Question

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

Answer 1

`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)`