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agve · 09-04-2004, 06:37 AM

Try this:

Factorize (x^4+1) like this:

Code:

(x^4+1) = (x^2+ax+b)(x^2+cx+d)

So you'll have:

Code:

1/(x^4+1) = 1/(x^2+ax+b)(x^2+cx+d)

Then, try to write

Code:

1/(x^2+ax+b)(x^2+cx+d)

like this:

Code:

P(x)/(x^2+ax+b) + Q(x)/(x^2+cx+d),

where P(x) and Q(x) are polynomials of first degree or lower.
Then you'll be able to integrate each part of that sum separately. You only need a simple substitution for each one to do it.

09-04-2004, 06:37 AM	#5 (permalink)
agve Upright	Try this: Factorize (x^4+1) like this: Code: (x^4+1) = (x^2+ax+b)(x^2+cx+d) So you'll have: Code: 1/(x^4+1) = 1/(x^2+ax+b)(x^2+cx+d) Then, try to write Code: 1/(x^2+ax+b)(x^2+cx+d) like this: Code: P(x)/(x^2+ax+b) + Q(x)/(x^2+cx+d), where P(x) and Q(x) are polynomials of first degree or lower. Then you'll be able to integrate each part of that sum separately. You only need a simple substitution for each one to do it. Last edited by agve; 09-04-2004 at 06:39 AM..