For the antiderivative of the function presented as two separate fractions: (3x²+2x)/(7x²) and (4)/(9x+2). Given the visual separation and the absence of an explicit operator (like $

The problem asks for the antiderivative of the function presented as two separate fractions: $\frac{3x^2+2x}{7x^2}$ and $\frac{4}{9x+2}$. Given the visual separation and the absence of an explicit operator (like $\times$ or $\cdot$), we will assume the function is the sum of these two terms.
So, we need to find the integral of $f(x) = \frac{3x^2+2x}{7x^2} + \frac{4}{9x+2}$.

For $x \neq 0$, we can cancel an $x$ from the numerator and denominator:

Now, split this into two separate fractions:

We need to find $\int f(x) \,dx = \int \left( \frac{3}{7} + \frac{2}{7x} + \frac{4}{9x+2} \right) \,dx$.

Integrate the first term:

Integrate the second term:

Integrate the third term:
For $\int \frac{4}{9x+2} \,dx$, use a u-substitution.
Let $u = 9x+2$.
Then, $du = 9 \,dx$, which means $dx = \frac{1}{9} \,du$.
Substitute these into the integral:

Substitute back $u = 9x+2$:

The final answer is $\boxed{\frac{3}{7}x + \frac{2}{7} \ln|x| + \frac{4}{9} \ln|9x+2| + C}$.