Partial Fractions for Improper Fractions

[Aerosion]

Homework Statement

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

Homework Equations

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?

 

[Mathgician]

divide first

 

[HallsofIvy]

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?