(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I basically need to find the integral of (-5x^3-1x^2+4)/(x^4+2x^3)

2. Relevant equations

Just the basic rules associated with partial fractions when re-writing a polynomial with constants.

3. 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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# Homework Help: Need help with partial fraction.

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