partial fraction decomposition

label Calculus
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Jun 4th, 2015

(y+2)/(y^2+y) = (y+2)/[y*(y+1)] = y/[y(y+1)] + 2/[y(y+1)] =

1/(y+1) + 2*[1/y - 1/(y+1)] = 2/y - 1/(y+1). This is the decomposition.

Indefinite integral of this is  2*ln(y) - ln(y+1) which is = ln[y^2/(y+1)].

From y=1/2 to 1 will be

ln(1/2) - ln(1/6) = ln(3).

Jun 4th, 2015

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Jun 4th, 2015
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Jun 4th, 2015
Jun 24th, 2017
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