10 thoughts on “Problem From Heck”

  1. Partial fractions turns it into the sum of two quadratics, complete the squares, and then use a trig substitution in each of the resulting integrals. Incredibly simple. Anyone who has trouble with this should not be teaching mathematics.

    1. How can you do partial fractions on this? It is not possible to factor x^4+1 into the product of two quadratics with integer coefficients.

  2. Obviously, ∫(1+x^4)^(-1) dx = ∫Σ(-1)^n * x^(4n) dx
    = Σ(-1)^n * x^(4n+1)/(4n+1)
    And I’m perfectly satisfied with that answer. Fuck partial fractions.

    1. you have some (uniform) convergence issues there and you should refer to Lebesgue’s integration theory

  3. Let a = sqrt(i), then

    1/(x^4+1) = 1/4 [1/(x+ia) – 1/(x-ia) – i/(x+a) + i/(x-a)]


    ∫dx/(x^4+1) = 1/4 [log (x+ia) – log (x-ia) – i log(x+a) + i log(x-a)]

    Insert something about branches of the logarithm…, simplify and collect terms to taste.

    WTF was that 2 page clusterf**k at the link?

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