`int(2x^3)/(x^4+1)dx`

Let `u=x^4+1`, then `du=4x^3dx`.

`int(2x^3)/(x^4+1)dx`

`=1/2int(du)/u`

`=1/2ln|u|+K`

`=1/2ln|x^4+1|+K`

In this example, we don't actually need the absolute value signs because `x^4+1>0` for all real values of `x`.