Partial Fractions problem

1. Apr 17, 2007

Aerosion

1. The problem statement, all variables and given/known data

integrate((x^3+72)/(x^2+6x+8))dx

2. Relevant equations

3. The attempt at a solution

I decided to use partial fractions method.

x^2+6x+8 factors to (x+4)(x+2)

x^3+72=A(x+2)+B(x+4)

when A=-2, 64=B(2), B=32
when B=-4, 8=A(-2), A=-4

-4*int(1/(x+4)) + 32*int(1/(x+2))

-4*ln(x+4) + 32*ln(x+2) <---ANSWR

What was wrong?

2. Apr 17, 2007

Mathgician

divide first

3. Apr 18, 2007

HallsofIvy

Staff Emeritus
The numerator has higher degree than the denominator. Partial fractions only works on "proper fractions". As Mathgician said, divide first to get a polynomial plus a fraction. Then use partial fractions on that remaining fraction.
However, that still does NOT give -4*ln(x+4) + 32*ln(x+2) as the answer: there will be a (1/2)x2- 6x part. Is it possible you've miscopied the problem?