Evaluate ther following:
`int (1)/(x(x^(5)+1))dx`

Explanation

Let `t=int(1)/(x(x^(5)+1))dx=int (x^(4))/(x^(5)(x^(5)+1))dx`
Put `x^(5)=t`, Then `5x^(4)dx=dt`
`therefore x^(4)dx=(dt)/(5)`
`therefore I=int (1)/(t(t+1)).(dt)/(5)`
`=(1)/(5)int ((t+1)-t)/(t(t+1))dt`
`=(1)/(5)int ((1)/(t)-(1)/(t+1))dt`
`=(1)/(5)[log|t|-log|t+1|]+c`
`=(1)/(5)log|(t)/(t+1)|+c`
`=(1)/(5)log|(x^(5))/(x^5+1)|+c`