`int z^2/(z^3 + 1) dz` Evaluate the indefinite integral.

You need to use the following substitution `z^3 + 1 = u` , such that:

`z^3+1 = u=> 3z^2 dz = du => z^2dz = (du)/3`

`int (z^2*dz)/(z^3+1) = (1/3)*int 1/u du`

`(1/3)*int 1/u du = (1/3)*ln|u| + c`

Replacing back   `z^3 + 1 ` for u yields:

`int (z^2*dz)/(z^3+1) = (1/3)*ln|z^3 + 1| + c`

Hence, evaluating the indefinite integral, yields `int (z^2*dz)/(z^3+1) = (1/3)*ln|z^3 + 1| + c`