You need to use the following substitution `x^2=u` , such that:
`x^2=u=>2xdx= du => xdx= (du)/2`
`int (x*dx)/(1+x^4) = (1/2)*int (du)/(1+u^2)`
`(1/2)*int (du)/(1+u^2) = (1/2)*arctan u + c`
Replacing back `x^2` for u yields:
`int (x*dx)/(1+x^4) = (arctan x^2)/2 + c`
Hence, evaluating the indefinite integral, yields `int (x*dx)/(1+x^4) = (arctan x^2)/2 + c.`
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