What is integral of function 3x^2/x^3+1 ?

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`