How do I solve this generalized integral??
I appriciate any guidance. Thank you
This is a truly ugly problem, but it can be solved . . .
The denominator is the sum of cubes: .
. . which factors: .
The quartic can also be factored . . .
Add and subtract
. . . (difference of squares)
The denominator is: .
You know what to do, right?
Apply partial fraction decomposition . . .
. . . . . . . . .
I'll wait in the car . . .
Consider the integral next to :
Sub. ( maybe i have been using this substitution much more times than trigo. sub. since I realized its power and magic ! )
Summation gives :
so we find that the answer is
If i am right , your generalized integral
I took Defunkt's advised (See the attached pdf): Complexifying integral.pdf