Question

Evaluate the integral. Integral of (x^3-4)/((x+5)(x+4)) dx with end limits 3 and -1. I've tried this a billion times. Can someone please help!

Answer 1

\[\int\limits_{-1}^{3}(x^3-4)/[(x+5)(x+4)]\]

Answer 2

I can help you.

Answer 3

You want to do a partial fraction decomposition.
First do long division:
Divide x^3-4 by x^2+9x+20 (the denominator multiplied out.
Then do partial fractions which gives:
x-9-68/(x+4)+129/(x+5)
Then integrating that you have:
(1/2)x^2-9x-68ln|x+4|+129ln|x+5|
Then evaluate:
I get:
-32+129ln(2)-68ln(7/3)=-.200