Solve ∫ intx^2 wrt xdy

$$\int \int x ^ { 2 } d x d y$$

Evaluate

$$\frac{yx^{3}}{3}+Сy+С_{1}$$

Solution Steps

Find the integral of \int x^{2}\mathrm{d}x using the table of common integrals rule \int a\mathrm{d}y=ay.

$$\int x^{2}\mathrm{d}xy$$

Simplify.

$$\left(\frac{x^{3}}{3}+С\right)y$$

If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\left(\frac{x^{3}}{3}+С\right)y+С$$

Differentiate w.r.t. x

$$yx^{2}$$