Question

integral of : x^2/y

Answer 1

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.