Question

Int_1+x^4/1+x^6 =?

Answer 1

`int (x^4+1)/(x^6+1)*dx=arctanx+1/3arctan(x^3)`

Explanation:

`int (x^4+1)/(x^6+1)*dx`

=`int (x^4-x^2+1)/(x^6+1)*dx`+`int x^2/(x^6+1)*dx`

=`int (x^4-x^2+1)/((x^4-x^2+1)*(x^2+1))*dx`+`1/3int (3x^2)/(x^6+1)*dx`

=`int dx/(x^2+1)`+`1/3arctan(x^3)`

=`arctanx+1/3arctan(x^3)`