How do you integrate $x/(1+x^4)$ ?

Question

6821 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-05T18:18:41

$int x/(1+x^4)dx =1/2arctan(x^2)$

Method

$int x/(1+x^4)dx = 1/2int (2xdx)/(1+(x^2)^2)=1/2int (d(x^2))/(1+(x^2)^2) ="I"$

let $x^2 =u$

$=>"I"= 1/2int (du)/(1+u^2) = 1/2arctanu = 1/2arctan(x^2)$

How do you integrate x/(1+x^4)x/(1+x^4)?