Anonymous asked in Science & MathematicsEngineering · 6 years ago

integration ∫(x-1)/((x^4-1)^2)? I want all setup.?


I want all setup.

2 Answers

  • 6 years ago
    Favorite Answer

    Echoing Bramble: don't ever write an integral without a differential, it doesn't mean anything.

    If I assume you meant the integral of

    (x-1) dx / [(x^4 - 1)^2],

    probably your best approach will be "partial fractions."

    1/ [(x+1)(x-1)^2 (x^2+1)^2] =

    = A/(x+1) + B/(x-1) + C/(x-1)^2 +

    + (Ex+F)/(x^2 + 1) + (Gx+H)/ (x^2+1)^2

    Then multiply all terms by the denominator of the LHS,

    and equate coefficients for each separate power of x.

    I admit this is UGLY, but I'm sure it's tractable, since the Wolfram Integrator gives a closed-form answer in elementary functions which are the obvious ones you'd expect from the above formulation (i.e., ln(x-1), ln(x+1), arctan(x), etc.).

  • 6 years ago

    Did you never learn the magic word "please"? It gets you a lot further than "I want". Moreover you're missing a "dx" which makes your question meaningless on top of ill-mannered!

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