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Math Help - Integral

  1. #1
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    Integral

    \int \frac{dx}{x(x^2+1)^2}
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  2. #2
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    \int\frac{1}{x}dx-\int\frac{x}{(x^{2}+1)^{2}}dx-\int\frac{x}{x^{2}+1}dx
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  3. #3
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    Quote Originally Posted by Apprentice123 View Post
    \int \frac{dx}{x(x^2+1)^2}
    \int \frac{dx}{x(x^2+1)^2}=-\int \frac{x^2-(x^2+1)}{x(x^2+1)^2}\;dx=-\int \frac{x}{(x^2+1)^2}\;dx\;-\int \frac{x^2-(x^2+1)}{x(x^2+1)}\;dx

    Thus \int \frac{dx}{x(x^2+1)^2}= -\int \frac{x}{(x^2+1)^2}\;dx-\int \frac{x}{(x^2+1)}\;dx+\int \frac{1}{x}\;dx
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