L                )              d  x  =  ∫      1          y              1        L            (      L      −      y      )        d  x  =  ∫      1          1      L            1          y      (      L      −      y      )        d  x                    =        ⏟                            1                  1          L                    =      L        ∫      L          y      (      L      −      y      )        d  x  =  ∫      L          −      y      (      y      −      L      )        d  x  =  ∫  −      L          y      (      y      −      L      )        d  x

moidu13x8 · Accepted Answer

It&#039;s algebra.      1          1      −              y        L              ⋅      L    L    =      L          L      −      y        =  −      L          y      −      L      I suppose you could call it &quot;multiplying by one&quot;; it&#039;s a pretty common trick when working with fractions.Calling it &quot;canceling the common terms&quot; is a little misleading, though. In this case, the common term is       1    L  ; when you &quot;cancel&quot; that from   1 you get   L.

Unknown process in integration For the integrand 1/(y(1-y/L)), cancel common terms in the numerator and denominator: =int -L/(y(y-L))dy. This is part of WolframAlpha’s calculations before creating partial fractions. What exactly is this method/theorem? And how does it work?

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