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zeppelinpage4
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Homework Statement
I basically need to find the integral of (-5x^3-1x^2+4)/(x^4+2x^3)
Homework Equations
Just the basic rules associated with partial fractions when re-writing a polynomial with constants.
The Attempt at a Solution
Since the degree of the denominator is 4 and the degree of the numerator is 3 I went straight to factoring out the denominator.
I ended up getting
(x^4+2x^3)=x^3(x+2)
From this point I went forward with the basic steps (I think I made the mistake here, I'm not sure how to re-write the form for (x^3), so I broke it into (x^2) & (x)).
[(-5x^3-1x^2+4)/(x^4+2x^3)]= [(Ax+B)/(x^2)]+[C/x]+[D/(x+2)]
When I multiply both sides by (x^4+2x^3) (this is the denominator on the left side)
I end up with
(-5x^3-1x^2+4)=x^3(A+C+D) + x^2(2A+B+2C) + x(2B)
Normally i'd solve for the constants A, B, C and D to fit the polynomial on the left side BUT I don't know how to account for the "+ 4" at the end of (-5x^3-1x^2+4).
I know
A+C+D=-5
2A+B+2C=-1
2B=0
?=4
I'm very lost at how to approach this and any advice or help that could give me some clue would be very much appreciated. It's been a tough week with midterms and my calc teacher hasn't been helping. =P
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