To solve the indefinite integral of the given function, we'll have to use substitution method because we notice that the numerator of the fraction represents the derivative of the denominator of this fraction.
Let `x^3 + 1 = t` .
We'll differentiate both sides:
`3x^2dx = dt`
We'll compute the integral:
`int (3x^2dx)/(x^3+1) = int dt/t`
`int dt/t = ln|t| + C`
We'll replace t by `x^3 + 1` and we'll get:
`int (3x^2dx)/(x^3 + 1) = ln |x^3 + 1| + C`
Therefore, the requested indefinite integral of the given function is `int (3x^2dx)/(x^3 + 1) = ln|x^3 + 1| + C`