Evaluating the integral

Question

∫ (a= -.5 and b=.5) of (x^7 - 2x^5 +3x^3 +4x^2 +x - 4)/(x^2 - 1)

 

I understand how to find most integrals.... and I thought when I saw this question I assumed that it would require a substitution. However, so far I have not been able to find a substitution that would work well for this problem. 

 

In the answer keys, it says that the answer is 4. Could you explain how they arrived at this answer? 

 

Thanks!

Answer 1

Actually, the trick is to perform polynomial long division. You will get a simple polynomial followed by a rational expression. The rational can be broken into a logarithm rule and an arcfunction all of which will indeed lead you to 4 exactly.

It is very complicated to type here, but I hope that points you in the right direction.