integrate

Question

x^2/(x^4+a^4) dx

Answer 1

This one takes some creativity.

since (u^2+a^2)^2 - 2a^4 = (u^2-a^2)^2 we can factor x^4+a^4 into

((x^2+a^2)+√2 a^2)((x^2+a^2)-√2 a^2)

Now we can use partial fractions to wind up with quadratic denominators. These integrate with messy but straightforward trig substitutions.

The result is nasty. The steps involved can be found at

http://www.wolframalpha.com/widgets/view.jsp?id=893912ad72b01acedd76b68aa3ffc4df

enter your formula into the box and let 'er rip!