`(1)/(x^(4)-1)`

Explanation

`int(1)/(x^(4)-1)dx`
`" "=int(1)/((x^()-1)(x^(2)+1))dx`
`" "=(1)/(2)int(2)/((x^(2)-1)(x^(2)+1))dx`
`" "=(1)/(2)int((x^(2)+1)-(x^(2)-1))/((x^(2)-1)(x^(2)+1))dx`
`" "=(1)/(2)int(1)/(x^(2)-1)dx-(1)/(2)int(1)/(x^(2)+1)dx`
`" "=(1)/(2).(1)/(2)log|(x-1)/(x+1)|-(1)/(2)tan^(-1)x+c`
`" "=(1)/(4)log|(x-1)/(x+1)|-(1)/(2)tan^(-1)x+c`