`e^(3logx)(x^(4)+1)^(-1)`

Explanation

माना `I=inte^(3logx)(x^(4)+1)^(-1)dx`
`=int(e^(logx^(3)))/((x^(4)+1))dx=int(x^(3))/((x^(4)+))dx`
`" "(because e^(logx)=x)`
माना`" "x^(4)+1=t rArr 4x^(3)dx=dt" "rArr" "x^(3)dx=(dt)/(4)`
`therefore" "I=(1)/(4)int(1)/(t)=(1)/(4)log|t|+C`
`" "=(1)/(4)log|x^(4)+1|+C`