To find the integral of the function \( \frac{x^2}{y} \), we can treat \( y \) as a constant with respect to \( x \) if we are integrating with respect to \( x \). The integral can be expressed as:
\[ \int \frac{x^2}{y} , dx \]
Since \( \frac{1}{y} \) is a constant, we can factor it out of the integral:
\[ = \frac{1}{y} \int x^2 , dx \]
Now, we can compute the integral of \( x^2 \):
\[ \int x^2 , dx = \frac{x^3}{3} + C \]
where \( C \) is the constant of integration. Substituting this back into our expression gives us:
\[ \frac{1}{y} \left( \frac{x^3}{3} + C \right) = \frac{x^3}{3y} + \frac{C}{y} \]
So the integral of \( \frac{x^2}{y} \) with respect to \( x \) is:
\[ \int \frac{x^2}{y} , dx = \frac{x^3}{3y} + C' \]
where \( C' = \frac{C}{y} \) is a constant of integration.