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long_division - P x x x − 1 Long Division = = Q x x −1...

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Unformatted text preview: P( x) x + x − 1 Long Division : = = ??? Q( x ) x −1 quo$ent
 Q(x)
 P(x)
 3 2 remainder
 x 3 + x 2 − 1 = ( x 2 + 2 x + 2)( x − 1) + (−1) P(x)
 quo$ent
 Q(x)
 remainder
 ⇓ x3 + x2 −1 −1 2 = ( x + 2 x + 2) + x −1 x −1 Compute ∫ P( x) dx Q( x ) If
degree(numerator)>degree(denominator),
do

 LONG
DIVISION.
Then
 € 1.  Factor
the
denominator
in
a
product
of
irreducible
 2.  Find
the
par$al
frac$on
decomposi$on
of
P(x)/Q(x)
 3.  Integrate
each
factor
 Factor
 (ax+b)
 (ax+b)n
 


Contribu-on
to
PFD
 A ax + b A1 An + ... + n ax + b ( ax + b) Ax + B 2 ax + bx + c € (ax2+bx+c)
 (ax2+bx+c)n
 € A1 x + B1 An x + Bn + ... + 2 2 n ax + bx + c ( ax + bx + c ) € ...
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