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Math Help - Simple question for integral

  1. #1
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    Simple question for integral

    \int \frac{dx}{x^4-1}

    \frac{1}{x^4-1}= \frac{1}{(x-1)(x+1)(x^2+1)}

    \frac{1}{x^4-1}=\frac{A}{(x-1)} +\frac{B}{x+1}+\frac{Cx+D}{x^2+1}

    why should i write Cx+D ,why not only C?
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  2. #2
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    Quote Originally Posted by the prince View Post
    \int \frac{dx}{x^4-1}

    \frac{1}{x^4-1}= \frac{1}{(x-1)(x+1)(x^2+1)}

    \frac{1}{x^4-1}=\frac{A}{(x-1)} +\frac{B}{x+1}+\frac{Cx+D}{x^2+1}

    why should i write Cx+D ,why not only C?
    Because by creating partial fractions, you expect that the each numerator is of a smaller degree than the denominator.

    If x^2 + 1, a degree 2 polynomial is the denominator, you would expect that the numerator would be a polynomial of smaller degree.

    The largest possible polynomial is therefore a linear function (degree 1).
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