How do I solve this generalized integral??
I appriciate any guidance. Thank you
Hello, 4Math!
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
should be
I took Defunkt's advised (See the attached pdf): Complexifying integral.pdf
and complexified the integral. It was not easy. After tedious calculations I finally solved it but didn't know if it was correct. But we both get the same result, so I sure hope its correct. Thank you very much for your response.
Kind regards