Evaluate `int (tanx+tan^3x)/(1+tan^3x)dx`

Explanation

`(tanx+tan^3x)/(1+tan^3x)=(tanx(1+tan^2x))/(1+tan^3x)`

`=(tanxsec^2x)/(1+tan^3x)`

`int(tanxsec^2xdx)/(1+tan^3x)`

`tanx=t`

`sec^2xdx=dt`

`=int(tdt)/(1+t^3)`

`=int (t+t^2-t^2)/(1-t^3)`

`int(t(1+t))/(1+t^3)dt-int(t^2/(1+t3)dt`

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