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Posted January 21st, 2010 by alpha
in

$ \int \frac{x^3dx}{(1+x^2)^2} $

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answer

On January 21st, 2010 Structure says:
$$ \int \frac{x^3}{(1+x^2)^2}dx= \frac{1}{2}\int \frac{x^2dx}{(1+x^2)^2}2x dx =\frac{1}{2}\int \frac{1+x^2-1}{(1+x^2)^2}2x dx=\frac{1}{2}\int (\frac{1}{(1+x^2)}-\frac{1}{(1+x^2)^2})2x dx$$

=

$$\frac{1}{2}(\ln(1+x^2)+\frac{1}{1+x^2})+\Mathcal{C}$$

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