Monday, June 16, 2008

`int x/(1 + x^4) dx` Evaluate the indefinite integral.

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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