Evaluate: `inte^(3logx)(x^4+1)^(-1)\ dx`

Explanation

`" Let " I= inte^(3log x) (x^(4) +1)^(-1) dx`
`=int (e^(log x^(3)))/((x^(4)+1))dx= int(x^(3))/((x^(4)+1))dx`
`" Let " x^(4) +1=trArr 4x^(3) dx=dt rArr x^(3) dx=(dt)/(4)`
`:. I=(1)/(4)int (1)/(t) dt=(1)/(4)log |t|+C`
`=(1)/(4) log |x^(4)+1|+C`